diff options
126 files changed, 3543 insertions, 757 deletions
diff --git a/.github/workflows/list_missing.yml b/.github/workflows/list_missing.yml index 48cbe03..0ed7e01 100644 --- a/.github/workflows/list_missing.yml +++ b/.github/workflows/list_missing.yml @@ -1,9 +1,21 @@ on: [push, pull_request] jobs: - pdf: + missing: name: List missing runs-on: ubuntu-latest steps: - uses: actions/checkout@v4 - run: ./test/test.sh --missing + - run: ./test/test.sh --coverage >> $GITHUB_ENV + - uses: schneegans/dynamic-badges-action@v1.7.0 + with: + auth: ${{ secrets.GIST_COVERAGE_SECRET }} + gistID: 73fb3c58350c58b623f221fc237def62 + filename: tcr_coverage.json + label: coverage + message: ${{ env.COVERED }}/${{ env.TOTAL }} + namedLogo: GitHub + valColorRange: ${{ env.TOTAL }} + minColorRange: ${{ env.REQUIRED }} + maxColorRange: ${{ env.TOTAL }} diff --git a/.github/workflows/test_all.yml b/.github/workflows/test_all.yml index eddc002..bb2489b 100644 --- a/.github/workflows/test_all.yml +++ b/.github/workflows/test_all.yml @@ -2,13 +2,13 @@ on: workflow_dispatch: jobs: - pdf: + all: strategy: matrix: os: [ubuntu-latest, ubuntu-22.04] name: Test all (${{ matrix.os }}) runs-on: ${{ matrix.os }} - timeout-minutes: 10 + timeout-minutes: 20 steps: - uses: actions/checkout@v4 - run: ./test/test.sh diff --git a/.github/workflows/test_datastructures.yml b/.github/workflows/test_datastructures.yml index 9e58389..dffcf0a 100644 --- a/.github/workflows/test_datastructures.yml +++ b/.github/workflows/test_datastructures.yml @@ -10,7 +10,7 @@ on: workflow_dispatch: jobs: - pdf: + datastructures: strategy: matrix: os: [ubuntu-latest, ubuntu-22.04] diff --git a/.github/workflows/test_geometry.yml b/.github/workflows/test_geometry.yml index c1cc95d..fc45e5c 100644 --- a/.github/workflows/test_geometry.yml +++ b/.github/workflows/test_geometry.yml @@ -10,7 +10,7 @@ on: workflow_dispatch: jobs: - pdf: + geometry: strategy: matrix: os: [ubuntu-latest, ubuntu-22.04] diff --git a/.github/workflows/test_graph.yml b/.github/workflows/test_graph.yml index b402d21..505707c 100644 --- a/.github/workflows/test_graph.yml +++ b/.github/workflows/test_graph.yml @@ -10,7 +10,7 @@ on: workflow_dispatch: jobs: - pdf: + graph: strategy: matrix: os: [ubuntu-latest, ubuntu-22.04] diff --git a/.github/workflows/test_math.yml b/.github/workflows/test_math.yml index 6df75db..ef759c0 100644 --- a/.github/workflows/test_math.yml +++ b/.github/workflows/test_math.yml @@ -10,7 +10,7 @@ on: workflow_dispatch: jobs: - pdf: + math: strategy: matrix: os: [ubuntu-latest, ubuntu-22.04] diff --git a/.github/workflows/test_other.yml b/.github/workflows/test_other.yml index 07592d5..14c0550 100644 --- a/.github/workflows/test_other.yml +++ b/.github/workflows/test_other.yml @@ -10,7 +10,7 @@ on: workflow_dispatch: jobs: - pdf: + other: strategy: matrix: os: [ubuntu-latest, ubuntu-22.04] diff --git a/.github/workflows/test_pdf.yml b/.github/workflows/test_pdf.yml index e1d660b..ab273f7 100644 --- a/.github/workflows/test_pdf.yml +++ b/.github/workflows/test_pdf.yml @@ -10,12 +10,9 @@ on: workflow_dispatch: jobs: - pdf: - strategy: - matrix: - os: [ubuntu-latest, ubuntu-22.04] - name: Test pdf (${{ matrix.os }}) - runs-on: ${{ matrix.os }} + pdf_22-04: + name: Test pdf (ubuntu-22.04) + runs-on: ubuntu-22.04 timeout-minutes: 5 steps: - uses: actions/checkout@v4 @@ -23,3 +20,20 @@ jobs: sudo apt-get update sudo apt-get install latexmk texlive-latex-base texlive-latex-recommended texlive-latex-extra texlive-lang-german texlive-fonts-extra - run: make + + pdf_latest: + name: Test pdf (ubuntu-latest) + runs-on: ubuntu-22.04 + timeout-minutes: 5 + steps: + - uses: actions/checkout@v4 + - run: | + sudo apt-get update + sudo apt-get install latexmk texlive-latex-base texlive-latex-recommended texlive-latex-extra texlive-lang-german texlive-fonts-extra + - run: make + - uses: exuanbo/actions-deploy-gist@v1 + with: + token: ${{ secrets.GIST_COVERAGE_SECRET }} + gist_id: 73fb3c58350c58b623f221fc237def62 + file_path: tcr.pdf + file_type: binary diff --git a/.github/workflows/test_string.yml b/.github/workflows/test_string.yml index 8ca5e1b..0d79040 100644 --- a/.github/workflows/test_string.yml +++ b/.github/workflows/test_string.yml @@ -10,7 +10,7 @@ on: workflow_dispatch: jobs: - pdf: + string: strategy: matrix: os: [ubuntu-latest, ubuntu-22.04] diff --git a/.github/workflows/test_template.yml b/.github/workflows/test_template.yml index 827b9ac..01f57bb 100644 --- a/.github/workflows/test_template.yml +++ b/.github/workflows/test_template.yml @@ -10,7 +10,7 @@ on: workflow_dispatch: jobs: - pdf: + template: strategy: matrix: os: [ubuntu-latest, ubuntu-22.04] @@ -224,5 +224,6 @@ TSWLatexianTemp* # files produced by the testing system *.test *.ok -*.tmp.cpp *.d +# ignore build test awk files +test/awk/* diff --git a/content/datastructures/datastructures.tex b/content/datastructures/datastructures.tex index a0eea64..4bbe507 100644 --- a/content/datastructures/datastructures.tex +++ b/content/datastructures/datastructures.tex @@ -52,7 +52,7 @@ \method{insert}{fügt wert $\mathit{val}$ an stelle $i$ ein (verschiebt alle Positionen $\geq i$)}{\log(n)} \method{remove}{löscht werte $[i,i+\mathit{count})$}{\log(n)} \end{methods} - \sourcecode{datastructures/treap2.cpp} + \sourcecode{datastructures/treap.cpp} \end{algorithm} \begin{algorithm}{Range Minimum Query} diff --git a/content/datastructures/dynamicConvexHull.cpp b/content/datastructures/dynamicConvexHull.cpp index 2bd67a6..7148e31 100644 --- a/content/datastructures/dynamicConvexHull.cpp +++ b/content/datastructures/dynamicConvexHull.cpp @@ -1,22 +1,22 @@ struct Line { - mutable ll m, b, p; + mutable ll m, c, p; bool operator<(const Line& o) const {return m < o.m;} bool operator<(ll x) const {return p < x;} }; -struct HullDynamic : multiset<Line, less<>> { - // (for doubles, use inf = 1/.0, div(a,b) = a/b) - ll div(ll a, ll b) {return a / b - ((a ^ b) < 0 && a % b);} +struct HullDynamic : multiset<Line, less<>> { // max über Geraden + // (for doubles, use INF = 1/.0, div(a,c) = a/c) + ll div(ll a, ll c) {return a / c - ((a ^ c) < 0 && a % c);} bool isect(iterator x, iterator y) { if (y == end()) {x->p = INF; return false;} - if (x->m == y->m) x->p = x->b > y->b ? INF : -INF; - else x->p = div(y->b - x->b, x->m - y->m); + if (x->m == y->m) x->p = x->c > y->c ? INF : -INF; + else x->p = div(y->c - x->c, x->m - y->m); return x->p >= y->p; } - void add(ll m, ll b) { - auto x = insert({m, b, 0}); + void add(ll m, ll c) { + auto x = insert({m, c, 0}); while (isect(x, next(x))) erase(next(x)); if (x != begin()) { --x; @@ -29,6 +29,6 @@ struct HullDynamic : multiset<Line, less<>> { ll query(ll x) { auto l = *lower_bound(x); - return l.m * x + l.b; + return l.m * x + l.c; } }; diff --git a/content/datastructures/lichao.cpp b/content/datastructures/lichao.cpp index f66778e..1318ca7 100644 --- a/content/datastructures/lichao.cpp +++ b/content/datastructures/lichao.cpp @@ -8,13 +8,13 @@ struct Fun { // Default: Linear function. Change as needed. // Default: Computes min. Change lines with comment for max. struct Lichao { - static constexpr Fun id = {0, inf}; // {0, -inf} + static constexpr Fun id = {0, INF}; // {0, -INF} int n, cap; vector<Fun> seg; - Lichao() : n(sz(xs)), cap(2<<__lg(n)), seg(2*cap, id) {} + Lichao() : n(sz(xs)), cap(2 << __lg(n)), seg(2 * cap, id) {} void _insert(Fun f, int l, int r, int i) { - while (i < 2*cap){ + while (i < 2 * cap) { int m = (l+r)/2; if (m >= n) {r = m; i = 2*i; continue;} Fun &g = seg[i]; @@ -26,7 +26,7 @@ struct Lichao { void _segmentInsert(Fun f, int l, int r, int a, int b, int i) { if (l <= a && b <= r) _insert(f, a, b, i); - else if (a < r && l < b){ + else if (a < r && l < b) { int m = (a+b)/2; _segmentInsert(f, l, r, a, m, 2*i); _segmentInsert(f, l, r, m, b, 2*i+1); @@ -36,7 +36,7 @@ struct Lichao { } ll _query(int x) { - ll ans = inf; // -inf + ll ans = INF; // -INF for (int i = x + cap; i > 0; i /= 2) { ans = min(ans, seg[i](x)); // max } diff --git a/content/datastructures/monotonicConvexHull.cpp b/content/datastructures/monotonicConvexHull.cpp index e7b9b3e..2bdeccf 100644 --- a/content/datastructures/monotonicConvexHull.cpp +++ b/content/datastructures/monotonicConvexHull.cpp @@ -16,7 +16,7 @@ struct Envelope { ls.pop_back(); } ls.push_back({m, b}); - ptr = min(ptr, sz(ls) - 1); + ptr = min(ptr, (int)sz(ls) - 1); } ll query(ll x) { diff --git a/content/datastructures/pbds.cpp b/content/datastructures/pbds.cpp index d00b635..734bf91 100644 --- a/content/datastructures/pbds.cpp +++ b/content/datastructures/pbds.cpp @@ -15,10 +15,10 @@ using Tree = tree<T, null_type, less<T>, rb_tree_tag, T.order_of_key(x); // number of elements strictly less than x auto it = T.find_by_order(k); // k-th element +constexpr uint64_t RNG = ll(2e18 * acos(-1)) | 199; // random odd template<typename T> struct chash { - static const uint64_t C = ll(2e18 * acos(-1)) | 199; // random odd size_t operator()(T o) const { - return __builtin_bswap64(hash<T>()(o) * C); + return __builtin_bswap64(hash<T>()(o) * RNG); }}; template<typename K, typename V> using hashMap = gp_hash_table<K, V, chash<K>>; diff --git a/content/datastructures/persistent.cpp b/content/datastructures/persistent.cpp index 4093cdc..f26680d 100644 --- a/content/datastructures/persistent.cpp +++ b/content/datastructures/persistent.cpp @@ -4,15 +4,15 @@ struct persistent { vector<pair<int, T>> data;
persistent(int& time, T value = {})
- : time(time), data(1, {time, value}) {}
+ : time(time), data(1, {2*time, value}) {}
T get(int t) {
- return prev(upper_bound(all(data), pair{t+1, T{}}))->second;
+ return prev(upper_bound(all(data),pair{2*t+1, T{}}))->second;
}
int set(T value) {
- time += 2;
- data.push_back({time, value});
+ time++;
+ data.push_back({2*time, value});
return time;
}
};
diff --git a/content/datastructures/persistentArray.cpp b/content/datastructures/persistentArray.cpp index 60d8b17..8326700 100644 --- a/content/datastructures/persistentArray.cpp +++ b/content/datastructures/persistentArray.cpp @@ -10,8 +10,8 @@ struct persistentArray { T get(int p, int t) {return data[p].get(t);}
int set(int p, T value) {
- mods.push_back({p, time});
- return data[p].set(value);
+ mods.push_back({p, data[p].set(value)});
+ return mods.back().second;
}
void reset(int t) {
diff --git a/content/datastructures/treap.cpp b/content/datastructures/treap.cpp index c96e36a..c5a60e9 100644 --- a/content/datastructures/treap.cpp +++ b/content/datastructures/treap.cpp @@ -1,79 +1,79 @@ -struct node { - int key, prio, left, right, size; - node(int key, int prio) : key(key), prio(prio), left(-1), - right(-1), size(1) {}; -}; +mt19937 rng(0xc4bd5dad); +struct Treap { + struct Node { + ll val; + int prio, size = 1, l = -1, r = -1; + Node(ll x) : val(x), prio(rng()) {} + }; -vector<node> treap; + vector<Node> treap; + int root = -1; -int getSize(int root) { - return root < 0 ? 0 : treap[root].size; -} + int getSize(int v) { + return v < 0 ? 0 : treap[v].size; + } -void update(int root) { - if (root < 0) return; - treap[root].size = 1 + getSize(treap[root].left) - + getSize(treap[root].right); -} + void upd(int v) { + if (v < 0) return; + auto& V = treap[v]; + V.size = 1 + getSize(V.l) + getSize(V.r); + // Update Node Code + } -pair<int, int> split(int root, int minKeyRight) { - if (root < 0) return {-1, -1}; - if (treap[root].key >= minKeyRight) { - auto leftSplit = split(treap[root].left, minKeyRight); - treap[root].left = leftSplit.second; - update(root); - leftSplit.second = root; - return leftSplit; - } else { - auto rightSplit = split(treap[root].right, minKeyRight); - treap[root].right = rightSplit.first; - update(root); - rightSplit.first = root; - return rightSplit; -}} + void push(int v) { + if (v < 0) return; + //auto& V = treap[v]; + //if (V.lazy) { + // Lazy Propagation Code + // if (V.l >= 0) treap[V.l].lazy = true; + // if (V.r >= 0) treap[V.r].lazy = true; + // V.lazy = false; + //} + } -int merge (int left, int right) { - if (left < 0) return right; - if (right < 0) return left; - if (treap[left].prio < treap[right].prio) { //min priority heap - treap[left].right = merge(treap[left].right, right); - update(left); - return left; - } else { - treap[right].left = merge(left, treap[right].left); - update(right); - return right; -}} + pair<int, int> split(int v, int k) { + if (v < 0) return {-1, -1}; + auto& V = treap[v]; + push(v); + if (getSize(V.l) >= k) { // "V.val >= k" for lower_bound(k) + auto [left, right] = split(V.l, k); + V.l = right; + upd(v); + return {left, v}; + } else { + // and only "k" + auto [left, right] = split(V.r, k - getSize(V.l) - 1); + V.r = left; + upd(v); + return {v, right}; + }} -//insert values with high priority first -int insert(int root, int key, int prio) { - int next = sz(treap); - treap.emplace_back(key, prio); - auto t = split(root, key); - //returns new root - return merge(merge(t.first, next), t.second); -} + int merge(int left, int right) { + if (left < 0) return right; + if (right < 0) return left; + if (treap[left].prio < treap[right].prio) { + push(left); + treap[left].r = merge(treap[left].r, right); + upd(left); + return left; + } else { + push(right); + treap[right].l = merge(left, treap[right].l); + upd(right); + return right; + }} -int remove(int root, int key) { - if (root < 0) return -1; - if (key < treap[root].key) { - treap[root].left = remove(treap[root].left, key); - update(root); - return root; - } else if (key > treap[root].key) { - treap[root].right = remove(treap[root].right, key); - update(root); - return root; - } else { //check prio? - return merge(treap[root].left, treap[root].right); -}} + void insert(int i, ll val) { // and i = val + auto [left, right] = split(root, i); + treap.emplace_back(val); + left = merge(left, sz(treap) - 1); + root = merge(left, right); + } -int kth(int root, int k) { - if (root < 0) return -1; - int leftSize = getSize(treap[root].left); - if (k < leftSize) return kth(treap[root].left, k); - else if (k > leftSize) { - return kth(treap[root].right, k - 1 - leftSize); + void remove(int i, int count = 1) { + auto [left, t_right] = split(root, i); + auto [middle, right] = split(t_right, count); + root = merge(left, right); } - return root; -} + // for query use remove and read middle BEFORE remerging +}; diff --git a/content/datastructures/treap2.cpp b/content/datastructures/treap2.cpp deleted file mode 100644 index e40da0d..0000000 --- a/content/datastructures/treap2.cpp +++ /dev/null @@ -1,79 +0,0 @@ -mt19937 rng(0xc4bd5dad); -struct Treap { - struct Node { - ll val; - int prio, size = 1, l = -1, r = -1; - Node(ll x): val(x), prio(rng()) {} - }; - - vector<Node> treap; - int root = -1; - - int getSize(int v) { - return v < 0 ? 0 : treap[v].size; - } - - void upd(int v) { - if (v < 0) return; - auto &V = treap[v]; - V.size = 1 + getSize(V.l) + getSize(V.r); - // Update Node Code - } - - void push(int v) { - if (v < 0) return; - //auto &V = treap[v]; - //if (V.lazy) { - // Lazy Propagation Code - // if (V.l >= 0) treap[V.l].lazy = true; - // if (V.r >= 0) treap[V.r].lazy = true; - // V.lazy = false; - //} - } - - pair<int, int> split(int v, int k) { - if (v < 0) return {-1, -1}; - auto &V = treap[v]; - push(v); - if (getSize(V.l) >= k) { // "V.val >= k" for lower_bound(k) - auto [left, right] = split(V.l, k); - V.l = right; - upd(v); - return {left, v}; - } else { - // and only "k" - auto [left, right] = split(V.r, k - getSize(V.l) - 1); - V.r = left; - upd(v); - return {v, right}; - }} - - int merge(int left, int right) { - if (left < 0) return right; - if (right < 0) return left; - if (treap[left].prio < treap[right].prio) { - push(left); - treap[left].r = merge(treap[left].r, right); - upd(left); - return left; - } else { - push(right); - treap[right].l = merge(left, treap[right].l); - upd(right); - return right; - }} - - void insert(int i, ll val) { // and i = val - auto [left, right] = split(root, i); - treap.emplace_back(val); - left = merge(left, ssize(treap) - 1); - root = merge(left, right); - } - - void remove(int i, int count = 1) { - auto [left, t_right] = split(root, i); - auto [middle, right] = split(t_right, count); - root = merge(left, right); - } - // for query use remove and read middle BEFORE remerging -}; diff --git a/content/geometry/convexHull.cpp b/content/geometry/convexHull.cpp index 6d89e05..1173924 100644 --- a/content/geometry/convexHull.cpp +++ b/content/geometry/convexHull.cpp @@ -11,8 +11,8 @@ vector<pt> convexHull(vector<pt> pts){ while (k > t && cross(h[k-2], h[k-1], *it) <= 0) k--; h[k++] = *it; }}; - half(all(pts), 1);// Untere Hülle. - half(next(pts.rbegin()), pts.rend(), k);// Obere Hülle. + half(all(pts), 1); // Untere Hülle. + half(next(pts.rbegin()), pts.rend(), k); // Obere Hülle. h.resize(k); return h; } diff --git a/content/geometry/formulas3d.cpp b/content/geometry/formulas3d.cpp index dee3ce8..63de2ce 100644 --- a/content/geometry/formulas3d.cpp +++ b/content/geometry/formulas3d.cpp @@ -26,23 +26,23 @@ int ccw(pt3 a, pt3 b, pt3 c, pt3 p) { return (orien > EPS) - (orien < -EPS); } -// Entfernung von Punkt p zur Ebene a,b,c. +// Entfernung von Punkt p zur Ebene a, b, c. double distToPlane(pt3 a, pt3 b, pt3 c, pt3 p) { - pt3 n = cross(b-a, c-a); - return (abs(dot(n, p)) - dot(n, a)) / abs(n); + pt3 n = cross(b - a, c - a); + return abs(dot(n, a - p)) / abs(n); } -// Liegt p in der Ebene a,b,c? +// Liegt p in der Ebene a, b, c? bool pointOnPlane(pt3 a, pt3 b, pt3 c, pt3 p) { return ccw(a, b, c, p) == 0; } -// Schnittpunkt von der Grade a-b und der Ebene c,d,e +// Schnittpunkt von der Grade a-b und der Ebene c, d, e // die Grade darf nicht parallel zu der Ebene sein! pt3 linePlaneIntersection(pt3 a, pt3 b, pt3 c, pt3 d, pt3 e) { - pt3 n = cross(d-c, e-c); - pt3 d = b - a; - return a - d * (dot(n, a) - dot(n, c)) / dot(n, d); + pt3 n = cross(d - c, e - c); + pt3 dir = b - a; + return a + dir * dot(n, c - a) / dot(n, dir); } // Abstand zwischen der Grade a-b und c-d diff --git a/content/geometry/hpi.cpp b/content/geometry/hpi.cpp index 3509e0e..02c71e3 100644 --- a/content/geometry/hpi.cpp +++ b/content/geometry/hpi.cpp @@ -1,4 +1,4 @@ -constexpr ll inf = 0x1FFF'FFFF'FFFF'FFFF;//THIS CODE IS WIP +constexpr ll INF = 0x1FFF'FFFF'FFFF'FFFF; //THIS CODE IS WIP bool left(pt p) {return real(p) < 0 || (real(p) == 0 && imag(p) < 0);} @@ -27,22 +27,22 @@ struct hp { if (ort == 0) return cross(from, to, a.from) < 0; return cross(b.dir(), a.dir()) * ort > 0; } - ll y = cross(a.dir(), b.dir()); - ll z = cross(b.from - a.from, b.dir()); - ptl i = mul(y, a.from) + mul(z, a.dir()); //intersect a and b - // check if i is outside/right of x - return imag(conj(mul(sgn(y),dir()))*(i-mul(y,from))) < 0; + ll x = cross(a.dir(), b.dir()); + ll y = cross(b.from - a.from, b.dir()); + ptl i = mul(x, a.from) + mul(y, a.dir()); //intersect a and b + // check if i is outside/right of this + return imag(conj(mul(sgn(x),dir()))*(i-mul(x,from))) < 0; } }; constexpr ll lim = 2e9+7; deque<hp> intersect(vector<hp> hps) { - hps.push_back(hp(pt{lim+1,-1})); - hps.push_back(hp(pt{lim+1,1})); + hps.push_back(hp(pt{lim + 1, -1})); + hps.push_back(hp(pt{lim + 1, 1})); sort(all(hps)); - deque<hp> dq = {hp(pt{-lim, 1})}; + deque<hp> dq = {hp(pt{-lim - 1, 1})}; for (auto x : hps) { while (sz(dq) > 1 && x.check(dq.end()[-1], dq.end()[-2])) dq.pop_back(); @@ -60,7 +60,7 @@ deque<hp> intersect(vector<hp> hps) { while (sz(dq) > 2 && dq[0].check(dq.end()[-1], dq.end()[-2])) dq.pop_back(); - while (sz(dq) > 2 && dq.end()[-1].check(dq[0], dq[1])) + while (sz(dq) > 2 && dq.back().check(dq[0], dq[1])) dq.pop_front(); if (sz(dq) < 3) return {}; diff --git a/content/geometry/lines.cpp b/content/geometry/lines.cpp index 95536a4..36de1db 100644 --- a/content/geometry/lines.cpp +++ b/content/geometry/lines.cpp @@ -1,10 +1,10 @@ struct line { - double a, b, c; // ax + by + c = 0; vertikale Line: b = 0, sonst: b = 1 - line(pt p, pt q) : a(-imag(q-p)), b(real(q-p)), c(cross({b, -a},p)) {} + double a, b, c; // ax + by + c = 0; vertikale Gerade: b = 0 + line(pt p, pt q) : a(imag(p-q)), b(real(q-p)), c(cross({-b, a}, p)) {} }; -line pointsToLine(pt p1, pt p2) { - line l; +line pointsToLine(pt p1, pt p2) { // vertikale Gerade: b = 1 oder b = 0 + line l(0, 0); if (abs(real(p1 - p2)) < EPS) { l.a = 1; l.b = 0.0; l.c = -real(p1); } else { @@ -15,19 +15,19 @@ line pointsToLine(pt p1, pt p2) { return l; } -bool parallel(line l1, line l2) { +bool parallel(line l1, line l2) { // braucht b in {0, 1} return (abs(l1.a - l2.a) < EPS) && (abs(l1.b - l2.b) < EPS); } -bool same(line l1, line l2) { +bool same(line l1, line l2) { // braucht b in {0, 1} return parallel(l1, l2) && (abs(l1.c - l2.c) < EPS); } -bool intersect(line l1, line l2, pt& p) { +bool intersect(line l1, line l2, pt& res) { // braucht b in {0, 1} if (parallel(l1, l2)) return false; double y, x = (l2.b * l1.c - l1.b * l2.c) / (l2.a * l1.b - l1.a * l2.b); if (abs(l1.b) > EPS) y = -(l1.a * x + l1.c); else y = -(l2.a * x + l2.c); - p = {x, y}; + res = {x, y}; return true; } diff --git a/content/geometry/linesAndSegments.cpp b/content/geometry/linesAndSegments.cpp index 1e21cba..ddab554 100644 --- a/content/geometry/linesAndSegments.cpp +++ b/content/geometry/linesAndSegments.cpp @@ -5,7 +5,7 @@ bool pointOnLine(pt a, pt b, pt p) { // Test auf Linienschnitt zwischen a-b und c-d. (nicht identisch) bool lineIntersection(pt a, pt b, pt c, pt d) { - return abs(cross(a - b, c - d)) < EPS; + return abs(cross(a - b, c - d)) > EPS; } // Berechnet den Schnittpunkt der Graden a-b und c-d. diff --git a/content/geometry/polygon.cpp b/content/geometry/polygon.cpp index 3178290..064d81f 100644 --- a/content/geometry/polygon.cpp +++ b/content/geometry/polygon.cpp @@ -29,7 +29,7 @@ bool inside(pt p, const vector<pt>& poly) { bool in = false; for (int i = 0; i + 1 < sz(poly); i++) { pt a = poly[i], b = poly[i + 1]; - if (pointOnLineSegment(a, b, p)) return false; + if (pointOnSegment(a, b, p)) return false; if (real(a) > real(b)) swap(a,b); if (real(a) <= real(p) && real(p) < real(b) && cross(p, a, b) < 0) { diff --git a/content/geometry/segmentIntersection.cpp b/content/geometry/segmentIntersection.cpp index 4262ddc..afc01b2 100644 --- a/content/geometry/segmentIntersection.cpp +++ b/content/geometry/segmentIntersection.cpp @@ -18,8 +18,8 @@ struct event { int id, type; bool operator<(const event& o) const { if (real(p) != real(o.p)) return real(p) < real(o.p); - if (type != o.type) return type > o.type; - return imag(p) < imag(o.p); + if (imag(p) != imag(o.p)) return imag(p) < imag(o.p); + return type > o.type; } }; @@ -29,7 +29,7 @@ bool lessPT(const pt& a, const pt& b) { } bool intersect(const seg& a, const seg& b) { - return lineSegmentIntersection(a.a, a.b, b.a, b.b); + return segmentIntersection(a.a, a.b, b.a, b.b); //@\sourceref{geometry/linesAndSegments.cpp}@ } pair<int, int> intersect(vector<seg>& segs) { diff --git a/content/geometry/spheres.cpp b/content/geometry/spheres.cpp index ec22262..d34bca9 100644 --- a/content/geometry/spheres.cpp +++ b/content/geometry/spheres.cpp @@ -1,3 +1,16 @@ +// 3D Punkt in kartesischen Koordinaten. +struct point{ + double x, y, z; + point() {} + point(double x, double y, double z) : x(x), y(y), z(z) {} + point(double lat, double lon) { + lat *= PI / 180.0; lon *= PI / 180.0; + x = cos(lat) * sin(lon); + y = cos(lat) * cos(lon); + z = sin(lat); + } +}; + // Great Circle Distance mit Längen- und Breitengrad. double gcDist(double pLat, double pLon, double qLat, double qLon, double radius) { @@ -11,19 +24,6 @@ double gcDist(double pLat, double pLon, } // Great Circle Distance mit kartesischen Koordinaten. -double gcDist(point p, point q) { +double gcDist(point p, point q) { // radius = 1 return acos(p.x * q.x + p.y * q.y + p.z * q.z); -} - -// 3D Punkt in kartesischen Koordinaten. -struct point{ - double x, y, z; - point() {} - point(double x, double y, double z) : x(x), y(y), z(z) {} - point(double lat, double lon) { - lat *= PI / 180.0; lon *= PI / 180.0; - x = cos(lat) * sin(lon); - y = cos(lat) * cos(lon); - z = sin(lat); - } -}; +}
\ No newline at end of file diff --git a/content/graph/bitonicTSP.cpp b/content/graph/bitonicTSP.cpp index 6470232..eee5082 100644 --- a/content/graph/bitonicTSP.cpp +++ b/content/graph/bitonicTSP.cpp @@ -27,5 +27,5 @@ auto bitonicTSP() { (lt.back() == 1 ? lt : ut).push_back(0); reverse(all(lt)); lt.insert(lt.end(), all(ut)); - return lt;// Enthält Knoten 0 zweimal. An erster und letzter Position. + return lt; // Enthält Knoten 0 zweimal. An erster und letzter Position. } diff --git a/content/graph/bitonicTSPsimple.cpp b/content/graph/bitonicTSPsimple.cpp index 8b6e6c5..cacfb9c 100644 --- a/content/graph/bitonicTSPsimple.cpp +++ b/content/graph/bitonicTSPsimple.cpp @@ -23,5 +23,5 @@ auto bitonicTSP() { rl.push_back(v); p2 = v; }} lr.insert(lr.end(), rl.rbegin(), rl.rend()); - return lr;// Enthält Knoten 0 zweimal. An erster und letzter Position. + return lr; // Enthält Knoten 0 zweimal. An erster und letzter Position. } diff --git a/content/graph/connect.cpp b/content/graph/connect.cpp index ffcd6c2..7940b37 100644 --- a/content/graph/connect.cpp +++ b/content/graph/connect.cpp @@ -10,7 +10,7 @@ struct connect { } void addEdge(int u, int v, int id) { - lct.nodes[id + n] = LCT::Node(id + n, id + n); + lct.nodes[id + n] = LCT::Node(id + n, id); edges[id] = {u, v}; if (connected(u, v)) { int old = lct.query(&lct.nodes[u], &lct.nodes[v]); diff --git a/content/graph/dinic.cpp b/content/graph/dinic.cpp new file mode 100644 index 0000000..2e58a2d --- /dev/null +++ b/content/graph/dinic.cpp @@ -0,0 +1,55 @@ +struct Edge { + int to, rev; + ll f, c; +}; + +vector<vector<Edge>> adj; +int s, t; +vector<int> pt, dist; + +void addEdge(int u, int v, ll c) { + adj[u].push_back({v, (int)sz(adj[v]), 0, c}); + adj[v].push_back({u, (int)sz(adj[u]) - 1, 0, 0}); +} + +bool bfs() { + dist.assign(sz(adj), -1); + dist[s] = 0; + queue<int> q({s}); + while (!q.empty() && dist[t] < 0) { + int v = q.front(); q.pop(); + for (Edge& e : adj[v]) { + if (dist[e.to] < 0 && e.c - e.f > 0) { + dist[e.to] = dist[v] + 1; + q.push(e.to); + }}} + return dist[t] >= 0; +} + +ll dfs(int v, ll flow = INF) { + if (v == t || flow == 0) return flow; + for (; pt[v] < sz(adj[v]); pt[v]++) { + Edge& e = adj[v][pt[v]]; + if (dist[e.to] != dist[v] + 1) continue; + ll cur = dfs(e.to, min(e.c - e.f, flow)); + if (cur > 0) { + e.f += cur; + adj[e.to][e.rev].f -= cur; + return cur; + }} + return 0; +} + +ll maxFlow(int source, int target) { + s = source, t = target; + ll flow = 0; + while (bfs()) { + pt.assign(sz(adj), 0); + ll cur; + do { + cur = dfs(s); + flow += cur; + } while (cur > 0); + } + return flow; +} diff --git a/content/graph/dinicScaling.cpp b/content/graph/dinicScaling.cpp index f4e833a..0974b78 100644 --- a/content/graph/dinicScaling.cpp +++ b/content/graph/dinicScaling.cpp @@ -26,17 +26,18 @@ bool bfs(ll lim) { return dist[t] >= 0; } -bool dfs(int v, ll flow) { - if (v == t) return true; +ll dfs(int v, ll flow) { + if (v == t || flow == 0) return flow; for (; pt[v] < sz(adj[v]); pt[v]++) { Edge& e = adj[v][pt[v]]; if (dist[e.to] != dist[v] + 1) continue; - if (e.c - e.f >= flow && dfs(e.to, flow)) { - e.f += flow; - adj[e.to][e.rev].f -= flow; - return true; + ll cur = dfs(e.to, min(e.c - e.f, flow)); + if (cur > 0) { + e.f += cur; + adj[e.to][e.rev].f -= cur; + return cur; }} - return false; + return 0; } ll maxFlow(int source, int target) { @@ -45,7 +46,11 @@ ll maxFlow(int source, int target) { for (ll lim = (1LL << 62); lim >= 1; lim /= 2) { while (bfs(lim)) { pt.assign(sz(adj), 0); - while (dfs(s, lim)) flow += lim; + ll cur; + do { + cur = dfs(s, lim); + flow += cur; + } while (cur > 0); }} return flow; } diff --git a/content/graph/pushRelabel.cpp b/content/graph/pushRelabel.cpp index 73a9eae..ec36026 100644 --- a/content/graph/pushRelabel.cpp +++ b/content/graph/pushRelabel.cpp @@ -29,7 +29,7 @@ ll maxFlow(int s, int t) { cur.assign(n, 0); H.assign(n, 0); H[s] = n; - ec[t] = 1;//never set t to active... + ec[t] = 1; //never set t to active... vector<int> co(2*n); co[0] = n - 1; for (Edge& e : adj[s]) addFlow(e, e.c); diff --git a/content/graph/reroot.cpp b/content/graph/reroot.cpp index 4c6a748..379c839 100644 --- a/content/graph/reroot.cpp +++ b/content/graph/reroot.cpp @@ -1,62 +1,48 @@ -// Usual Tree DP can be broken down in 4 steps: -// - Initialize dp[v] = identity -// - Iterate over all children w and take a value for w -// by looking at dp[w] and possibly the edge label of v -> w -// - combine the values of those children -// usually this operation should be commutative and associative -// - finalize the dp[v] after iterating over all children +using W = ll; // edge weight type +vector<vector<pair<int, W>>> adj; + struct Reroot { - using T = ll; + using T = ll; // dp type - // identity element - T E() {} - // x: dp value of child - // e: index of edge going to child - T takeChild(T x, int e) {} - T comb(T x, T y) {} - // called after combining all dp values of children - T fin(T x, int v) {} + static constexpr T E = 0; // neutral element + T takeChild(int v, int c, W w, T x) {} // move child along edge + static T comb(T x, T y) {} + T fin(int v, T x) {} // add v to own dp value x - vector<vector<pair<int, int>>> g; - vector<int> ord, pae; vector<T> dp; - T dfs(int v) { - ord.push_back(v); - for (auto [w, e] : g[v]) { - g[w].erase(find(all(g[w]), pair(v, e^1))); - pae[w] = e^1; - dp[v] = comb(dp[v], takeChild(dfs(w), e)); + T dfs0(int v, int from = -1) { + T val = E; + for (auto [u, w] : adj[v]) { + if (u == from) continue; + val = comb(val, takeChild(v, u, w, dfs0(u, v))); } - return dp[v] = fin(dp[v], v); + return dp[v] = fin(v, val); } - vector<T> solve(int n, vector<pair<int, int>> edges) { - g.resize(n); - for (int i = 0; i < n-1; i++) { - g[edges[i].first].emplace_back(edges[i].second, 2*i); - g[edges[i].second].emplace_back(edges[i].first, 2*i+1); + void dfs1(int v, int from = -1) { + vector<T> pref = {E}; + for (auto [u, w] : adj[v]) { + pref.push_back(takeChild(v, u, w, dp[u])); } - pae.assign(n, -1); - dp.assign(n, E()); - dfs(0); - vector<T> updp(n, E()), res(n, E()); - for (int v : ord) { - vector<T> pref(sz(g[v])+1), suff(sz(g[v])+1); - if (v != 0) pref[0] = takeChild(updp[v], pae[v]); - for (int i = 0; i < sz(g[v]); i++){ - auto [u, w] = g[v][i]; - pref[i+1] = suff[i] = takeChild(dp[u], w); - pref[i+1] = comb(pref[i], pref[i+1]); - } - for (int i = sz(g[v])-1; i >= 0; i--) { - suff[i] = comb(suff[i], suff[i+1]); - } - for (int i = 0; i < sz(g[v]); i++) { - updp[g[v][i].first] = fin(comb(pref[i], suff[i+1]), v); - } - res[v] = fin(pref.back(), v); + auto suf = pref; + partial_sum(all(pref), pref.begin(), comb); + exclusive_scan(suf.rbegin(), suf.rend(), + suf.rbegin(), E, comb); + + for (int i = 0; i < sz(adj[v]); i++) { + auto [u, w] = adj[v][i]; + if (u == from) continue; + dp[v] = fin(v, comb(pref[i], suf[i + 1])); + dfs1(u, v); } - return res; + dp[v] = fin(v, suf[0]); + } + + auto solve() { + dp.assign(sz(adj), E); + dfs0(0); + dfs1(0); + return dp; } }; diff --git a/content/graph/scc.cpp b/content/graph/scc.cpp index ac9a40b..32f1099 100644 --- a/content/graph/scc.cpp +++ b/content/graph/scc.cpp @@ -1,11 +1,12 @@ -vector<vector<int>> adj, sccs; -int counter; +vector<vector<int>> adj; +int counter, sccCounter; vector<bool> inStack; vector<int> low, idx, s; //idx enthält Index der SCC pro Knoten. void visit(int v) { int old = low[v] = counter++; - s.push_back(v); inStack[v] = true; + s.push_back(v); + inStack[v] = true; for (auto u : adj[v]) { if (low[u] < 0) visit(u); @@ -13,20 +14,20 @@ void visit(int v) { } if (old == low[v]) { - sccs.push_back({}); + sccCounter++; for (int u = -1; u != v;) { - u = s.back(); s.pop_back(); inStack[u] = false; - idx[u] = sz(sccs) - 1; - sccs.back().push_back(u); + u = s.back(); + s.pop_back(); + inStack[u] = false; + idx[u] = sccCounter - 1; }}} void scc() { inStack.assign(sz(adj), false); low.assign(sz(adj), -1); idx.assign(sz(adj), -1); - sccs.clear(); - counter = 0; + counter = sccCounter = 0; for (int i = 0; i < sz(adj); i++) { if (low[i] < 0) visit(i); }} diff --git a/content/graph/virtualTree.cpp b/content/graph/virtualTree.cpp index 27d2d6c..6233b27 100644 --- a/content/graph/virtualTree.cpp +++ b/content/graph/virtualTree.cpp @@ -3,13 +3,13 @@ vector<int> in, out; void virtualTree(vector<int> ind) { // indices of used nodes sort(all(ind), [&](int x, int y) {return in[x] < in[y];}); - for (int i = 0, n = sz(ind); i < n - 1; i++) { - ind.push_back(lca(ind[i], ind[i + 1])); + for (int i = 1, n = sz(ind); i < n; i++) { + ind.push_back(lca(ind[i - 1], ind[i])); } sort(all(ind), [&](int x, int y) {return in[x] < in[y];}); ind.erase(unique(all(ind)), ind.end()); - int n = ind.size(); + int n = sz(ind); vector<vector<int>> tree(n); vector<int> st = {0}; for (int i = 1; i < n; i++) { diff --git a/content/latexHeaders/layout.sty b/content/latexHeaders/layout.sty index 096cf23..01915f3 100644 --- a/content/latexHeaders/layout.sty +++ b/content/latexHeaders/layout.sty @@ -10,9 +10,8 @@ % Headline and bottomline. \usepackage{scrlayer-scrpage} \pagestyle{scrheadings} -\clearscrheadfoot -\ihead{\university} -\chead{\teamname} +\clearpairofpagestyles +\ihead{\university{} -- \teamname{}} \ohead{\pagemark} % Shift the title up to waste less space. @@ -43,7 +42,7 @@ % use less space... %\usepackage[subtle, sections, indent, leading, charwidths]{savetrees} -\usepackage[moderate,sections]{savetrees} +\usepackage[moderate]{savetrees} \RedeclareSectionCommands[ beforeskip=1pt plus 5pt, afterskip=0.1pt plus 1.5pt diff --git a/content/latexHeaders/math.sty b/content/latexHeaders/math.sty index c34cc99..d758f71 100644 --- a/content/latexHeaders/math.sty +++ b/content/latexHeaders/math.sty @@ -6,6 +6,7 @@ \usepackage{mathtools} \usepackage{amssymb} \usepackage{ntheorem} +\usepackage{nicefrac} %\usepackage{pxfonts} \usepackage[scaled=0.945,largesc,looser]{newpxtext}%better than pxfonts... diff --git a/content/math/divSum.cpp b/content/math/divSum.cpp new file mode 100644 index 0000000..48302b5 --- /dev/null +++ b/content/math/divSum.cpp @@ -0,0 +1,8 @@ +ll divSum(ll n, ll m, ll a, ll b){ + if (m == 0) return 0; + ll ans = a/m * n*(n-1)/2 + b/m * n; + a %= m; + b %= m; + ll y = (a*(n-1)+b) / m; + return ans + y * (n-1) - divSum(y, a, m, m-b-1); +} diff --git a/content/math/gauss.cpp b/content/math/gauss.cpp index 8129fd2..d431e52 100644 --- a/content/math/gauss.cpp +++ b/content/math/gauss.cpp @@ -14,19 +14,17 @@ void takeAll(int n, int line) { int gauss(int n) { vector<bool> done(n, false); for (int i = 0; i < n; i++) { - int swappee = i; // Sucht Pivotzeile für bessere Stabilität. - for (int j = 0; j < n; j++) { - if (done[j]) continue; - if (abs(mat[j][i]) > abs(mat[i][i])) swappee = j; + int j = i; // Sucht Pivotzeile für bessere Stabilität. + for (int k = 0; k < n; k++) { + if (!done[k] && abs(mat[k][i]) > abs(mat[i][i])) j = k; } - swap(mat[i], mat[swappee]); + swap(mat[i], mat[j]); if (abs(mat[i][i]) > EPS) { normalLine(i); takeAll(n, i); done[i] = true; }} - // Ab jetzt nur checks bzgl. Eindeutigkeit/Existenz der Lösung. - for (int i = 0; i < n; i++) { + for (int i = 0; i < n; i++) { // gauss fertig, prüfe Lösung bool allZero = true; for (int j = i; j < n; j++) allZero &= abs(mat[i][j]) <= EPS; if (allZero && abs(mat[i][n]) > EPS) return INCONSISTENT; diff --git a/content/math/lgsFp.cpp b/content/math/lgsFp.cpp index 0241742..bf18c86 100644 --- a/content/math/lgsFp.cpp +++ b/content/math/lgsFp.cpp @@ -22,5 +22,4 @@ void gauss(int n, ll mod) { normalLine(i, mod); takeAll(n, i, mod); done[i] = true; -}} -// für Eindeutigkeit, Existenz etc. siehe LGS über R @\sourceref{math/gauss.cpp}@ +}} // für Eindeutigkeit, Existenz etc. siehe LGS über R @\sourceref{math/gauss.cpp}@ diff --git a/content/math/linearRecurrence.cpp b/content/math/linearRecurrence.cpp index 2501e64..a8adacd 100644 --- a/content/math/linearRecurrence.cpp +++ b/content/math/linearRecurrence.cpp @@ -1,33 +1,30 @@ -constexpr ll mod = 1'000'000'007; -vector<ll> modMul(const vector<ll>& a, const vector<ll>& b, - const vector<ll>& c) { - ll n = sz(c); - vector<ll> res(n * 2 + 1); - for (int i = 0; i <= n; i++) { //a*b - for (int j = 0; j <= n; j++) { - res[i + j] += a[i] * b[j]; - res[i + j] %= mod; +constexpr ll mod = 998244353; +// oder ntt mul @\sourceref{math/transforms/ntt.cpp}@ +vector<ll> mul(const vector<ll>& a, const vector<ll>& b) { + vector<ll> c(sz(a) + sz(b) - 1); + for (int i = 0; i < sz(a); i++) { + for (int j = 0; j < sz(b); j++) { + c[i+j] += a[i]*b[j] % mod; }} - for (int i = 2 * n; i > n; i--) { //res%c - for (int j = 0; j < n; j++) { - res[i - 1 - j] += res[i] * c[j]; - res[i - 1 - j] %= mod; - }} - res.resize(n + 1); - return res; + for (ll& x : c) x %= mod; + return c; } ll kthTerm(const vector<ll>& f, const vector<ll>& c, ll k) { - assert(sz(f) == sz(c)); - vector<ll> tmp(sz(c) + 1), a(sz(c) + 1); - tmp[0] = a[1] = 1; //tmp = (x^k) % c - - for (k++; k > 0; k /= 2) { - if (k & 1) tmp = modMul(tmp, a, c); - a = modMul(a, a, c); - } - - ll res = 0; - for (int i = 0; i < sz(c); i++) res += (tmp[i+1] * f[i]) % mod; - return res % mod; + int n = sz(c); + vector<ll> q(n + 1, 1); + for (int i = 0; i < n; i++) q[i + 1] = (mod - c[i]) % mod; + vector<ll> p = mul(f, q); + p.resize(n); + p.push_back(0); + do { + vector<ll> q2 = q; + for (int i = 1; i <= n; i += 2) q2[i] = (mod - q2[i]) % mod; + vector<ll> x = mul(p, q2), y = mul(q, q2); + for (int i = 0; i <= n; i++){ + p[i] = i == n ? 0 : x[2*i + (k&1)]; + q[i] = y[2*i]; + } + } while (k /= 2); + return p[0]; } diff --git a/content/math/linearRecurrenceOld.cpp b/content/math/linearRecurrenceOld.cpp new file mode 100644 index 0000000..2501e64 --- /dev/null +++ b/content/math/linearRecurrenceOld.cpp @@ -0,0 +1,33 @@ +constexpr ll mod = 1'000'000'007; +vector<ll> modMul(const vector<ll>& a, const vector<ll>& b, + const vector<ll>& c) { + ll n = sz(c); + vector<ll> res(n * 2 + 1); + for (int i = 0; i <= n; i++) { //a*b + for (int j = 0; j <= n; j++) { + res[i + j] += a[i] * b[j]; + res[i + j] %= mod; + }} + for (int i = 2 * n; i > n; i--) { //res%c + for (int j = 0; j < n; j++) { + res[i - 1 - j] += res[i] * c[j]; + res[i - 1 - j] %= mod; + }} + res.resize(n + 1); + return res; +} + +ll kthTerm(const vector<ll>& f, const vector<ll>& c, ll k) { + assert(sz(f) == sz(c)); + vector<ll> tmp(sz(c) + 1), a(sz(c) + 1); + tmp[0] = a[1] = 1; //tmp = (x^k) % c + + for (k++; k > 0; k /= 2) { + if (k & 1) tmp = modMul(tmp, a, c); + a = modMul(a, a, c); + } + + ll res = 0; + for (int i = 0; i < sz(c); i++) res += (tmp[i+1] * f[i]) % mod; + return res % mod; +} diff --git a/content/math/math.tex b/content/math/math.tex index f670a70..644fbc8 100644 --- a/content/math/math.tex +++ b/content/math/math.tex @@ -109,8 +109,6 @@ sich alle Lösungen von $x^2-ny^2=c$ berechnen durch: \sourcecode{math/millerRabin.cpp}
\method{rho}{findet zufälligen Teiler}{\sqrt[\leftroot{3}\uproot{2}4]{n}}
\sourcecode{math/rho.cpp}
- %\method{squfof}{findet zufälligen Teiler}{\sqrt[\leftroot{4}\uproot{2}4]{n}}
- %\sourcecode{math/squfof.cpp}
\end{algorithm}
\begin{algorithm}{Teiler}
@@ -138,8 +136,9 @@ sich alle Lösungen von $x^2-ny^2=c$ berechnen durch: Sei $f(n)=c_{0}f(n-1)+c_{1}f(n-2)+\dots + c_{n-1}f(0)$ eine lineare Rekurrenz.
\begin{methods}
- \method{kthTerm}{Berechnet $k$-ten Term einer Rekurrenz $n$-ter Ordnung}{\log(k)\cdot n^2}
+ \method{kthTerm}{Berechnet $k$-ten Term einer Rekurrenz $n$-ter Ordnung}{\log(k)\cdot \text{mul}(n)}
\end{methods}
+ Die Polynom-Multiplikation kann auch mit NTT gemacht werden!
\sourcecode{math/linearRecurrence.cpp}
Alternativ kann der \mbox{$k$-te} Term in \runtime{n^3\log(k)} berechnet werden:
$$\renewcommand\arraystretch{1.5}
@@ -308,7 +307,10 @@ sich alle Lösungen von $x^2-ny^2=c$ berechnen durch: \method{gauss}{löst LGS}{n^3}
\sourcecode{math/gauss.cpp}
-\vfill\null\columnbreak
+\begin{algorithm}{Inversionszahl}
+ \vspace{-2pt}
+ \sourcecode{math/inversions.cpp}
+\end{algorithm}
\begin{algorithm}{Numerisch Extremstelle bestimmen}
\sourcecode{math/goldenSectionSearch.cpp}
@@ -318,7 +320,6 @@ sich alle Lösungen von $x^2-ny^2=c$ berechnen durch: \sourcecode{math/simpson.cpp}
\end{algorithm}
-
\begin{algorithm}{Polynome, FFT, NTT \& andere Transformationen}
Multipliziert Polynome $A$ und $B$.
\begin{itemize}
@@ -342,21 +343,6 @@ sich alle Lösungen von $x^2-ny^2=c$ berechnen durch: \sourcecode{math/transforms/seriesOperations.cpp}
\end{algorithm}
-\begin{algorithm}{Inversionszahl}
- \sourcecode{math/inversions.cpp}
-\end{algorithm}
-
-\subsection{Satz von \textsc{Sprague-Grundy}}
-Weise jedem Zustand $X$ wie folgt eine \textsc{Grundy}-Zahl $g\left(X\right)$ zu:
-\[
-g\left(X\right) := \min\left\{
-\mathbb{Z}_0^+ \setminus
-\left\{g\left(Y\right) \mid Y \text{ von } X \text{ aus direkt erreichbar}\right\}
-\right\}
-\]
-$X$ ist genau dann gewonnen, wenn $g\left(X\right) > 0$ ist.\\
-Wenn man $k$ Spiele in den Zuständen $X_1, \ldots, X_k$ hat, dann ist die \textsc{Grundy}-Zahl des Gesamtzustandes $g\left(X_1\right) \oplus \ldots \oplus g\left(X_k\right)$.
-
\subsection{Kombinatorik}
\paragraph{\textsc{Wilson}'s Theorem}
@@ -389,7 +375,9 @@ so gilt %\begin{algorithm}{Binomialkoeffizienten}
\paragraph{Binomialkoeffizienten}
Die Anzahl der \mbox{$k$-elementigen} Teilmengen einer \mbox{$n$-elementigen} Menge.
-
+
+ \input{math/tables/binom}
+
\begin{methods}
\method{precalc}{berechnet $n!$ und $n!^{-1}$ vor}{\mathit{lim}}
\method{calc\_binom}{berechnet Binomialkoeffizient}{1}
@@ -498,7 +486,7 @@ Die Anzahl der Partitionen von $n$ mit Elementen aus ${1,\dots,k}$. \begin{align*}
p_0(0)=1 \qquad p_k(n)&=0 \text{ für } k > n \text{ oder } n \leq 0 \text{ oder } k \leq 0\\
p_k(n)&= p_k(n-k) + p_{k-1}(n-1)\\[2pt]
- p(n)&=\sum_{k=1}^{n} p_k(n)=p_n(2n)=\sum\limits_{k\neq0}^\infty(-1)^{k+1}p\bigg(n - \frac{k(3k-1)}{2}\bigg)
+ p(n)=\sum_{k=1}^{n} p_k(n)&=p_n(2n)=\sum\limits_{k=1}^\infty(-1)^{k+1}\bigg[p\bigg(n - \frac{k(3k-1)}{2}\bigg) + p\bigg(n - \frac{k(3k+1)}{2}\bigg)\bigg]
\end{align*}
\begin{itemize}
\item in Formel $3$ kann abgebrochen werden wenn $\frac{k(3k-1)}{2} > n$.
@@ -508,6 +496,59 @@ Die Anzahl der Partitionen von $n$ mit Elementen aus ${1,\dots,k}$. \subsection{The Twelvefold Way \textnormal{(verteile $n$ Bälle auf $k$ Boxen)}}
\input{math/tables/twelvefold}
+\subsection{Platonische Körper}
+\input{math/tables/platonic}
+
+\input{math/tables/probability}
+
+\subsection{Satz von \textsc{Sprague-Grundy}}
+Weise jedem Zustand $X$ wie folgt eine \textsc{Grundy}-Zahl $g\left(X\right)$ zu:
+\[
+g\left(X\right) := \min\left\{
+\mathbb{Z}_0^+ \setminus
+\left\{g\left(Y\right) \mid Y \text{ von } X \text{ aus direkt erreichbar}\right\}
+\right\}
+\]
+$X$ ist genau dann gewonnen, wenn $g\left(X\right) > 0$ ist.\\
+Wenn man $k$ Spiele in den Zuständen $X_1, \ldots, X_k$ hat, dann ist die \textsc{Grundy}-Zahl des Gesamtzustandes $g\left(X_1\right) \oplus \ldots \oplus g\left(X_k\right)$.
+
+\subsection{Nim-Spiele}
+\begin{itemize}
+ \item[\ding{182}] letzter gewinnt (normal)
+ \item[\ding{183}] letzter verliert
+\end{itemize}
+\input{math/tables/nim}
+
+\subsection{Verschiedenes}
+\input{math/tables/stuff}
+
+\begin{algorithm}{Div Sum}
+ \method{divSum}{berechnet $\sum_{i=0}^{n-1} \left\lfloor \frac{a\cdot i + b}{m} \right\rfloor$}{\log(n)}
+ \textbf{Wichtig:} $b$ darf nicht negativ sein!
+ \sourcecode{math/divSum.cpp}
+\end{algorithm}
+
+\begin{algorithm}{Min Mod}
+ \begin{methods}
+ \method{firstVal}{berechnet den ersten Wert von $0,\ a, \ldots,\ a \cdot i \bmod{m}$,}{\log(m)}
+ \method{}{der in $[l, r]$ liegt. Gibt $-1$ zurück, falls er nicht existiert.}{}
+ \method{minMod}{berechnet das Minimum von $(a \cdot i + b) \bmod{m}$ für $i \in [0, n)$}{\log(m)}
+ \end{methods}
+ \textbf{Wichtig:} $0 \leq a, b, l, r < m$
+ \sourcecode{math/minMod.cpp}
+\end{algorithm}
+
+\subsection{Reihen}
+\input{math/tables/series}
+
+\subsection{Wichtige Zahlen}
+\input{math/tables/prime-composite}
+
+\subsection{Recover $\boldsymbol{x}$ and $\boldsymbol{y}$ from $\boldsymbol{y}$ from $\boldsymbol{x\*y^{-1}}$ }
+\method{recover}{findet $x$ und $y$ für $x=x\*y^{-1}\bmod m$}{\log(m)}
+\textbf{WICHTIG:} $x$ und $y$ müssen kleiner als $\sqrt{\nicefrac{m}{2}}$ sein!
+\sourcecode{math/recover.cpp}
+
\optional{
\subsection{Primzahlzählfunktion $\boldsymbol{\pi}$}
\begin{methods}
@@ -516,9 +557,10 @@ Die Anzahl der Partitionen von $n$ mit Elementen aus ${1,\dots,k}$. \method{pi}{zählt Primzahlen $\leq n$ ($n < N^2$)}{n^{2/3}}
\end{methods}
\sourcecode{math/piLehmer.cpp}
-}
-%\input{math/tables/numbers}
+\subsection{Primzahlzählfunktion $\boldsymbol{\pi}$}
+\sourcecode{math/piLegendre.cpp}
+}
\begin{algorithm}[optional]{Big Integers}
\sourcecode{math/bigint.cpp}
diff --git a/content/math/minMod.cpp b/content/math/minMod.cpp new file mode 100644 index 0000000..a80e783 --- /dev/null +++ b/content/math/minMod.cpp @@ -0,0 +1,22 @@ +ll firstVal(ll a, ll m, ll l, ll r) { + if (l == 0) return 0; + if (a == 0) return -1; + if ((l-1)/a < r/a) return (l+a-1) / a*a; + ll s = (r+a-1) / a*a; + ll v = firstVal(m % a, a, s-r, s-l); + return v < 0 ? -1 : s - v; +} + +ll minMod(ll n, ll m, ll a, ll b) { + if (a == 0) return b; + ll g = gcd(m, a); + ll c = b % g; + m /= g; + a /= g; + b /= g; + ll ai = multInv(a, m); + ll l = ai*b % m; + ll r = (n-1 + ai*b) % m; + if (n >= m || l > r) return c; + return a * firstVal(ai, m, l, r) % m * g + c; +}
\ No newline at end of file diff --git a/content/math/polynomial.cpp b/content/math/polynomial.cpp index 44f6207..84f3aaa 100644 --- a/content/math/polynomial.cpp +++ b/content/math/polynomial.cpp @@ -1,7 +1,7 @@ struct poly { vector<ll> data; - poly(int deg = 0) : data(max(1, deg)) {} + poly(int deg = 0) : data(1 + deg) {} poly(initializer_list<ll> _data) : data(_data) {} int size() const {return sz(data);} @@ -40,17 +40,18 @@ struct poly { //return p(x+a) poly operator<<(ll a) const { - poly res(size()); + poly res(size() - 1); for (int i = size() - 1; i >= 0; i--) { for (int j = size() - i - 1; j >= 1; j--) res[j] = (res[j] * a + res[j - 1]) % mod; - res[0] = (res[0] * a + res[i]) % mod; + res[0] = (res[0] * a + data[i]) % mod; } return res; } pair<poly, poly> divmod(const poly& d) const { int i = size() - d.size(); + if (i <= 0) return {{}, *this}; poly s(i + 1), r = *this; ll inv = multInv(d.data.back(), mod); for (; i >= 0; i--) { diff --git a/content/math/recover.cpp b/content/math/recover.cpp new file mode 100644 index 0000000..1a593f0 --- /dev/null +++ b/content/math/recover.cpp @@ -0,0 +1,13 @@ +ll sq(ll x) {return x*x;} + +array<ll, 2> recover(ll c, ll m) { + array<ll, 2> u = {m, 0}, v = {c, 1}; + while (m <= 2 * sq(v[0])) { + ll q = u[0] / v[0]; + u[0] -= q * v[0]; + u[1] -= q * v[1]; + swap(u, v); + } + if (v[1] <= 0 || 2 * sq(v[1]) >= m) return {-1, -1}; + return v; +} diff --git a/content/math/shortModInv.cpp b/content/math/shortModInv.cpp index f696cce..cf91ca0 100644 --- a/content/math/shortModInv.cpp +++ b/content/math/shortModInv.cpp @@ -1,3 +1,3 @@ ll multInv(ll x, ll m) { // x^{-1} mod m - return 1 < x ? m - multInv(m % x, x) * m / x : 1; + return 1 < x ? m - multInv(m % x, x) * m / x : 1; } diff --git a/content/math/squfof.cpp b/content/math/squfof.cpp deleted file mode 100644 index 1cb97de..0000000 --- a/content/math/squfof.cpp +++ /dev/null @@ -1,89 +0,0 @@ -using lll = __int128;
-
-constexpr lll multipliers[] = {1, 3, 5, 7,
- 11, 3*5, 3*7, 3*11,
- 5*7, 5*11, 7*11,
- 3*5*7, 3*5*11, 3*7*11,
- 5*7*11, 3*5*7*11};
-
-lll root(lll x) {
- lll r = sqrtl(x);
- while(r*r < x) r++;
- while(r*r > x) r--;
- return r;
-}
-
-lll croot(lll x) {
- lll r = cbrtl(x);
- while(r*r*r < x) r++;
- while(r*r*r > x) r--;
- return r;
-}
-
-lll squfof(lll N) {
- lll s = croot(N);
- if (s*s*s == N) return s;
- s = root(N);
- if (s*s == N) return s;
- for (lll k : multipliers) {
- lll D = k * N;
- lll Po, P, Pprev, q, b, r, i;
- Po = Pprev = P = root(D);
- lll Qprev = 1;
- lll Q = D - Po*Po;
- lll L = 2 * root(2 * s);
- lll B = 3 * L;
- for (i = 2; i < B; i++) {
- b = (Po + P) / Q;
- P = b*Q - P;
- q = Q;
- Q = Qprev + b * (Pprev - P);
- r = root(Q);
- if (!(i & 1) && r*r == Q) break;
- Qprev = q;
- Pprev = P;
- }
- if (i >= B) continue;
- b = (Po - P) / r;
- Pprev = P = b*r + P;
- Qprev = r;
- Q = (D-Pprev*Pprev)/Qprev;
- i = 0;
- do {
- b = (Po + P) / Q;
- Pprev = P;
- P = b*Q - P;
- q = Q;
- Q = Qprev + b * (Pprev - P);
- Qprev = q;
- i++;
- } while(P != Pprev);
- r = gcd(N, Qprev);
- if (r != 1 && r != N) return r;
- }
- exit(1);//try fallback to pollard rho
-}
-
-constexpr lll trialLim = 5'000;
-
-void factor(lll n, map<lll, int>& facts) {
- for (lll i = 2; i * i <= n && i <= trialLim; i++) {
- while (n % i == 0) {
- facts[i]++;
- n /= i;
- }}
- if (n > 1 && n < trialLim * trialLim) {
- facts[n]++;
- } else {
- vector<lll> todo = {n};
- while (!todo.empty()) {
- lll c = todo.back();
- todo.pop_back();
- if (c == 1) continue;
- if (isPrime(c)) {
- facts[c]++;
- } else {
- lll d = squfof(c);
- todo.push_back(d);
- todo.push_back(c / d);
-}}}}
diff --git a/content/math/tables.tex b/content/math/tables.tex deleted file mode 100644 index c422d73..0000000 --- a/content/math/tables.tex +++ /dev/null @@ -1,22 +0,0 @@ -\enlargethispage{0.2cm} -\begin{multicols*}{2} - \refstepcounter{subsection} - \subsectionmark{Tables} - \addcontentsline{toc}{subsection}{\protect\numberline{\thesubsection}Tables} - - \input{math/tables/binom} - \vfill - \input{math/tables/prime-composite} - \vfill - \input{math/tables/platonic} - \vfill - \input{math/tables/series} - - \columnbreak - - \input{math/tables/probability} - \vfill - \input{math/tables/stuff} - \vfill - \input{math/tables/nim} -\end{multicols*} diff --git a/content/math/tables/binom.tex b/content/math/tables/binom.tex index 878a6b0..9fc9ae3 100644 --- a/content/math/tables/binom.tex +++ b/content/math/tables/binom.tex @@ -1,28 +1,27 @@ -\begin{tabularx}{\linewidth}{|XXXX|} +\begin{expandtable} +\begin{tabularx}{\linewidth}{|C|} \hline - \multicolumn{4}{|c|}{Binomialkoeffizienten} \\ - \hline - \multicolumn{4}{|c|}{ $\frac{n!}{k!(n - k)!} \hfill=\hfill \binom{n}{k} \hfill=\hfill \binom{n}{n - k} \hfill=\hfill \frac{n}{k}\binom{n - 1}{k - 1} \hfill=\hfill \frac{n-k+1}{k}\binom{n}{k - 1} \hfill=\hfill - \binom{n - 1}{k} + \binom{n - 1}{k - 1} \hfill=\hfill + \frac{k+1}{n-k}\binom{n}{k + 1} \hfill=\hfill$\\ + + $\binom{n - 1}{k - 1} + \binom{n - 1}{k} \hfill=\hfill + \binom{n + 1}{k + 1} - \binom{n}{k + 1} \hfill=\hfill (-1)^k \binom{k - n - 1}{k} \hfill\approx\hfill - 2^{n} \cdot \frac{2}{\sqrt{2\pi n}}\cdot\exp\left(-\frac{2(x - \frac{n}{2})^2}{n}\right)$ - } \\ + 2^{n} \cdot \frac{2}{\sqrt{2\pi n}}\cdot\exp\left(-\frac{2(x - \frac{n}{2})^2}{n}\right)$\\ \grayhline - $\sum\limits_{k = 0}^n \binom{n}{k} = 2^n$ & - $\sum\limits_{k = 0}^n \binom{k}{m} = \binom{n + 1}{m + 1}$ & - $\sum\limits_{i = 0}^n \binom{n}{i}^2 = \binom{2n}{n}$ & - $\sum\limits_{k = 0}^n\binom{r + k}{k} = \binom{r + n + 1}{n}$\\ + $\sum\limits_{k = 0}^n \binom{n}{k} = 2^n\hfill + \sum\limits_{k = 0}^n \binom{k}{m} = \binom{n + 1}{m + 1}\hfill + \sum\limits_{i = 0}^n \binom{n}{i}^2 = \binom{2n}{n}\hfill + \sum\limits_{k = 0}^n\binom{r + k}{k} = \binom{r + n + 1}{n}$\\ - $\binom{n}{m}\binom{m}{k} = \binom{n}{k}\binom{n - k}{m - k}$ & - $\sum\limits_{k = 0}^n \binom{r}{k}\binom{s}{n - k} = \binom{r + s}{n}$ & - \multicolumn{2}{l|}{ - $\sum\limits_{i = 1}^n \binom{n}{i} F_i = F_{2n} \quad F_n = n\text{-th Fib.}$ - }\\ + $\binom{n}{m}\binom{m}{k} = \binom{n}{k}\binom{n - k}{m - k}\hfill + \sum\limits_{k = 0}^n \binom{r}{k}\binom{s}{n - k} = \binom{r + s}{n}\hfill + \sum\limits_{i = 1}^n \binom{n}{i} \mathit{Fib}_i = \mathit{Fib}_{2n}$\\ \hline \end{tabularx} +\end{expandtable} diff --git a/content/math/tables/nim.tex b/content/math/tables/nim.tex index 8490d42..66e289e 100644 --- a/content/math/tables/nim.tex +++ b/content/math/tables/nim.tex @@ -1,7 +1,6 @@ +\begin{expandtable} \begin{tabularx}{\linewidth}{|p{0.37\linewidth}|X|} \hline - \multicolumn{2}{|c|}{Nim-Spiele (\ding{182} letzter gewinnt (normal), \ding{183} letzter verliert)} \\ - \hline Beschreibung & Strategie \\ \hline @@ -94,3 +93,5 @@ Periode ab $n = 72$ der Länge $12$.\\ \hline \end{tabularx} +\end{expandtable} +
\ No newline at end of file diff --git a/content/math/tables/numbers.tex b/content/math/tables/numbers.tex deleted file mode 100644 index 1dc9f38..0000000 --- a/content/math/tables/numbers.tex +++ /dev/null @@ -1,59 +0,0 @@ -\begin{expandtable} -\begin{tabularx}{\linewidth}{|l|X|} - \hline - \multicolumn{2}{|c|}{Berühmte Zahlen} \\ - \hline - \textsc{Fibonacci} & - $f(0) = 0 \quad - f(1) = 1 \quad - f(n+2) = f(n+1) + f(n)$ \\ - \grayhline - - \textsc{Catalan} & - $C_0 = 1 \qquad - C_n = \sum\limits_{k = 0}^{n - 1} C_kC_{n - 1 - k} = - \frac{1}{n + 1}\binom{2n}{n} = \frac{2(2n - 1)}{n+1} \cdot C_{n-1}$ \\ - \grayhline - - \textsc{Euler} I & - $\eulerI{n}{0} = \eulerI{n}{n-1} = 1 \qquad - \eulerI{n}{k} = (k+1) \eulerI{n-1}{k} + (n-k) \eulerI{n-1}{k-1} $ \\ - \grayhline - - \textsc{Euler} II & - $\eulerII{n}{0} = 1 \quad - \eulerII{n}{n} = 0 \quad$\\ - & $\eulerII{n}{k} = (k+1) \eulerII{n-1}{k} + (2n-k-1) \eulerII{n-1}{k-1}$ \\ - \grayhline - - \textsc{Stirling} I & - $\stirlingI{0}{0} = 1 \qquad - \stirlingI{n}{0} = \stirlingI{0}{n} = 0 \qquad - \stirlingI{n}{k} = \stirlingI{n-1}{k-1} + (n-1) \stirlingI{n-1}{k}$ \\ - \grayhline - - \textsc{Stirling} II & - $\stirlingII{n}{1} = \stirlingII{n}{n} = 1 \qquad - \stirlingII{n}{k} = k \stirlingII{n-1}{k} + \stirlingII{n-1}{k-1} = - \frac{1}{k!} \sum\limits_{j=0}^{k} (-1)^{k-j}\binom{k}{j}j^n$\\ - \grayhline - - \textsc{Bell} & - $B_1 = 1 \qquad - B_n = \sum\limits_{k = 0}^{n - 1} B_k\binom{n-1}{k} - = \sum\limits_{k = 0}^{n}\stirlingII{n}{k}$\\ - \grayhline - - \textsc{Partitions} & - $p(0,0) = 1 \quad - p(n,k) = 0 \text{ für } k > n \text{ oder } n \leq 0 \text{ oder } k \leq 0$ \\ - & $p(n,k) = p(n-k,k) + p(n-1,k-1)$\\ - \grayhline - - \textsc{Partitions} & - $f(0) = 1 \quad f(n) = 0~(n < 0)$ \\ - & $f(n)=\sum\limits_{k=1}^\infty(-1)^{k-1}f(n - \frac{k(3k+1)}{2})+\sum\limits_{k=1}^\infty(-1)^{k-1}f(n - \frac{k(3k-1)}{2})$\\ - - \hline -\end{tabularx} -\end{expandtable} diff --git a/content/math/tables/platonic.tex b/content/math/tables/platonic.tex index f4ee554..2866ccf 100644 --- a/content/math/tables/platonic.tex +++ b/content/math/tables/platonic.tex @@ -1,39 +1,39 @@ +\begin{expandtable} \begin{tabularx}{\linewidth}{|X|CCCX|} \hline - \multicolumn{5}{|c|}{Platonische Körper} \\ - \hline - Übersicht & Seiten & Ecken & Kanten & dual zu \\ + Übersicht & |F| & |V| & |E| & dual zu \\ \hline Tetraeder & 4 & 4 & 6 & Tetraeder \\ - Würfel/Hexaeder & 6 & 8 & 12 & Oktaeder \\ - Oktaeder & 8 & 6 & 12 & Würfel/Hexaeder\\ + Würfel & 6 & 8 & 12 & Oktaeder \\ + Oktaeder & 8 & 6 & 12 & Würfel\\ Dodekaeder & 12 & 20 & 30 & Ikosaeder \\ Ikosaeder & 20 & 12 & 30 & Dodekaeder \\ \hline \multicolumn{5}{|c|}{Färbungen mit maximal $n$ Farben (bis auf Isomorphie)} \\ \hline - \multicolumn{3}{|l}{Ecken vom Oktaeder/Seiten vom Würfel} & + \multicolumn{3}{|l}{|V| vom Oktaeder/|F| vom Würfel} & \multicolumn{2}{l|}{$(n^6 + 3n^4 + 12n^3 + 8n^2)/24$} \\ - \multicolumn{3}{|l}{Ecken vom Würfel/Seiten vom Oktaeder} & + \multicolumn{3}{|l}{|V| vom Würfel/|F| vom Oktaeder} & \multicolumn{2}{l|}{$(n^8 + 17n^4 + 6n^2)/24$} \\ - \multicolumn{3}{|l}{Kanten vom Würfel/Oktaeder} & + \multicolumn{3}{|l}{|E| vom Würfel/Oktaeder} & \multicolumn{2}{l|}{$(n^{12} + 6n^7 + 3n^6 + 8n^4 + 6n^3)/24$} \\ - \multicolumn{3}{|l}{Ecken/Seiten vom Tetraeder} & + \multicolumn{3}{|l}{|V|/|F| vom Tetraeder} & \multicolumn{2}{l|}{$(n^4 + 11n^2)/12$} \\ - \multicolumn{3}{|l}{Kanten vom Tetraeder} & + \multicolumn{3}{|l}{|E| vom Tetraeder} & \multicolumn{2}{l|}{$(n^6 + 3n^4 + 8n^2)/12$} \\ - \multicolumn{3}{|l}{Ecken vom Ikosaeder/Seiten vom Dodekaeder} & + \multicolumn{3}{|l}{|V| vom Ikosaeder/|F| vom Dodekaeder} & \multicolumn{2}{l|}{$(n^{12} + 15n^6 + 44n^4)/60$} \\ - \multicolumn{3}{|l}{Ecken vom Dodekaeder/Seiten vom Ikosaeder} & + \multicolumn{3}{|l}{|V| vom Dodekaeder/|F| vom Ikosaeder} & \multicolumn{2}{l|}{$(n^{20} + 15n^{10} + 20n^8 + 24n^4)/60$} \\ - \multicolumn{3}{|l}{Kanten vom Dodekaeder/Ikosaeder (evtl. falsch)} & + \multicolumn{3}{|l}{|E| vom Dodekaeder/Ikosaeder} & \multicolumn{2}{l|}{$(n^{30} + 15n^{16} + 20n^{10} + 24n^6)/60$} \\ \hline \end{tabularx} +\end{expandtable} diff --git a/content/math/tables/prime-composite.tex b/content/math/tables/prime-composite.tex index 99b3348..073b4ba 100644 --- a/content/math/tables/prime-composite.tex +++ b/content/math/tables/prime-composite.tex @@ -1,26 +1,31 @@ -\begin{tabularx}{\linewidth}{|r|r|rIr|rIrIr|C|} +\begin{expandtable} +\begin{tabularx}{\linewidth}{|r|rIr|rIr|r|r|} \hline - \multicolumn{8}{|c|}{Important Numbers} \\ + \multirow{2}{*}{$10^x$} + & \multirow{2}{*}{Highly Composite} + & \multirow{2}{*}{\# Divs} + & \multicolumn{2}{|c|}{Prime} + & \multirow{2}{*}{\# Primes} & \multirow{2}{*}{Primorial} \\ + & & & $<$ & $>$ & & \\ \hline - $10^x$ & Highly Composite & \# Divs & $<$ Prime & $>$ Prime & \# Primes & primorial & \\ - \hline - 1 & 6 & 4 & $-3$ & $+1$ & 4 & 2 & \\ - 2 & 60 & 12 & $-3$ & $+1$ & 25 & 3 & \\ - 3 & 840 & 32 & $-3$ & $+9$ & 168 & 4 & \\ - 4 & 7\,560 & 64 & $-27$ & $+7$ & 1\,229 & 5 & \\ - 5 & 83\,160 & 128 & $-9$ & $+3$ & 9\,592 & 6 & \\ - 6 & 720\,720 & 240 & $-17$ & $+3$ & 78\,498 & 7 & \\ - 7 & 8\,648\,640 & 448 & $-9$ & $+19$ & 664\,579 & 8 & \\ - 8 & 73\,513\,440 & 768 & $-11$ & $+7$ & 5\,761\,455 & 8 & \\ - 9 & 735\,134\,400 & 1\,344 & $-63$ & $+7$ & 50\,847\,534 & 9 & \\ - 10 & 6\,983\,776\,800 & 2\,304 & $-33$ & $+19$ & 455\,052\,511 & 10 & \\ - 11 & 97\,772\,875\,200 & 4\,032 & $-23$ & $+3$ & 4\,118\,054\,813 & 10 & \\ - 12 & 963\,761\,198\,400 & 6\,720 & $-11$ & $+39$ & 37\,607\,912\,018 & 11 & \\ - 13 & 9\,316\,358\,251\,200 & 10\,752 & $-29$ & $+37$ & 346\,065\,536\,839 & 12 & \\ - 14 & 97\,821\,761\,637\,600 & 17\,280 & $-27$ & $+31$ & 3\,204\,941\,750\,802 & 12 & \\ - 15 & 866\,421\,317\,361\,600 & 26\,880 & $-11$ & $+37$ & 29\,844\,570\,422\,669 & 13 & \\ - 16 & 8\,086\,598\,962\,041\,600 & 41\,472 & $-63$ & $+61$ & 279\,238\,341\,033\,925 & 13 & \\ - 17 & 74\,801\,040\,398\,884\,800 & 64\,512 & $-3$ & $+3$ & 2\,623\,557\,157\,654\,233 & 14 & \\ - 18 & 897\,612\,484\,786\,617\,600 & 103\,680 & $-11$ & $+3$ & 24\,739\,954\,287\,740\,860 & 16 & \\ + 1 & 6 & 4 & $-3$ & $+1$ & 4 & 2 \\ + 2 & 60 & 12 & $-3$ & $+1$ & 25 & 3 \\ + 3 & 840 & 32 & $-3$ & $+9$ & 168 & 4 \\ + 4 & 7\,560 & 64 & $-27$ & $+7$ & 1\,229 & 5 \\ + 5 & 83\,160 & 128 & $-9$ & $+3$ & 9\,592 & 6 \\ + 6 & 720\,720 & 240 & $-17$ & $+3$ & 78\,498 & 7 \\ + 7 & 8\,648\,640 & 448 & $-9$ & $+19$ & 664\,579 & 8 \\ + 8 & 73\,513\,440 & 768 & $-11$ & $+7$ & 5\,761\,455 & 8 \\ + 9 & 735\,134\,400 & 1\,344 & $-63$ & $+7$ & 50\,847\,534 & 9 \\ + 10 & 6\,983\,776\,800 & 2\,304 & $-33$ & $+19$ & 455\,052\,511 & 10 \\ + 11 & 97\,772\,875\,200 & 4\,032 & $-23$ & $+3$ & 4\,118\,054\,813 & 10 \\ + 12 & 963\,761\,198\,400 & 6\,720 & $-11$ & $+39$ & 37\,607\,912\,018 & 11 \\ + 13 & 9\,316\,358\,251\,200 & 10\,752 & $-29$ & $+37$ & 346\,065\,536\,839 & 12 \\ + 14 & 97\,821\,761\,637\,600 & 17\,280 & $-27$ & $+31$ & 3\,204\,941\,750\,802 & 12 \\ + 15 & 866\,421\,317\,361\,600 & 26\,880 & $-11$ & $+37$ & 29\,844\,570\,422\,669 & 13 \\ + 16 & 8\,086\,598\,962\,041\,600 & 41\,472 & $-63$ & $+61$ & 279\,238\,341\,033\,925 & 13 \\ + 17 & 74\,801\,040\,398\,884\,800 & 64\,512 & $-3$ & $+3$ & 2\,623\,557\,157\,654\,233 & 14 \\ + 18 & 897\,612\,484\,786\,617\,600 & 103\,680 & $-11$ & $+3$ & 24\,739\,954\,287\,740\,860 & 16 \\ \hline \end{tabularx} +\end{expandtable} diff --git a/content/math/tables/probability.tex b/content/math/tables/probability.tex index f265d10..29f92e1 100644 --- a/content/math/tables/probability.tex +++ b/content/math/tables/probability.tex @@ -1,19 +1,15 @@ -\begin{tabularx}{\linewidth}{|LICIR|} +\begin{expandtable} +\begin{tabularx}{\linewidth}{|LIR|} \hline - \multicolumn{3}{|c|}{ + \multicolumn{2}{|c|}{ Wahrscheinlichkeitstheorie ($A,B$ Ereignisse und $X,Y$ Variablen) } \\ \hline - $\E(X + Y) = \E(X) + \E(Y)$ & - $\E(\alpha X) = \alpha \E(X)$ & - $X, Y$ unabh. $\Leftrightarrow \E(XY) = \E(X) \cdot \E(Y)$\\ - - $\Pr[A \vert B] = \frac{\Pr[A \land B]}{\Pr[B]}$ & - $A, B$ disj. $\Leftrightarrow \Pr[A \land B] = \Pr[A] \cdot \Pr[B]$ & - $\Pr[A \lor B] = \Pr[A] + \Pr[B] - \Pr[A \land B]$ \\ + $\E(X + Y) = \E(X) + \E(Y)$ & $\Pr[A \vert B] = \frac{\Pr[A \land B]}{\Pr[B]}$ \\ + $\E(\alpha X) = \alpha \E(X)$ & $\Pr[A \lor B] = \Pr[A] + \Pr[B] - \Pr[A \land B]$ \\ + $X, Y$ unabh. $\Leftrightarrow \E(XY) = \E(X) \cdot \E(Y)$ & $A, B$ disj. $\Leftrightarrow \Pr[A \land B] = \Pr[A] \cdot \Pr[B]$\\ \hline \end{tabularx} -\vfill \begin{tabularx}{\linewidth}{|Xlr|lrX|} \hline \multicolumn{6}{|c|}{\textsc{Bertrand}'s Ballot Theorem (Kandidaten $A$ und $B$, $k \in \mathbb{N}$)} \\ @@ -25,3 +21,4 @@ $\#A \geq \#B + k$ & $Num = \frac{a - k + 1 - b}{a - k + 1} \binom{a + b - k}{b}$ & \\ \hline \end{tabularx} +\end{expandtable} diff --git a/content/math/tables/series.tex b/content/math/tables/series.tex index 3042781..9618c2b 100644 --- a/content/math/tables/series.tex +++ b/content/math/tables/series.tex @@ -1,33 +1,33 @@ -\begin{tabularx}{\linewidth}{|XIXIXIX|} - \hline - \multicolumn{4}{|c|}{Reihen} \\ +\begin{expandtable} +\begin{tabularx}{\linewidth}{|XIXIX|} \hline $\sum\limits_{i = 1}^n i = \frac{n(n+1)}{2}$ & $\sum\limits_{i = 1}^n i^2 = \frac{n(n + 1)(2n + 1)}{6}$ & - $\sum\limits_{i = 1}^n i^3 = \frac{n^2 (n + 1)^2}{4}$ & - $H_n = \sum\limits_{i = 1}^n \frac{1}{i}$ \\ + $\sum\limits_{i = 1}^n i^3 = \frac{n^2 (n + 1)^2}{4}$ \\ \grayhline - $\sum\limits_{i = 0}^n c^i = \frac{c^{n + 1} - 1}{c - 1} \quad c \neq 1$ & - $\sum\limits_{i = 0}^\infty c^i = \frac{1}{1 - c} \quad \vert c \vert < 1$ & - $\sum\limits_{i = 1}^\infty c^i = \frac{c}{1 - c} \quad \vert c \vert < 1$ & - $\sum\limits_{i = 0}^\infty ic^i = \frac{c}{(1 - c)^2} \quad \vert c \vert < 1$ \\ + $\sum\limits_{i = 0}^n c^i = \frac{c^{n + 1} - 1}{c - 1} \hfill c \neq 1$ & + $\sum\limits_{i = 0}^\infty c^i = \frac{1}{1 - c} \hfill \vert c \vert < 1$ & + $\sum\limits_{i = 1}^\infty c^i = \frac{c}{1 - c} \hfill \vert c \vert < 1$ \\ \grayhline - + \multicolumn{2}{|lI}{ $\sum\limits_{i = 0}^n ic^i = \frac{nc^{n + 2} - (n + 1)c^{n + 1} + c}{(c - 1)^2} \quad c \neq 1$ } & - \multicolumn{2}{l|}{ + $\sum\limits_{i = 0}^\infty ic^i = \frac{c}{(1 - c)^2} \hfill \vert c \vert < 1$ \\ + \grayhline + + \multicolumn{2}{|lI}{ $\sum\limits_{i = 1}^n iH_i = \frac{n(n + 1)}{2}H_n - \frac{n(n - 1)}{4}$ - } \\ + } & + $H_n = \sum\limits_{i = 1}^n \frac{1}{i}$ \\ \grayhline \multicolumn{2}{|lI}{ - $\sum\limits_{i = 1}^n H_i = (n + 1)H_n - n$ - } & - \multicolumn{2}{l|}{ $\sum\limits_{i = 1}^n \binom{i}{m}H_i = \binom{n + 1}{m + 1} \left(H_{n + 1} - \frac{1}{m + 1}\right)$ - } \\ + } & + $\sum\limits_{i = 1}^n H_i = (n + 1)H_n - n$ \\ \hline \end{tabularx} +\end{expandtable} diff --git a/content/math/tables/stuff.tex b/content/math/tables/stuff.tex index 3cf8b4c..82f2d3f 100644 --- a/content/math/tables/stuff.tex +++ b/content/math/tables/stuff.tex @@ -1,6 +1,7 @@ -\begin{tabularx}{\linewidth}{|ll|} +\begin{expandtable} +\begin{tabularx}{\linewidth}{|Ll|} \hline - \multicolumn{2}{|C|}{Verschiedenes} \\ + \multicolumn{2}{|c|}{Verschiedenes} \\ \hline Türme von Hanoi, minimale Schirttzahl: & $T_n = 2^n - 1$ \\ @@ -20,7 +21,7 @@ \#Wälder mit $k$ gewurzelten Bäumen & $\frac{k}{n}\binom{n}{k}n^{n-k}$ \\ - \#Wälder mit $k$ gewurzelten Bäumen mit vorgegebenen Wurzelknoten& + \#Wälder mit $k$ gewurzelten~Bäumen mit vorgegebenen Wurzelknoten& $\frac{k}{n}n^{n-k}$ \\ Derangements & @@ -29,4 +30,4 @@ $\lim\limits_{n \to \infty} \frac{!n}{n!} = \frac{1}{e}$ \\ \hline \end{tabularx} - +\end{expandtable} diff --git a/content/math/transforms/seriesOperations.cpp b/content/math/transforms/seriesOperations.cpp index 4743674..b405698 100644 --- a/content/math/transforms/seriesOperations.cpp +++ b/content/math/transforms/seriesOperations.cpp @@ -4,7 +4,7 @@ vector<ll> poly_inv(const vector<ll>& a, int n) { vector<ll> a2 = a, q2 = q; a2.resize(2*len), q2.resize(2*len); ntt(q2); - for (int j : {0, 1}) { + for (int _ : {0, 1}) { ntt(a2); for (int i = 0; i < 2*len; i++) a2[i] = a2[i]*q2[i] % mod; ntt(a2, true); @@ -24,10 +24,13 @@ vector<ll> poly_deriv(vector<ll> a) { } vector<ll> poly_integr(vector<ll> a) { - if (a.empty()) return {0}; - a.push_back(a.back() * powMod(sz(a), mod-2, mod) % mod); - for (int i = sz(a)-2; i > 0; i--) - a[i] = a[i-1] * powMod(i, mod-2, mod) % mod; + static vector<ll> inv = {0, 1}; + for (static int i = 2; i <= sz(a); i++) + inv.push_back(mod - mod / i * inv[mod % i] % mod); + + a.push_back(0); + for (int i = sz(a) - 1; i > 0; i--) + a[i] = a[i-1] * inv[i] % mod; a[0] = 0; return a; } @@ -35,8 +38,7 @@ vector<ll> poly_integr(vector<ll> a) { vector<ll> poly_log(vector<ll> a, int n) { a = mul(poly_deriv(a), poly_inv(a, n)); a.resize(n-1); - a = poly_integr(a); - return a; + return poly_integr(a); } vector<ll> poly_exp(vector<ll> a, int n) { diff --git a/content/other/bitOps.cpp b/content/other/bitOps.cpp index 8079305..6230c86 100644 --- a/content/other/bitOps.cpp +++ b/content/other/bitOps.cpp @@ -3,13 +3,6 @@ for (int subset = bitmask; subset > 0; subset = (subset - 1) & bitmask) -// Zählt Anzahl der gesetzten Bits. -int numberOfSetBits(int i) { - i = i - ((i >> 1) & 0x5555'5555); - i = (i & 0x3333'3333) + ((i >> 2) & 0x3333'3333); - return (((i + (i >> 4)) & 0x0F0F'0F0F) * 0x0101'0101) >> 24; -} - // Nächste Permutation in Bitmaske // (z.B. 00111 => 01011 => 01101 => ...) ll nextPerm(ll v) { diff --git a/content/other/divideAndConquer.cpp b/content/other/divideAndConquer.cpp index 830dc7f..9bd5f0c 100644 --- a/content/other/divideAndConquer.cpp +++ b/content/other/divideAndConquer.cpp @@ -5,7 +5,7 @@ void rec(int i, int j0, int j1, int m0, int m1) { if (j1 < j0) return; int jmid = (j0 + j1) / 2; - dp[i][jmid] = inf; + dp[i][jmid] = INF; int bestk = m0; for (int k = m0; k < min(jmid, m1 + 1); ++k) { if (dp[i - 1][k] + C[k + 1][jmid] < dp[i][jmid]) { @@ -18,7 +18,7 @@ void rec(int i, int j0, int j1, int m0, int m1) { } ll calc(int n, int m) { - dp = vector<vector<ll>>(m, vector<ll>(n, inf)); + dp = vector<vector<ll>>(m, vector<ll>(n, INF)); for (int i = 0; i < n; i++) dp[0][i] = C[0][i]; for (int i = 1; i < m; i++) { rec(i, 0, n - 1, 0, n - 1); diff --git a/content/other/fastSubsetSum.cpp b/content/other/fastSubsetSum.cpp new file mode 100644 index 0000000..84396f6 --- /dev/null +++ b/content/other/fastSubsetSum.cpp @@ -0,0 +1,21 @@ +int fastSubsetSum(vector<int> w, int t){ + int a = 0, b = 0; + while(b < sz(w) && a + w[b] <= t) a += w[b++]; + if(b == sz(w)) return a; + int m = *max_element(all(w)); + vector<int> dp(2*m, -1), old; + dp[m+a-t] = b; + for(int i = b; i < sz(w); i++){ + old = dp; + for(int j = 0; j < m; j++){ + dp[j+w[i]] = max(dp[j+w[i]], old[j]); + } + for(int j = 2*m-1; j > m; j--){ + for(int k = max(old[j], 0); k < dp[j]; k++){ + dp[j-w[k]] = max(dp[j-w[k]], k); + } + } + } + for(a = t; dp[m+a-t] < 0; a--); + return a; +}
\ No newline at end of file diff --git a/content/other/josephus2.cpp b/content/other/josephus2.cpp index 5086e13..33544ea 100644 --- a/content/other/josephus2.cpp +++ b/content/other/josephus2.cpp @@ -1,8 +1,5 @@ int rotateLeft(int n) { // Der letzte Ãœberlebende, 1-basiert. - for (int i = 31; i >= 0; i--) { - if (n & (1 << i)) { - n &= ~(1 << i); - break; - }} - n <<= 1; n++; return n; + int bits = __lg(n); + n ^= 1 << bits; + return 2 * n + 1; } diff --git a/content/other/knuth.cpp b/content/other/knuth.cpp index 1d513c8..aa54924 100644 --- a/content/other/knuth.cpp +++ b/content/other/knuth.cpp @@ -1,5 +1,5 @@ ll calc(int n, int m, const vector<vector<ll>>& C) { - vector<vector<ll>> dp(m, vector<ll>(n, inf)); + vector<vector<ll>> dp(m, vector<ll>(n, INF)); vector<vector<int>> opt(m, vector<int>(n + 1, n - 1)); for (int i = 0; i < n; i++) dp[0][i] = C[0][i]; diff --git a/content/other/other.tex b/content/other/other.tex index 7a3c52b..59b5790 100644 --- a/content/other/other.tex +++ b/content/other/other.tex @@ -13,6 +13,19 @@ \sourcecode{other/timed.cpp}
\end{algorithm}
+\begin{algorithm}{Overflow-sichere arithmetische Operationen}
+ Gibt zurück, ob es einen Overflow gab. Wenn nicht, enthält \code{c} das Ergebnis.
+ \begin{expandtable}
+ \begin{tabularx}{\linewidth}{|lR|}
+ \hline
+ Addition & \code{__builtin_saddll_overflow(a, b, \&c)} \\
+ Subtraktion & \code{__builtin_ssubll_overflow(a, b, \&c)} \\
+ Multiplikation & \code{__builtin_smulll_overflow(a, b, \&c)} \\
+ \hline
+ \end{tabularx}
+ \end{expandtable}
+\end{algorithm}
+
\begin{algorithm}{Bit Operations}
\begin{expandtable}
\begin{tabularx}{\linewidth}{|Ll|}
@@ -31,19 +44,6 @@ \sourcecode{other/bitOps.cpp}
\end{algorithm}
-\begin{algorithm}{Overflow-sichere arithmetische Operationen}
- Gibt zurück, ob es einen Overflow gab. Wenn nicht, enthält \code{c} das Ergebnis.
- \begin{expandtable}
- \begin{tabularx}{\linewidth}{|lR|}
- \hline
- Addition & \code{__builtin_saddll_overflow(a, b, \&c)} \\
- Subtraktion & \code{__builtin_ssubll_overflow(a, b, \&c)} \\
- Multiplikation & \code{__builtin_smulll_overflow(a, b, \&c)} \\
- \hline
- \end{tabularx}
- \end{expandtable}
-\end{algorithm}
-
\begin{algorithm}{Pragmas}
\sourcecode{other/pragmas.cpp}
\end{algorithm}
@@ -72,6 +72,12 @@ \sourcecode{other/sos.cpp}
\end{algorithm}
+\begin{algorithm}{Fast Subset Sum}
+ \method{fastSubsetSum}{findet maximale subset $\mathit{sum}\leq t$}{n \cdot A}
+ Die Laufzeit hängt vom maximalen Wert $A$ in der Menge ab.
+ \sourcecode{other/fastSubsetSum.cpp}
+\end{algorithm}
+
\begin{algorithm}{Parallel Binary Search}
\sourcecode{other/pbs.cpp}
\end{algorithm}
diff --git a/content/other/pbs.cpp b/content/other/pbs.cpp index 7cb60e5..f4db2fd 100644 --- a/content/other/pbs.cpp +++ b/content/other/pbs.cpp @@ -1,19 +1,19 @@ // Q = # of queries, bucket sort is sometimes faster -vector<int> low(Q, 0), high(Q, MAX_OPERATIONS); +vector<int> low(Q, -1), high(Q, MAX_OPERATIONS); while (true) { vector<pair<int, int>> focus; - for (int i = 0; i < Q; i++) if (low[i] < high[i]) { - focus.emplace_back((low[i] + high[i]) / 2, i); - } + for (int i = 0; i < Q; i++) { + if (low[i] + 1 < high[i]) { + focus.emplace_back((low[i] + high[i]) / 2, i); + }} if (focus.empty()) break; sort(all(focus)); // reset simulation for (int step = 0; auto [mid, i] : focus) { - while (step <= mid) { + for (; step <= mid; step++) { // simulation step - step++; } if (/* requirement already fulfilled */) high[i] = mid; - else low[i] = mid + 1; -}} // answer in low (and high) + else low[i] = mid; +}} // answer in low (MAX_OPERATIONS if never ok) diff --git a/content/other/stuff.cpp b/content/other/stuff.cpp index 41543ad..e4e37e2 100644 --- a/content/other/stuff.cpp +++ b/content/other/stuff.cpp @@ -1,13 +1,7 @@ -// Alles-Header. -#include <bits/stdc++.h> - // Setzt deutsche Tastaturlayout / toggle mit alt + space setxkbmap de setxkbmap de,us -option grp:alt_space_toggle -// Schnelle Ein-/Ausgabe mit cin/cout. -cin.tie(nullptr)->ios::sync_with_stdio(false); - // Set mit eigener Sortierfunktion. set<point2, decltype(comp)> set1(comp); diff --git a/content/string/ahoCorasick.cpp b/content/string/ahoCorasick.cpp index eac312c..390d16d 100644 --- a/content/string/ahoCorasick.cpp +++ b/content/string/ahoCorasick.cpp @@ -4,7 +4,7 @@ struct AhoCorasick { int suffix = 0, ch, cnt = 0; array<int, ALPHABET_SIZE> nxt = {}; - vert(int p, int c) : suffix(-p), ch(c) {} + vert(int p, int c) : suffix(-p), ch(c) {fill(all(nxt), -1);} }; vector<vert> aho = {{0, -1}}; @@ -12,7 +12,7 @@ struct AhoCorasick { int v = 0; for (auto c : s) { int idx = c - OFFSET; - if (!aho[v].nxt[idx]) { + if (aho[v].nxt[idx] == -1) { aho[v].nxt[idx] = sz(aho); aho.emplace_back(v, idx); } @@ -30,8 +30,8 @@ struct AhoCorasick { } int go(int v, int idx) { // Root is v=0, idx is char - OFFSET - if (aho[v].nxt[idx]) return aho[v].nxt[idx]; - else return v == 0 ? 0 : go(getSuffix(v), idx); + if (aho[v].nxt[idx] != -1) return aho[v].nxt[idx]; + return v == 0 ? 0 : aho[v].nxt[idx] = go(getSuffix(v), idx); } vector<vector<int>> adj; diff --git a/content/string/duval.cpp b/content/string/duval.cpp index bf36cce..253bae1 100644 --- a/content/string/duval.cpp +++ b/content/string/duval.cpp @@ -6,9 +6,8 @@ vector<pair<int, int>> duval(const string& s) { if (s[k] < s[j]) k = i; else k++; } - while (i <= k) { + for (; i <= k; i += j - k) { res.push_back({i, i + j - k}); - i += j - k; }} return res; } @@ -16,6 +15,5 @@ vector<pair<int, int>> duval(const string& s) { int minrotation(const string& s) { auto parts = duval(s+s); for (auto [l, r] : parts) { - if (l < sz(s) && r >= sz(s)) { - return l; -}}} + if (r >= sz(s)) return l; +}} diff --git a/content/tcr.tex b/content/tcr.tex index afac53c..3b686ef 100644 --- a/content/tcr.tex +++ b/content/tcr.tex @@ -1,6 +1,9 @@ - -%maybe size 9pt if too many pages -\documentclass[a4paper,fontsize=7.8pt]{scrartcl} +\documentclass[ + paper=a4, + DIV=calc, + fontsize=7.8pt, + usegeometry +]{scrartcl} % General information. \newcommand{\teamname}{Infinite Loopers} @@ -54,11 +57,7 @@ \input{graph/graph} \input{geometry/geometry} \input{math/math} -\end{multicols*} \clearpage - \input{math/tables} -\begin{multicols*}{3} - \raggedcolumns \input{string/string} \input{python/python} \input{other/other} diff --git a/content/template/template.cpp b/content/template/template.cpp index c9a492c..7430d23 100644 --- a/content/template/template.cpp +++ b/content/template/template.cpp @@ -7,9 +7,9 @@ using namespace std; using ll = long long; using ld = long double; - + void solve() {} - + int main() { cin.tie(0)->sync_with_stdio(false); cout << setprecision(16); diff --git a/content/tests/gcc5bug.cpp b/content/tests/gcc5bug.cpp index f49603e..6aaeea9 100644 --- a/content/tests/gcc5bug.cpp +++ b/content/tests/gcc5bug.cpp @@ -1,4 +1,4 @@ //https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68203 struct A { - pair<int, int> values[1000000]; + pair<int, int> values[1000000]; }; diff --git a/test/GNUmakefile b/test/GNUmakefile index 10e3b34..5e57930 100644 --- a/test/GNUmakefile +++ b/test/GNUmakefile @@ -1,6 +1,7 @@ -TESTS = $(basename $(shell find . -type f -name '*.cpp')) -CXX = g++ -std=gnu++20 -I ../content/ -O2 -Wall -Wextra -Wshadow -Werror +TESTS = $(basename $(shell find . -path ./awk -prune -o -type f -name '*.cpp' -print)) +AWK = $(basename $(shell find . -type f -name '*.awk')) +CXX = g++ -std=gnu++20 -I awk/ -I ../content/ -O2 -Wall -Wextra -Wshadow -Werror test: $(TESTS:=.ok) @@ -8,11 +9,12 @@ missing: @find ../content -name '*.cpp' | sed 's|^../content/||' \ | while read -r f ; do [ -e "$$f" ] || echo "$$f" ; done \ | sort > missing.tmp - @sort missing.ignore | comm -23 missing.tmp - + @sort missing.ignore | comm -3 missing.tmp - @rm missing.tmp clean: rm -f $(TESTS:=.test) $(TESTS:=.ok) $(TESTS:=.d) + rm -rf awk/ %.ok: %.test timeout --foreground --verbose 60 prlimit -s$$((1<<32)) ./$< @@ -21,10 +23,14 @@ clean: %.test: %.cpp $(CXX) -o $@ $< -%.d: %.cpp +awk/%: %.awk ../content/% + @mkdir -p $(dir $@) + awk -f $*.awk < ../content/$* > $@ + +%.d: %.cpp $(addprefix awk/,$(AWK)) $(CXX) -M -MT '$*.test $*.d' -MF $@ $< .PHONY: test clean -.SECONDARY: $(TESTS:=.test) +.SECONDARY: $(TESTS:=.test) $(addprefix awk/,$(AWK)) include $(TESTS:=.d) diff --git a/test/datastructures/LCT.cpp b/test/datastructures/LCT.cpp new file mode 100644 index 0000000..58d76d7 --- /dev/null +++ b/test/datastructures/LCT.cpp @@ -0,0 +1,198 @@ +#include "../util.h" +#pragma GCC diagnostic ignored "-Wshadow" +#include <datastructures/LCT.cpp> + +struct Naive { + vector<set<int>> adj; + vector<ll> weight; + Naive(int n) : adj(n), weight(n, queryDefault) {} + + pair<ll, bool> dfs_path(int from, int to, ll delta = queryDefault, int prev = -1) { + if (from == to) { + weight[from] += delta; + return {weight[from], true}; + } + for (int x : adj[from]) { + if (x == prev) continue; + auto [res, seen] = dfs_path(x, to, delta, from); + if (seen) { + weight[from] += delta; + return {res + weight[from], true}; + } + } + return {queryDefault, false}; + } + + bool connected(int x, int y) { + return dfs_path(x, y).second; + } + + void link(int x, int y) { + adj[x].insert(y); + adj[y].insert(x); + } + + void cut(int x, int y) { + adj[x].erase(y); + adj[y].erase(x); + } + + int lca(int root, int a, int b) { + int res = -1; + auto dfs_lca = [&](auto&& self, int c, int prev = -1) -> pair<bool, bool>{ + bool seenA = c == a; + bool seenB = c == b; + for (int x : adj[c]) { + if (x == prev) continue; + auto [tmpA, tmpB] = self(self, x, c); + seenA |= tmpA; + seenB |= tmpB; + } + if (seenA && seenB && res < 0) res = c; + return {seenA, seenB}; + }; + dfs_lca(dfs_lca, root); + return res; + } + + ll query(int from, int to) { + return dfs_path(from, to).first; + } + + void modify(int from, int to, ll delta) { + dfs_path(from, to, delta); + } + + int random(int x) { + vector<int> seen; + auto dfs_comp = [&](auto&& self, int c, int prev = -1) -> void { + seen.push_back(c); + for (int x : adj[c]) { + if (x == prev) continue; + self(self, x, c); + } + }; + dfs_comp(dfs_comp, x); + return seen[Random::integer<int>(sz(seen))]; + } + + int randomAdj(int x) { + if (adj[x].empty()) return -1; + vector<int> seen(all(adj[x])); + return seen[Random::integer<int>(sz(seen))]; + } +}; + +void stress_test() { + ll queries = 0; + ll connected = 0; + ll link = 0; + ll lca = 0; + ll sum = 0; + ll modify = 0; + ll cut = 0; + for (int tries = 0; tries < 500; tries++) { + int n = Random::integer<int>(1, 100); + int m = Random::integer<int>(100, 10'000); + + LCT lct(n); + Naive naive(n); + for (int i = 0; i < m; i++) { + bool testConnected = Random::integer<int>(2) == 0; + bool testLink = Random::integer<int>(2) == 0; + bool testLCA = Random::integer<int>(2) == 0; + bool testSum = Random::integer<int>(2) == 0; + bool testModify = Random::integer<int>(2) == 0; + bool testCut = Random::integer<int>(2) == 0; + + { + int a = Random::integer<int>(0, n); + int b = Random::integer<int>(0, n); + + auto expected = naive.connected(a, b); + if (testConnected) { + connected++; + auto got = lct.connected(&lct.nodes[a], &lct.nodes[b]); + if (got != expected) cerr << "error: 1" << FAIL; + } + + if (!expected && testLink) { + lct.link(&lct.nodes[a], &lct.nodes[b]); + naive.link(a, b); + link++; + expected = true; + } + + if (testLCA && expected) { + int c = naive.random(a); + lct.makeRoot(&lct.nodes[c]); + auto gotLCA = lct.lca(&lct.nodes[a], &lct.nodes[b])->id; + auto expectedLCA = naive.lca(c, a, b); + if (gotLCA != expectedLCA) cerr << "error: 2" << FAIL; + lca++; + } + + if (testSum && expected) { + auto gotSum = lct.query(&lct.nodes[a], &lct.nodes[b]); + auto expectedSum = naive.query(a, b); + if (gotSum != expectedSum) cerr << "error: 3" << FAIL; + sum++; + } + + if (testModify && expected) { + ll w = Random::integer<ll>(-1000, 1000); + lct.modify(&lct.nodes[a], &lct.nodes[b], w);//must a and b directly connected?? + naive.modify(a, b, w); + modify++; + } + } + { + int a = Random::integer<int>(0, n); + int b = naive.randomAdj(a); + if (b >= 0 && testCut) { + lct.cut(&lct.nodes[a], &lct.nodes[b]); + naive.cut(a, b); + cut++; + } + } + queries++; + } + } + cerr << "tested random queries: " << queries << endl; + cerr << " connected: " << connected << endl; + cerr << " link: " << link << endl; + cerr << " lca: " << lca << endl; + cerr << " sum: " << sum << endl; + cerr << " modify: " << modify << endl; + cerr << " cut: " << cut << endl; +} + +constexpr int N = 200'000; +constexpr int M = 500'000; +void performance_test() { + timer t; + t.start(); + LCT lct(N); + t.stop(); + hash_t hash = 0; + for (int operations = 0; operations < N; operations++) { + int a = Random::integer<int>(0, N); + int b = Random::integer<int>(0, N); + ll w = Random::integer<ll>(-1000, 1000); + + t.start(); + if (!lct.connected(&lct.nodes[a], &lct.nodes[b])) { + lct.link(&lct.nodes[a], &lct.nodes[b]); + } + lct.modify(&lct.nodes[a], &lct.nodes[b], w); + hash += lct.query(&lct.nodes[a], &lct.nodes[b]); + t.stop(); + } + if (t.time > 500) cerr << "too slow: " << t.time << FAIL; + cerr << "tested performance: " << t.time << "ms (hash: " << hash << ")" << endl; +} + +int main() { + stress_test(); + performance_test(); +} diff --git a/test/datastructures/dynamicConvexHull.cpp b/test/datastructures/dynamicConvexHull.cpp new file mode 100644 index 0000000..e0345af --- /dev/null +++ b/test/datastructures/dynamicConvexHull.cpp @@ -0,0 +1,67 @@ +#include "../util.h" +namespace dch { + constexpr ll INF = LL::INF; + #include <datastructures/dynamicConvexHull.cpp> +} + +struct Line { + ll m, c; + Line(ll m_, ll c_) : m(m_), c(c_) {} + ll operator()(ll x) {return m*x+c;} +}; + +void stress_test(ll range) { + ll queries = 0; + for (int tries = 0; tries < 1000; tries++) { + int n = Random::integer<int>(1, 100); + + vector<Line> naive; + + dch::HullDynamic hd; + for (int i = 0; i < n; i++) { + ll m = Random::integer<ll>(-range, range); + ll c = Random::integer<ll>(-range, range); + hd.add(m, c); + naive.emplace_back(m, c); + + for (int j = 0; j < 100; j++) { + ll x = Random::integer<ll>(-range, range); + + ll got = hd.query(x); + ll expected = naive[0](x); + for (auto l : naive) expected = max(expected, l(x)); + + if (got != expected) cerr << "got: " << got << ", expected: " << expected << FAIL; + queries++; + } + } + } + cerr << "tested random queries: " << queries << endl; +} + +constexpr int N = 1'000'000; +void performance_test() { + timer t; + dch::HullDynamic hd; + + hash_t hash = 0; + for (int operations = 0; operations < N; operations++) { + ll m = Random::integer<ll>(-1'000'000'000, 1'000'000'000); + ll c = Random::integer<ll>(-1'000'000'000, 1'000'000'000); + ll x = Random::integer<ll>(-1'000'000'000, 1'000'000'000); + + t.start(); + hd.add(m, c); + hash += hd.query(x); + t.stop(); + } + if (t.time > 200) cerr << "too slow: " << t.time << FAIL; + cerr << "tested performance: " << t.time << "ms (hash: " << hash << ")" << endl; +} + +int main() { + stress_test(100); + stress_test(1'000); + stress_test(1'000'000); + performance_test(); +} diff --git a/test/datastructures/dynamicConvexHull.lichao.cpp b/test/datastructures/dynamicConvexHull.lichao.cpp new file mode 100644 index 0000000..d50ca60 --- /dev/null +++ b/test/datastructures/dynamicConvexHull.lichao.cpp @@ -0,0 +1,37 @@ +#include "../util.h" +constexpr ll INF = LL::INF; +#include <datastructures/dynamicConvexHull.cpp> +#include <datastructures/lichao.cpp> + +void stress_test(ll range) { + ll queries = 0; + for (int tries = 0; tries < 1000; tries++) { + int n = Random::integer<int>(1, 100); + xs = Random::distinct(n, -range, range); + sort(all(xs)); + + HullDynamic hd; + Lichao lichao; + for (int i = 0; i < 1000; i++) { + ll m = Random::integer<ll>(-range, range); + ll c = Random::integer<ll>(-range, range); + hd.add(m, c); + lichao.insert({-m, -c}); + + for (ll x : xs) { + ll gotA = hd.query(x); + ll gotB = -lichao.query(x); + + if (gotA != gotB) cerr << "gotA: " << gotA << ", gotB: " << gotB << FAIL; + queries++; + } + } + } + cerr << "tested random queries: " << queries << endl; +} + +int main() { + stress_test(100); + stress_test(1'000); + stress_test(1'000'000); +} diff --git a/test/datastructures/fenwickTree2.cpp b/test/datastructures/fenwickTree2.cpp index d332dc8..bc0753f 100644 --- a/test/datastructures/fenwickTree2.cpp +++ b/test/datastructures/fenwickTree2.cpp @@ -9,7 +9,7 @@ void stress_test() { ll queries = 0; for (int tries = 0; tries < 100; tries++) { int n = Random::integer<int>(10, 100); - vector<ll> naive(n);// = Random::integers<ll>(n, -1000, 1000); + vector<ll> naive = Random::integers<ll>(n, -1000, 1000); init(naive); for (int operations = 0; operations < 1000; operations++) { { diff --git a/test/datastructures/lazyPropagation.cpp b/test/datastructures/lazyPropagation.cpp index 7b0e448..3030e1c 100644 --- a/test/datastructures/lazyPropagation.cpp +++ b/test/datastructures/lazyPropagation.cpp @@ -1,5 +1,5 @@ #include "../util.h" -constexpr ll inf = LL::INF; +constexpr ll INF = LL::INF; #include <datastructures/lazyPropagation.cpp> constexpr int N = 1000'000; diff --git a/test/datastructures/lichao.cpp b/test/datastructures/lichao.cpp new file mode 100644 index 0000000..f4b797b --- /dev/null +++ b/test/datastructures/lichao.cpp @@ -0,0 +1,75 @@ +#include "../util.h" +constexpr ll INF = LL::INF; +#include <datastructures/lichao.cpp> + +void stress_test(ll range) { + ll queries = 0; + for (int tries = 0; tries < 1000; tries++) { + int n = Random::integer<int>(1, 100); + xs = Random::distinct<ll>(n, -range, range); + sort(all(xs)); + + vector<ll> naive(n, INF); + Lichao tree; + + for (int operations = 0; operations < 1000; operations++) { + { + ll m = Random::integer<ll>(-100, 100); + ll c = Random::integer<ll>(-range, range); + ll l = Random::integer<ll>(-range, range); + ll r = Random::integer<ll>(-range, range); + Fun f{m, c}; + + tree.segmentInsert(f, l, r); + for (int i = 0; i < n; i++) { + if (l <= xs[i] && xs[i] < r) naive[i] = min(naive[i], f(i)); + } + } + { + queries++; + int i = Random::integer<int>(0, n); + ll got = tree.query(xs[i]); + ll expected = naive[i]; + if (got != expected) cerr << xs[i] << endl; + if (got != expected) cerr << "got: " << got << ", expected: " << expected << FAIL; + } + } + } + cerr << "tested random queries: " << queries << endl; +} + +constexpr int N = 200'000; +void performance_test() { + timer t; + xs = Random::distinct<ll>(N, -1'000'000'000, 1'000'000'000); + sort(all(xs)); + + t.start(); + Lichao tree; + t.stop(); + + hash_t hash = 0; + for (int operations = 0; operations < N; operations++) { + + ll m = Random::integer<ll>(-1'000'000, 1'000'000); + ll c = Random::integer<ll>(-1'000'000, 1'000'000); + ll l = Random::integer<ll>(-1'000'000'000, 1'000'000'000); + ll r = Random::integer<ll>(-1'000'000'000, 1'000'000'000); + ll x = xs[Random::integer<int>(N)]; + Fun f{m, c}; + + t.start(); + tree.segmentInsert(f, l, r); + hash ^= tree.query(x); + t.stop(); + } + if (t.time > 1000) cerr << "too slow: " << t.time << FAIL; + cerr << "tested performance: " << t.time << "ms (hash: " << hash << ")" << endl; +} + +int main() { + stress_test(100); + stress_test(1'000); + stress_test(1'000'000); + performance_test(); +} diff --git a/test/datastructures/monotonicConvexHull.cpp b/test/datastructures/monotonicConvexHull.cpp new file mode 100644 index 0000000..3ae7c4d --- /dev/null +++ b/test/datastructures/monotonicConvexHull.cpp @@ -0,0 +1,132 @@ +#include "../util.h" +#include <datastructures/monotonicConvexHull.cpp> + +struct Line { + ll m, c; + Line(ll m_, ll c_) : m(m_), c(c_) {} + ll operator()(ll x) {return m*x+c;} +}; + +void stress_test(ll range) { + ll queries = 0; + for (int tries = 0; tries < 1000; tries++) { + int n = Random::integer<int>(1, 100); + auto ms = Random::integers<ll>(n, -range, range); + sort(all(ms), greater<>{}); + auto cs = ms; + for (int l = 0, r = 0; l < n;) { + while (r < n && ms[l] == ms[r]) r++; + auto tmp = Random::distinct<ll>(r - l, -range, range); + sort(all(tmp), greater<>{}); + for (int c : tmp) { + cs[l] = c; + l++; + } + } + + auto xs = Random::integers<ll>(n*100, -range*n, range*n); + sort(all(xs)); + int i = 0; + + vector<Line> naive; + + Envelope mch; + for (int k = 0; k < n; k++) { + ll m = ms[k]; + ll c = cs[k]; + + mch.add(m, c); + naive.emplace_back(m, c); + + for (int j = i + 100; i < j; i++) { + ll x = xs[i]; + + ll got = mch.query(x); + ll expected = naive[0](x); + for (auto l : naive) expected = min(expected, l(x)); + + if (got != expected) cerr << "got: " << got << ", expected: " << expected << FAIL; + queries++; + } + } + } + cerr << "tested random queries: " << queries << endl; +} + +void stress_test_independent(ll range) { + ll queries = 0; + for (int tries = 0; tries < 1000; tries++) { + int n = Random::integer<int>(1, 100); + auto ms = Random::integers<ll>(n, -range, range); + sort(all(ms), greater<>{}); + auto cs = ms; + for (int l = 0, r = 0; l < n;) { + while (r < n && ms[l] == ms[r]) r++; + auto tmp = Random::distinct<ll>(r - l, -range, range); + sort(all(tmp), greater<>{}); + for (int c : tmp) { + cs[l] = c; + l++; + } + } + + vector<Line> naive; + + Envelope mch; + for (int i = 0; i < n; i++) { + ll m = ms[i]; + ll c = cs[i]; + + mch.add(m, c); + naive.emplace_back(m, c); + + auto xs = Random::integers<ll>(100, -range, range); + sort(all(xs)); + auto tmp = mch; + + for (auto x : xs) { + ll got = tmp.query(x); + ll expected = naive[0](x); + for (auto l : naive) expected = min(expected, l(x)); + + if (got != expected) cerr << "got: " << got << ", expected: " << expected << FAIL; + queries++; + } + } + } + cerr << "tested random independent queries: " << queries << endl; +} + +constexpr int N = 1'000'000; +void performance_test() { + timer t; + auto ms = Random::distinct<ll>(N, -1'000'000'000, 1'000'000'000); + sort(all(ms), greater<>{}); + auto xs = Random::distinct<ll>(N, -1'000'000'000, 1'000'000'000); + sort(all(xs)); + Envelope mch; + + hash_t hash = 0; + for (int operations = 0; operations < N; operations++) { + ll c = Random::integer<ll>(-1'000'000'000, 1'000'000'000); + ll m = ms[operations]; + ll x = xs[operations]; + + t.start(); + mch.add(m, c); + hash += mch.query(x); + t.stop(); + } + if (t.time > 100) cerr << "too slow: " << t.time << FAIL; + cerr << "tested performance: " << t.time << "ms (hash: " << hash << ")" << endl; +} + +int main() { + stress_test(100); + stress_test(1'000); + stress_test(1'000'000); + stress_test_independent(100); + stress_test_independent(1'000); + stress_test_independent(1'000'000); + performance_test(); +} diff --git a/test/datastructures/persistent.cpp b/test/datastructures/persistent.cpp new file mode 100644 index 0000000..4e304fa --- /dev/null +++ b/test/datastructures/persistent.cpp @@ -0,0 +1,35 @@ +#include "../util.h" +#pragma GCC diagnostic ignored "-Wshadow" +#include <datastructures/persistent.cpp> + +void stress_test() { + ll queries = 0; + for (int tries = 0; tries < 100'000; tries++) { + int n = Random::integer<int>(1, 30); + + int timeRef = Random::integer<int>(1, 30); + persistent<double> got(timeRef); + map<int, double> expected; + + for (int i = 0; i < n; i++) { + timeRef += Random::integer<int>(1, 30); + double x = Random::real<double>(-1'000, 1'000); + auto t = got.set(x); + + if (!expected.empty() && t <= expected.rbegin()->first) cerr << "error: time travel" << FAIL; + expected[t] = x; + } + + double tmp = 0; + for (int i = expected.begin()->first; i < expected.rbegin()->first + 10; i++) { + if (expected.find(i) != expected.end()) tmp = expected[i]; + if (got.get(i) != tmp) cerr << "got: " << got.get(i) << ", " << "expected: " << tmp << FAIL; + } + queries += n; + } + cerr << "tested random queries: " << queries << endl; +} + +int main() { + stress_test(); +} diff --git a/test/datastructures/persistentArray.cpp b/test/datastructures/persistentArray.cpp new file mode 100644 index 0000000..6712089 --- /dev/null +++ b/test/datastructures/persistentArray.cpp @@ -0,0 +1,48 @@ +#include "../util.h" +#pragma GCC diagnostic ignored "-Wshadow" +#include <datastructures/persistent.cpp> +#include <datastructures/persistentArray.cpp> + +void stress_test() { + ll queries = 0; + for (int tries = 0; tries < 2'000; tries++) { + int n = Random::integer<int>(1, 30)*1000; + int m = Random::integer<int>(1, 30); + + persistentArray<double> got(m); + vector<double> cur(m); + vector<pair<int, vector<double>>> expected; + for (int i = 0; i < n; i++) { + int op = Random::integer<int>(0, 20); + if (op <= 10) { + int j = Random::integer<int>(0, m); + double x = Random::real<double>(-1'000, 1'000); + + auto t = got.set(j, x); + if (!expected.empty() && t <= expected.rbegin()->first) cerr << "error: time travel" << FAIL; + + cur[j] = x; + expected.emplace_back(t, cur); + } else if (op <= 16) { + if (sz(expected) < 1) continue; + int j = Random::integer<int>(0, sz(expected)); + for (int k = 0; k < m; k++) { + if (got.get(k, expected[j].first) != expected[j].second[k]) cerr << "got: " << got.get(k, expected[j].first) << ", expected: " << expected[j].second[k] << FAIL; + } + } else { + if (sz(expected) < 1) continue; + int j = Random::integer<int>(0, sz(expected)); + got.reset(expected[j].first); + expected.resize(j + 1); + cur = expected.back().second; + } + + } + queries += n; + } + cerr << "tested random queries: " << queries << endl; +} + +int main() { + stress_test(); +} diff --git a/test/datastructures/stlRope.cpp b/test/datastructures/stlRope.cpp new file mode 100644 index 0000000..7405e4e --- /dev/null +++ b/test/datastructures/stlRope.cpp @@ -0,0 +1,6 @@ +#include "../util.h" +#include <datastructures/stlRope.cpp> + +int main() { + test(); +} diff --git a/test/datastructures/stlRope.cpp.awk b/test/datastructures/stlRope.cpp.awk new file mode 100644 index 0000000..df7c361 --- /dev/null +++ b/test/datastructures/stlRope.cpp.awk @@ -0,0 +1,27 @@ +/rope<int> v;/ { + print "void test() {" + print "ll num = 5;" + print "ll start = 2;" + print "ll length = 4;" + print "ll offset = 3;" +} +/v.push_back(num);/ { + print "v.push_back(0);" + print "v.push_back(1);" + print "v.push_back(2);" + print "v.push_back(3);" + print "v.push_back(4);" +} +/rope<int> sub/ { + print "v.push_back(6);" + print "v.push_back(7);" +} +/for\(auto it/ { + print "vector<int> got, expected = {0,1,6,2,3,4,5,7};" +} +END { + print " got.push_back(*it);" + print "if (got != expected) cerr << \"error\" << endl;" + print "}" +} +{ print } diff --git a/test/datastructures/treap.cpp b/test/datastructures/treap.cpp new file mode 100644 index 0000000..2fc9d63 --- /dev/null +++ b/test/datastructures/treap.cpp @@ -0,0 +1,85 @@ +#include "../util.h" +#include <datastructures/treap.cpp> + +void add(Treap& t, vector<ll>& ans, int v) { + if (v < 0) return; + add(t, ans, t.treap[v].l); + ans.push_back(t.treap[v].val); + add(t, ans, t.treap[v].r); +} + +vector<ll> to_vec(Treap& t) { + vector<ll> ans; + add(t, ans, t.root); + return ans; +} + +void stress_test(int T, int n) { + for (int tries = 0; tries < T; tries++) { + int ins = Random::integer<int>(1, n); + int rem = Random::integer<int>(0, ins+1); + + vector<ll> a; + Treap t; + while (ins + rem > 0) { + bool is_ins = Random::integer(0, ins+rem) < ins; + if (a.empty()) is_ins = true; + + if (is_ins) { + int ind = Random::integer<int>(0, (int)sz(a)+1); + ll val = Random::integer((ll)-1e18, (ll)1e18+1); + t.insert(ind, val); + a.insert(a.begin() + ind, val); + ins--; + } else { + int ind = Random::integer<int>(0, (int)sz(a)); + int cnt = Random::integer<int>(1, 1 + min<int>({(int)sz(a)-ind, rem, (int)sqrt(n)})); + t.remove(ind, cnt); + a.erase(a.begin() + ind, a.begin() + ind + cnt); + rem -= cnt; + } + } + if (to_vec(t) != a) cerr << "Failed stress test" << FAIL; + } + cerr << "Tested " << T << " random tests with n<=" << n << endl; +} + +constexpr int N = 200'000; +void performance_test() { + timer t; + + t.start(); + Treap tr; + t.stop(); + + hash_t hash = 0; + for (int operations = 0; operations < N; operations++) { + int ind = Random::integer<int>(0, operations+1); + ll val = Random::integer((ll)-1e18, (ll)1e18+1); + + t.start(); + tr.insert(ind, val); + hash ^= tr.root; + t.stop(); + } + while (tr.root != -1) { + t.start(); + int sz = tr.getSize(tr.root); + t.stop(); + + int ind = Random::integer<int>(0, sz); + int cnt = Random::integer<int>(1, 1 + min<int>(sz-ind, 10)); + t.start(); + tr.remove(ind, cnt); + t.stop(); + } + if (t.time > 1000) cerr << "too slow: " << t.time << FAIL; + cerr << "tested performance: " << t.time << "ms (hash: " << hash << ")" << endl; +} + +int main() { + stress_test(10000, 10); + stress_test(1000, 100); + stress_test(100, 10000); + performance_test(); +} diff --git a/test/geometry.h b/test/geometry.h index 7886fe2..0167d5c 100644 --- a/test/geometry.h +++ b/test/geometry.h @@ -1,6 +1,6 @@ -#include <geometry/sortAround.cpp> - namespace details { + #include <geometry/sortAround.cpp> + // Liegt p auf der Strecke a-b? bool pointInLineSegment(pt a, pt b, pt p) { if (cross(a, b, p) != 0) return false; @@ -59,7 +59,7 @@ namespace Random { for (size_t i = 0; i < dirs.size(); i++) { dirs[i] = pt(x[i], y[i]); } - sortAround(0, dirs); + details::sortAround(0, dirs); vector<pt> res = {{0, 0}}; ll maxX = 0; diff --git a/test/geometry/delaunay.cpp b/test/geometry/delaunay.cpp index 7f8ec30..5740b95 100644 --- a/test/geometry/delaunay.cpp +++ b/test/geometry/delaunay.cpp @@ -16,11 +16,11 @@ vector<pt> convexHull(vector<pt> pts){ vector<pt> h(2 * sz(pts)); auto half = [&](auto begin, auto end, int t) { for (auto it = begin; it != end; it++) { - while (k > t && cross(h[k-2], h[k-1], *it) < 0) k--;//allow collinear points! + while (k > t && cross(h[k-2], h[k-1], *it) < 0) k--; //allow collinear points! h[k++] = *it; }}; - half(all(pts), 1);// Untere Hülle. - half(next(pts.rbegin()), pts.rend(), k);// Obere Hülle. + half(all(pts), 1); // Untere Hülle. + half(next(pts.rbegin()), pts.rend(), k); // Obere Hülle. h.resize(k); return h; } diff --git a/test/geometry/formulas3d.cpp b/test/geometry/formulas3d.cpp new file mode 100644 index 0000000..f6c04b7 --- /dev/null +++ b/test/geometry/formulas3d.cpp @@ -0,0 +1,236 @@ +#include "../util.h" +constexpr double EPS = 1e-6; +struct pt3 { + double x, y, z; + pt3 operator-(const pt3 o) const { + return {x-o.x, y-o.y, z-o.z}; + } + pt3 operator+(const pt3 o) const { + return {x+o.x, y+o.y, z+o.z}; + } + + pt3 operator*(double m) const { + return {x*m, y*m, z*m}; + } + + pt3 operator/(double d) const { + return {x/d, y/d, z/d}; + } + + friend ostream& operator<<(ostream& os, pt3 p) { + return os << "(" << p.x << ", " << p.y << ", " << p.z << ")"; + } +}; + +pt3 cross(pt3 a, pt3 b); +double abs(pt3 p); +double distToLine(pt3 a, pt3 b, pt3 p) { + return abs(cross(p - a, b - a)) / abs(b - a); +} + +#include <geometry/formulas3d.cpp> + +namespace Random { + pt3 point3d(ll l, ll r) { + return { + (double)integer<ll>(l, r), + (double)integer<ll>(l, r), + (double)integer<ll>(l, r), + }; + } + + template<size_t C> + std::array<pt3, C> distinct(ll l, ll r) { + std::array<pt3, C> res = {}; + for (size_t i = 0; i < C; i++) { + bool unqiue; + do { + res[i] = point3d(l, r); + unqiue = true; + for (size_t j = 0; j < i; j++) { + unqiue &= res[j].x != res[i].x || + res[j].y != res[i].y || + res[j].z != res[i].z; + } + } while (!unqiue); + } + return res; + } +} + +void test_dot(ll range) { + ll queries = 0; + for (int tries = 0; tries < 100'000; tries++) { + auto p = Random::point3d(-range, range); + auto q = Random::point3d(-range, range); + + auto expected = p.x*q.x + p.y*q.y + p.z*q.z; + auto got = dot(p, q); + + if (got != expected) cerr << "got: " << got << ", expected: " << expected << FAIL; + queries++; + } + cerr << "tested dot: " << queries << endl; +} + +void test_cross(ll range) { + ll queries = 0; + for (int tries = 0; tries < 100'000; tries++) { + auto p = Random::point3d(-range, range); + auto q = Random::point3d(-range, range); + + auto expected = pt3{p.y*q.z - p.z*q.y, + p.z*q.x - p.x*q.z, + p.x*q.y - p.y*q.x}; + auto got = cross(p, q); + + if (got.x != expected.x) cerr << "error: x" << FAIL; + if (got.y != expected.y) cerr << "error: y" << FAIL; + if (got.z != expected.z) cerr << "error: z" << FAIL; + queries++; + } + cerr << "tested cross: " << queries << endl; +} + +void test_abs(ll range) { + ll queries = 0; + for (int tries = 0; tries < 100'000; tries++) { + auto p = Random::point3d(-range, range); + + auto expected = sqrt(p.x*p.x + p.y*p.y + p.z*p.z); + auto got = abs(p); + + if (abs(got - expected) > 1e-6) cerr << "got: " << got << ", expected: " << expected << FAIL; + queries++; + } + cerr << "tested abs: " << queries << endl; +} + +void test_mixed(ll range) { + ll queries = 0; + for (int tries = 0; tries < 100'000; tries++) { + auto a = Random::point3d(-range, range); + auto b = Random::point3d(-range, range); + auto c = Random::point3d(-range, range); + + auto expected = dot(cross(a, b), c); + auto got = mixed(a, b, c); + + if (got != expected) cerr << "got: " << got << ", expected: " << expected << FAIL; + queries++; + } + cerr << "tested mixed: " << queries << endl; +} + +void test_ccw(ll range) { + ll queries = 0; + for (int tries = 0; tries < 100'000; tries++) { + auto a = Random::point3d(-range, range); + auto b = Random::point3d(-range, range); + auto c = Random::point3d(-range, range); + auto d = Random::point3d(-range, range); + + ll expected = mixed(b - a, c - a, d - a); + if (expected < 0) expected = -1; + if (expected > 0) expected = 1; + auto got = ccw(a, b, c, d); + + if (got != expected) cerr << "got: " << got << ", expected: " << expected << FAIL; + queries++; + } + cerr << "tested ccw: " << queries << endl; +} + +void test_distToPlane(ll range) { + ll queries = 0; + for (int tries = 0; tries < 100'000; tries++) { + auto [p, q] = Random::distinct<2>(-range, range); + auto [a, b, c] = Random::distinct<3>(-range, range); + + auto norm = cross(a - c, b - c); + norm = norm / abs(norm); + + auto gotA = distToPlane(a, b, c, p); + auto gotB = distToPlane(a, b, c, q); + auto got = ccw(a, b, c, p) * ccw(a, b, c, q) < 0 ? gotA + gotB : abs(gotA - gotB); + + auto expected = abs(dot(norm, p - q)); + + if (abs(got - expected) > 1e-6) cerr << "got: " << got << ", expected: " << expected << FAIL; + queries++; + } + cerr << "tested distToPlane: " << queries << endl; +} + +void stress_pointOnPlane(ll range) { + ll queries = 0; + for (int tries = 0; tries < 100'000; tries++) { + auto p = Random::point3d(-range, range); + auto [a, b, c] = Random::distinct<3>(-range, range); + + bool expected = ccw(a, b, c, p) == 0; + bool got = pointOnPlane(a, b, c, p); + + if (got != expected) cerr << "error" << FAIL; + queries++; + } + cerr << "tested pointOnPlane: " << queries << endl; +} + +void test_linePlaneIntersection(ll range) { + ll queries = 0; + for (int tries = 0; tries < 100'000; tries++) { + auto [p, q] = Random::distinct<2>(-range, range); + auto [a, b, c] = Random::distinct<3>(-range, range); + + if (abs(dot(p - q, cross(a-c, b-c))) < 1e-6) continue; + + auto got = linePlaneIntersection(p, q, a, b, c); + + if (distToLine(p, q, got) > 1e-6) cerr << "error: 1" << FAIL; + if (distToPlane(a, b, c, got) > 1e-6) cerr << "error: 2" << FAIL; + queries++; + } + cerr << "tested linePlaneIntersection: " << queries << endl; +} + +void test_lineLineDist(ll range) { + ll queries = 0; + for (int tries = 0; tries < 100'000; tries++) { + auto [p, q] = Random::distinct<2>(-range, range); + auto [a, b] = Random::distinct<2>(-range, range); + + double expected = 0; + if (ccw(a, b, p, q) != 0) { + pt3 c = a + p - q; + expected = distToPlane(a, b, c, p); + } + auto got = lineLineDist(p, q, a, b); + + if (abs(got - expected) > 1e-6) cerr << "got: " << got << ", expected: " << expected << FAIL; + queries++; + } + cerr << "tested lineLineDist: " << queries << endl; +} + +int main() { + test_dot(100); + test_dot(1'000'000); + test_cross(100); + test_cross(1'000'000); + test_abs(100); + test_abs(1'000'000); + test_mixed(100); + test_mixed(1'000'000); + test_ccw(100); + test_ccw(1'000'000); + + test_distToPlane(100); + test_distToPlane(1'000'000); + stress_pointOnPlane(100); + stress_pointOnPlane(1'000'000); + test_linePlaneIntersection(100); + test_linePlaneIntersection(1'000);//can be far away + test_lineLineDist(100); + test_lineLineDist(1'000'000); +} diff --git a/test/geometry/hpi.cpp b/test/geometry/hpi.cpp new file mode 100644 index 0000000..a2326bc --- /dev/null +++ b/test/geometry/hpi.cpp @@ -0,0 +1,291 @@ +#include "../util.h" +constexpr ll EPS = 0; +#define double ll +#define polar polar<ll> +#include <geometry/formulas.cpp> +#undef polar +#undef double +#include "../geometry.h" +ll sgn(ll x) { + return (x > 0) - (x < 0); +} +#include <geometry/hpi.cpp> + +//https://cp-algorithms.com/geometry/halfplane-intersection.html +namespace cpalgo { + // Redefine epsilon and infinity as necessary. Be mindful of precision errors. + const long double eps = 1e-9, inf = 1e9; + + // Basic point/vector struct. + struct Point { + + long double x, y; + explicit Point(long double x_ = 0, long double y_ = 0) : x(x_), y(y_) {} + Point(pt p) : x(real(p)), y(imag(p)) {} + + // Addition, substraction, multiply by constant, dot product, cross product. + + friend Point operator + (const Point& p, const Point& q) { + return Point(p.x + q.x, p.y + q.y); + } + + friend Point operator - (const Point& p, const Point& q) { + return Point(p.x - q.x, p.y - q.y); + } + + friend Point operator * (const Point& p, const long double& k) { + return Point(p.x * k, p.y * k); + } + + friend long double dot(const Point& p, const Point& q) { + return p.x * q.x + p.y * q.y; + } + + friend long double cross(const Point& p, const Point& q) { + return p.x * q.y - p.y * q.x; + } + + friend std::ostream& operator<<(std::ostream& os, const Point& p) { + return os << "(" << p.x << ", " << p.y << ")"; + } + + + }; + + // Basic half-plane struct. + struct Halfplane { + + // 'p' is a passing point of the line and 'pq' is the direction vector of the line. + Point p, pq; + long double angle; + + Halfplane() {} + Halfplane(const Point& a, const Point& b) : p(a), pq(b - a) { + angle = atan2l(pq.x, -pq.y);//patched to get same sort + } + Halfplane(array<pt, 2> ps) : Halfplane(ps[0], ps[1]) {} + Halfplane(hp h) : Halfplane(h.from, h.to) {} + + // Check if point 'r' is outside this half-plane. + // Every half-plane allows the region to the LEFT of its line. + bool out(const Point& r) { + return cross(pq, r - p) < -eps; + } + + // Comparator for sorting. + bool operator < (const Halfplane& e) const { + return angle < e.angle; + } + + // Intersection point of the lines of two half-planes. It is assumed they're never parallel. + friend Point inter(const Halfplane& s, const Halfplane& t) { + long double alpha = cross((t.p - s.p), t.pq) / cross(s.pq, t.pq); + return s.p + (s.pq * alpha); + } + + friend std::ostream& operator<<(std::ostream& os, const Halfplane& hp) { + return os << hp.p << " " << hp.p+hp.pq; + } + }; + + // Actual algorithm + vector<Point> hp_intersect(vector<Halfplane>& H) { + + /*Point box[4] = { // Bounding box in CCW order + Point(inf, inf), + Point(-inf, inf), + Point(-inf, -inf), + Point(inf, -inf) + }; + + for(int i = 0; i<4; i++) { // Add bounding box half-planes. + Halfplane aux(box[i], box[(i+1) % 4]); + H.push_back(aux); + }*/ + // Add bounding box half-planes, fixed: + H.push_back({pt( 1e9, 1e9), pt( 1e9-1, 1e9 )}); + H.push_back({pt(-1e9, 1e9), pt(-1e9 , 1e9-1)}); + H.push_back({pt(-1e9, -1e9), pt(-1e9+1, -1e9 )}); + H.push_back({pt( 1e9, -1e9), pt( 1e9 , -1e9+1)}); + + // Sort by angle and start algorithm + sort(H.begin(), H.end()); + deque<Halfplane> dq; + int len = 0; + for(int i = 0; i < int(H.size()); i++) { + + // Remove from the back of the deque while last half-plane is redundant + while (len > 1 && H[i].out(inter(dq[len-1], dq[len-2]))) { + dq.pop_back(); + --len; + } + + // Remove from the front of the deque while first half-plane is redundant + while (len > 1 && H[i].out(inter(dq[0], dq[1]))) { + dq.pop_front(); + --len; + } + + // Special case check: Parallel half-planes + if (len > 0 && fabsl(cross(H[i].pq, dq[len-1].pq)) < eps) { + // Opposite parallel half-planes that ended up checked against each other. + if (dot(H[i].pq, dq[len-1].pq) < 0.0) + return vector<Point>(); + + // Same direction half-plane: keep only the leftmost half-plane. + if (H[i].out(dq[len-1].p)) { + dq.pop_back(); + --len; + } + else continue; + } + + // Add new half-plane + dq.push_back(H[i]); + ++len; + } + + // Final cleanup: Check half-planes at the front against the back and vice-versa + while (len > 2 && dq[0].out(inter(dq[len-1], dq[len-2]))) { + dq.pop_back(); + --len; + } + + while (len > 2 && dq[len-1].out(inter(dq[0], dq[1]))) { + dq.pop_front(); + --len; + } + + // Report empty intersection if necessary + if (len < 3) return vector<Point>(); + + // Reconstruct the convex polygon from the remaining half-planes. + vector<Point> ret(len); + for(int i = 0; i+1 < len; i++) { + ret[i] = inter(dq[i], dq[i+1]); + } + ret.back() = inter(dq[len-1], dq[0]); + return ret; + } +} + +//check if a is dominated by b and c +bool naiveCheck(cpalgo::Halfplane a, cpalgo::Halfplane b, cpalgo::Halfplane c) { + return a.out(inter(b, c)); +} + +void test_check(ll range) { + ll queries = 0; + for (int tries = 0; tries < 100'000; tries++) { + auto a = Random::line(range); + auto b = Random::line(range); + auto c = b; + while (cross(b[0] - b[1], c[0] - c[1]) == 0) c = Random::line(range); + + bool got = hp(a[0], a[1]).check(hp(b[0], b[1]), hp(c[0], c[1])); + bool expected = naiveCheck(a, b, c); + + if (got != expected) { + cout << tries << endl; + cout << a[0] << " " << a[1] << endl; + cout << b[0] << " " << b[1] << endl; + cout << c[0] << " " << c[1] << endl; + cout << boolalpha << got << " " << expected << endl; + cerr << "error" << FAIL; + } + queries++; + } + cerr << "tested random queries: " << queries << endl; +} + +void stress_test(ll range) { + ll queries = 0; + for (int tries = 0; tries < 100'000; tries++) { + auto centre = Random::point<ll>(-range / 2, range / 2); + int n = Random::integer<int>(3, 30); + + vector<hp> hps1 = {//+cpalgo bounding box + {pt( 1e9, 1e9), pt(-1e9, 1e9)}, + {pt(-1e9, 1e9), pt(-1e9, -1e9)}, + {pt(-1e9, -1e9), pt( 1e9, -1e9)}, + {pt( 1e9, -1e9), pt( 1e9, 1e9)}, + }; + + vector<cpalgo::Halfplane> hps2; + for (int i = 0; i < n; i++) { + auto [a, b] = Random::line(range); + if (cross(a, b, centre) < 0) swap(a, b); + hps1.emplace_back(a, b); + hps2.emplace_back(a, b); + } + + auto expected = cpalgo::hp_intersect(hps2); + auto gotHp = intersect(hps1); + if (sz(gotHp) == 1) cerr << "WHAT?" << FAIL; + for (hp h : gotHp) { + if (h.dummy()) cerr << "DUMMY!" << FAIL;//we added a bounding box... + } + vector<cpalgo::Point> got; + if (!gotHp.empty()) { + gotHp.push_back(gotHp[0]); + for (int i = 0; i + 1 < sz(gotHp); i++) { + got.push_back(inter(cpalgo::Halfplane(gotHp[i]), cpalgo::Halfplane(gotHp[i + 1]))); + } + } + + bool eq = sz(got) == sz(expected); + for (ll i = 0; eq && i < sz(got); i++) { + eq &= float_error(got[i].x, expected[i].x) < 1e-6; + eq &= float_error(got[i].y, expected[i].y) < 1e-6; + } + + if (!eq) { + cerr << tries << endl; + cerr << setprecision(20) << endl; + for (auto tmp : hps2) cerr << tmp << endl; + cerr << endl; + for (auto tmp : expected) cerr << tmp << endl; + cerr << endl; + for (auto tmp : got) cerr << tmp << endl; + cerr << FAIL; + } + queries += n; + } + cerr << "tested random queries: " << queries << endl; +} + +/*constexpr int N = 1'000'000; +void performance_test() { + timer t; + hash_t hash = 0; + double maxTime = 0; + + vector<pt> ps; + for (int i = 0; i*i <= N; i++) { + for (int j = 0; j*j <= N; j++) { + ps.emplace_back(i, j); + } + } + t.start(); + hash = shortestDist(ps); + t.stop(); + maxTime = max(maxTime, t.time); + + ps = Random::points<ll>(N, -1'000'000'000, 1'000'000'000); + t.reset(); + t.start(); + hash += shortestDist(ps); + t.stop(); + maxTime = max(maxTime, t.time); + + if (maxTime > 500) cerr << "too slow: " << maxTime << FAIL; + cerr << "tested performance: " << maxTime << "ms (hash: " << hash << ")" << endl; +}*/ + +int main() { + test_check(10); + test_check(100); + stress_test(10); + stress_test(100); + //performance_test(); +} diff --git a/test/geometry/lines.cpp b/test/geometry/lines.cpp new file mode 100644 index 0000000..7b1b99a --- /dev/null +++ b/test/geometry/lines.cpp @@ -0,0 +1,107 @@ +#include "../util.h" +constexpr double EPS = 1e-6; +#define ll double +double gcd(double x, double /**/) {return x;} //hacky +#include <geometry/formulas.cpp> +#undef ll +#include <geometry/linesAndSegments.cpp> +#include <geometry/lines.cpp> + +#include "../geometry.h" + +void stress_pointsToLine(ll range) { + ll queries = 0; + for (int tries = 0; tries < 100'000; tries++) { + auto [a, b] = Random::line(range); + + line gotA(a, b); + if (real(a) != real(b)) { + gotA.a /= gotA.b; + gotA.c /= gotA.b; + gotA.b /= gotA.b; + } else { + gotA.c /= gotA.a; + gotA.a /= gotA.a; + } + line gotB = pointsToLine(a, b); + + if (!same(gotA, gotB)) cerr << "error" << FAIL; + queries++; + } + cerr << "tested pointsToLine: " << queries << endl; +} + +void stress_same(ll range) { + ll queries = 0; + for (int tries = 0; tries < 100'000; tries++) { + auto [a, b] = Random::line(range); + auto [c, d] = Random::line(range); + + line lAB = pointsToLine(a, b); + line lCD = pointsToLine(c, d); + + auto got = same(lAB, lCD); + auto expected = pointOnLine(a, b, c) && pointOnLine(a, b, d); + + if (got != expected) cerr << "error" << FAIL; + queries++; + } + cerr << "tested same: " << queries << endl; +} + +void stress_parallel(ll range) { + ll queries = 0; + for (int tries = 0; tries < 100'000; tries++) { + auto [a, b] = Random::line(range); + auto [c, d] = Random::line(range); + + line lAB = pointsToLine(a, b); + line lCD = pointsToLine(c, d); + + auto got = parallel(lAB, lCD); + auto expected = cross(b-a, d-c) == 0; + + if (got != expected) cerr << "error" << FAIL; + queries++; + } + cerr << "tested parallel: " << queries << endl; +} + +void stress_intersect(ll range) { + ll queries = 0; + for (int tries = 0; tries < 100'000; tries++) { + auto [a, b] = Random::line(range); + auto [c, d] = Random::line(range); + + line lAB = pointsToLine(a, b); + line lCD = pointsToLine(c, d); + + if (same(lAB, lCD)) continue; + + pt gotPT; + auto got = intersect(lAB, lCD, gotPT); + auto expected = lineIntersection(a, b, c, d); + + if (got != expected) cerr << "error: 1" << FAIL; + if (got) { + pt expectedPt = lineIntersection2(a, b, c, d); + if (float_error(real(gotPT), real(expectedPt)) > 1e-6) cerr << "error: 2" << FAIL; + if (float_error(imag(gotPT), imag(expectedPt)) > 1e-6) cerr << "error: 2" << FAIL; + } + queries++; + } + cerr << "tested intersect: " << queries << endl; +} + +int main() { + stress_pointsToLine(100); + stress_pointsToLine(100'000); + stress_same(10); + stress_same(100); + stress_same(1'000'000'000);//no precision issue since this will alwas be false... + stress_parallel(10); + stress_parallel(100); + stress_parallel(1'000'000'000); + stress_intersect(100); + stress_intersect(1'000'000'000); +} diff --git a/test/geometry/linesAndSegments.cpp b/test/geometry/linesAndSegments.cpp index 2943a67..a2da3ba 100644 --- a/test/geometry/linesAndSegments.cpp +++ b/test/geometry/linesAndSegments.cpp @@ -30,7 +30,7 @@ void stress_lineIntersection(ll range) { auto [c, d] = Random::line(range); if (ccw(a, b, c) == 0 && ccw(a, b, d) == 0) continue; - bool expected = ccw(0, a-b, c-d) == 0; + bool expected = ccw(0, a-b, c-d) != 0; bool got = lineIntersection(a, b, c, d); if (got != expected) cerr << "error" << FAIL; @@ -49,7 +49,7 @@ void stress_lineIntersection2(ll range) { auto got = lineIntersection2(a, b, c, d); if (distToLine(a, b, got) > 1e-6) cerr << "error: 1" << FAIL; - if (distToLine(a, b, got) > 1e-6) cerr << "error: 2" << FAIL; + if (distToLine(c, d, got) > 1e-6) cerr << "error: 2" << FAIL; queries++; } cerr << "tested lineIntersection2: " << queries << endl; @@ -172,7 +172,7 @@ void stress_segmentIntersection2(ll range) { if (!got.empty() != tmp) cerr << "error: 1" << FAIL; for (pt p : got) { if (distToSegment(a, b, p) > 1e-6) cerr << "error: 2" << FAIL; - if (distToSegment(a, b, p) > 1e-6) cerr << "error: 3" << FAIL; + if (distToSegment(c, d, p) > 1e-6) cerr << "error: 3" << FAIL; } if (tmp) { double gotDist = abs(got.front() - got.back()); @@ -220,7 +220,7 @@ int main() { stress_lineIntersection(100); stress_lineIntersection(1'000'000'000); stress_lineIntersection2(100); - stress_lineIntersection2(1'000'000); + stress_lineIntersection2(1'000);//intersection can bet at N^3... stress_distToLine(100); stress_distToLine(1'000'000'000); stress_projectToLine(100); diff --git a/test/geometry/polygon.cpp b/test/geometry/polygon.cpp index 1dd46ca..643ea70 100644 --- a/test/geometry/polygon.cpp +++ b/test/geometry/polygon.cpp @@ -10,7 +10,7 @@ double abs(pt p) { return hypot(real(p), imag(p)); } // Liegt p auf der Strecke a-b? -bool pointOnLineSegment(pt a, pt b, pt p) { +bool pointOnSegment(pt a, pt b, pt p) { if (cross(a, b, p) != 0) return false; auto dist = norm(a - b); return norm(a - p) <= dist && norm(b - p) <= dist; @@ -65,7 +65,7 @@ void test_windingNumber(ll range) { int cur = details::lineSegmentIntersection(p, p + pt(1, 2'000'000'007), ps[j], ps[j+1]); if (ptLess(ps[j], ps[j+1])) expected -= cur; else expected += cur; - onBorder |= pointOnLineSegment(ps[j], ps[j+1], p); + onBorder |= pointOnSegment(ps[j], ps[j+1], p); } if (onBorder) continue; if (area(ps) < 0) expected = -expected; @@ -93,7 +93,7 @@ void test_inside(ll range) { bool onBorder = false; for (int j = 0; j < n; j++) { count += details::lineSegmentIntersection(p, p + pt(1, 2'000'000'007), ps[j], ps[j+1]); - onBorder |= pointOnLineSegment(ps[j], ps[j+1], p); + onBorder |= pointOnSegment(ps[j], ps[j+1], p); } bool expected = (count % 2) && !onBorder; bool got = inside(p, ps); diff --git a/test/geometry/segmentIntersection.cpp b/test/geometry/segmentIntersection.cpp index 9862be5..6d3ddd6 100644 --- a/test/geometry/segmentIntersection.cpp +++ b/test/geometry/segmentIntersection.cpp @@ -14,7 +14,7 @@ bool pointOnLineSegment(pt a, pt b, pt p) { } // Test auf Streckenschnitt zwischen a-b und c-d. -bool lineSegmentIntersection(pt a, pt b, pt c, pt d) { +bool segmentIntersection(pt a, pt b, pt c, pt d) { if (ccw(a, b, c) == 0 && ccw(a, b, d) == 0) return pointOnLineSegment(a,b,c) || pointOnLineSegment(a,b,d) || @@ -42,7 +42,7 @@ vector<seg> randomSegs(int n, ll range) { bool naive(vector<seg>& segs) { for (ll i = 0; i < sz(segs); i++) { for (ll j = 0; j < i; j++) { - if (lineSegmentIntersection(segs[i].a, segs[i].b, segs[j].a, segs[j].b)) return true; + if (segmentIntersection(segs[i].a, segs[i].b, segs[j].a, segs[j].b)) return true; } } return false; @@ -60,7 +60,7 @@ void stress_test(ll range) { if (got != (b >= 0)) cerr << "error: invalid ans" << FAIL; auto expected = naive(segs); if (got != expected) cerr << "error: intersection not found" << FAIL; - if (got && !lineSegmentIntersection(segs[a].a, segs[a].b, segs[b].a, segs[b].b)) cerr << "error: no intersection" << FAIL; + if (got && !segmentIntersection(segs[a].a, segs[a].b, segs[b].a, segs[b].b)) cerr << "error: no intersection" << FAIL; queries += n; intersection += got; notIntersection += !got; diff --git a/test/geometry/spheres.cpp b/test/geometry/spheres.cpp new file mode 100644 index 0000000..16e0ebd --- /dev/null +++ b/test/geometry/spheres.cpp @@ -0,0 +1,28 @@ +#include "../util.h" +constexpr double PI = acos(-1.0); +#pragma GCC diagnostic ignored "-Wshadow" +#include <geometry/spheres.cpp> + +void test_consistent() { + ll queries = 0; + for (int tries = 0; tries < 100'000; tries++) { + auto pLat = Random::real<double>(-180, 180); + auto pLon = Random::real<double>(0, 360); + auto qLat = Random::real<double>(-180, 180); + auto qLon = Random::real<double>(0, 360); + + point p(pLat, pLon); + point q(qLat, qLon); + + auto gotA = gcDist(pLat, pLon, qLat, qLon, 1); + auto gotB = gcDist(p, q); + + if (abs(gotA - gotB) > 1e-6) cerr << "gotA: " << gotA << ", gotB: " << gotB << FAIL; + queries++; + } + cerr << "tested random: " << queries << endl; +} + +int main() { + test_consistent(); +} diff --git a/test/graph/connect.cpp b/test/graph/connect.cpp new file mode 100644 index 0000000..bba8104 --- /dev/null +++ b/test/graph/connect.cpp @@ -0,0 +1,140 @@ +#include "../util.h" +#pragma GCC diagnostic ignored "-Wshadow" +#include "connectMinLCT.h" +constexpr ll INF = 0x3FFF'FFFF; +#include <graph/connect.cpp> + +struct Naive { + vector<multiset<int>> adj; + vector<int> seen; + int counter; + Naive(int n) : adj(n), seen(n), counter(0) {} + + template<typename F> + void dfs(int x, F&& f) { + counter++; + vector<int> todo = {x}; + seen[x] = counter; + while (!todo.empty()) { + x = todo.back(); + todo.pop_back(); + f(x); + for (ll y : adj[x]) { + if (seen[y] != counter) { + seen[y] = counter; + todo.push_back(y); + } + } + } + } + + bool connected(int a, int b) { + bool res = false; + dfs(a, [&](int x){res |= x == b;}); + return res; + } + + void addEdge(int a, int b) { + adj[a].insert(b); + adj[b].insert(a); + } + + void eraseEdge(int a, int b) { + adj[a].erase(adj[a].find(b)); + adj[b].erase(adj[b].find(a)); + } +}; + +void stress_test() { + ll queries = 0; + for (int tries = 0; tries < 2'000; tries++) { + int n = Random::integer<int>(2, 30); + int m = Random::integer<int>(30, 300); + + vector<int> insertOrder(m); + iota(all(insertOrder), 0); + shuffle(all(insertOrder), Random::rng); + vector<pair<int, int>> edges(m, {-1, -1}); + + connect con(n, m); + Naive naive(n); + + int deleted = 0; + for (int i = 0; i < m; i++) { + { + int a = Random::integer<int>(0, n); + int b = a; + while (b == a) b = Random::integer<int>(0, n); + edges[insertOrder[i]] = {a, b}; + + con.addEdge(a, b, insertOrder[i]); + naive.addEdge(a, b); + } + + while (deleted < m && edges[deleted] != pair<int, int>{-1, -1} && Random::integer<int>(2) == 0) { + auto [a, b] = edges[deleted]; + + con.eraseEdge(deleted); + naive.eraseEdge(a, b); + deleted++; + } + + for (int j = 0; j < n; j++) { + int a = Random::integer<int>(0, n); + int b = Random::integer<int>(0, n); + + auto got = con.connected(a, b); + auto expected = naive.connected(a, b); + + if (got != expected) cerr << "error" << FAIL; + } + + queries += n; + } + } + cerr << "tested random queries: " << queries << endl; +} + +constexpr int N = 100'000; +constexpr int M = 500'000; +void performance_test() { + timer t; + t.start(); + connect con(N, M); + t.stop(); + + vector<int> insertOrder(M); + iota(all(insertOrder), 0); + shuffle(all(insertOrder), Random::rng); + vector<bool> inserted(M); + + for (int i = 0, j = 0; i < N; i++) { + int a = Random::integer<int>(0, N); + int b = a; + while (b == a) b = Random::integer<int>(0, N); + + t.start(); + con.addEdge(a, b, insertOrder[i]); + t.stop(); + inserted[i] = true; + + while (j < M && inserted[j] && Random::integer<int>(2) == 0) { + t.start(); + con.eraseEdge(j); + t.stop(); + } + } + hash_t hash = 0; + for (int i = 1; i < N; i++) { + t.start(); + hash += con.connected(i - 1, i); + t.stop(); + } + if (t.time > 1000) cerr << "too slow: " << t.time << FAIL; + cerr << "tested performance: " << t.time << "ms (hash: " << hash << ")" << endl; +} + +int main() { + stress_test(); + performance_test(); +} diff --git a/test/graph/connectMinLCT.h b/test/graph/connectMinLCT.h new file mode 100644 index 0000000..4d509f7 --- /dev/null +++ b/test/graph/connectMinLCT.h @@ -0,0 +1,173 @@ +constexpr ll queryDefault = 0x3FFF'FFFF; +constexpr ll updateDefault = 0; +//modifiable: +ll _modify(ll x, ll y) { + return min(x, y); +} +ll _query(ll x, ll y) { + return min(x, y); +} +ll _update(ll delta, int /*length*/) { + return delta; +} + +//generic: +ll joinValueDelta(ll value, ll delta) { + if (delta == updateDefault) return value; + return _modify(value, delta); +} + +ll joinDeltas(ll delta1, ll delta2) { + if (delta1 == updateDefault) return delta2; + if (delta2 == updateDefault) return delta1; + return _modify(delta1, delta2); +} + +struct LCT { + struct Node { + ll nodeValue, subTreeValue, delta; + bool revert; + int id, size; + Node *left, *right, *parent; + + Node(int id = 0, int val = queryDefault) : + nodeValue(val), subTreeValue(val), delta(updateDefault), + revert(false), id(id), size(1), + left(nullptr), right(nullptr), parent(nullptr) {} + + bool isRoot() { + return !parent || (parent->left != this && + parent->right != this); + } + + void push() { + if (revert) { + revert = false; + swap(left, right); + if (left) left->revert ^= 1; + if (right) right->revert ^= 1; + } + nodeValue = joinValueDelta(nodeValue, delta); + subTreeValue = joinValueDelta(subTreeValue, + _update(delta, size)); + if (left) left->delta = joinDeltas(left->delta, delta); + if (right) right->delta = joinDeltas(right->delta, delta); + delta = updateDefault; + } + + ll getSubtreeValue() { + return joinValueDelta(subTreeValue, _update(delta, size)); + } + + void update() { + subTreeValue = joinValueDelta(nodeValue, delta); + size = 1; + if (left) { + subTreeValue = _query(subTreeValue, + left->getSubtreeValue()); + size += left->size; + } + if (right) { + subTreeValue = _query(subTreeValue, + right->getSubtreeValue()); + size += right->size; + }} + }; + + vector<Node> nodes; + + LCT(int n) : nodes(n) { + for (int i = 0; i < n; i++) nodes[i].id = i; + } + + void connect(Node* ch, Node* p, int isLeftChild) { + if (ch) ch->parent = p; + if (isLeftChild >= 0) { + if (isLeftChild) p->left = ch; + else p->right = ch; + }} + + void rotate(Node* x) { + Node* p = x->parent; + Node* g = p->parent; + bool isRootP = p->isRoot(); + bool leftChildX = (x == p->left); + + connect(leftChildX ? x->right : x->left, p, leftChildX); + connect(p, x, !leftChildX); + connect(x, g, isRootP ? -1 : p == g->left); + p->update(); + } + + void splay(Node* x) { + while (!x->isRoot()) { + Node* p = x->parent; + Node* g = p->parent; + if (!p->isRoot()) g->push(); + p->push(); + x->push(); + if (!p->isRoot()) rotate((x == p->left) == + (p == g->left) ? p : x); + rotate(x); + } + x->push(); + x->update(); + } + + Node* expose(Node* x) { + Node* last = nullptr; + for (Node* y = x; y; y = y->parent) { + splay(y); + y->left = last; + last = y; + } + splay(x); + return last; + } + + void makeRoot(Node* x) { + expose(x); + x->revert ^= 1; + } + + bool connected(Node* x, Node* y) { + if (x == y) return true; + expose(x); + expose(y); + return x->parent; + } + + void link(Node* x, Node* y) { + assert(!connected(x, y)); // not yet connected! + makeRoot(x); + x->parent = y; + } + + void cut(Node* x, Node* y) { + makeRoot(x); + expose(y); + //must be a tree edge! + assert(!(y->right != x || x->left != nullptr)); + y->right->parent = nullptr; + y->right = nullptr; + } + + Node* lca(Node* x, Node* y) { + assert(connected(x, y)); + expose(x); + return expose(y); + } + + ll query(Node* from, Node* to) { + makeRoot(from); + expose(to); + if (to) return to->getSubtreeValue(); + return queryDefault; + } + + void modify(Node* from, Node* to, ll delta) { + makeRoot(from); + expose(to); + to->delta = joinDeltas(to->delta, delta); + } +}; diff --git a/test/graph/dinic.cpp b/test/graph/dinic.cpp new file mode 100644 index 0000000..5af7c6f --- /dev/null +++ b/test/graph/dinic.cpp @@ -0,0 +1,62 @@ +#include "../util.h" +constexpr ll INF = LL::INF; +namespace dinic { +#include <graph/dinic.cpp> +} + +namespace pushRelabel { +#include <graph/pushRelabel.cpp> +} + +void stress_test() { + ll queries = 0; + for (int tries = 0; tries < 20'000; tries++) { + int n = Random::integer<int>(2, 30); + int m = Random::integer<int>(n-1, max<int>(n, min<int>(500, n*(n-1) / 2 + 1))); + + dinic::adj.assign(n, {}); + pushRelabel::adj.assign(n, {}); + + Graph<NoData, true> g(n); + g.erdosRenyi(m); + g.forEdges([](int a, int b){ + ll w = Random::integer<ll>(1, 1'000'000'000'000ll); + dinic::addEdge(a, b, w); + pushRelabel::addEdge(a, b, w); + }); + + ll got = dinic::maxFlow(0, n - 1); + ll expected = pushRelabel::maxFlow(0, n - 1); + + if (got != expected) cerr << "got: " << got << ", expected: " << expected << FAIL; + queries += n; + } + cerr << "tested random queries: " << queries << endl; +} + +constexpr int N = 50000; +constexpr int M = 200000; +void performance_test() { + using namespace dinic; + timer t; + Graph<NoData> g(N); + g.erdosRenyi(M); + adj.assign(N, {}); + g.forEdges([](int a, int b){ + ll w1 = Random::integer<ll>(1, 1'000'000'000'000ll); + ll w2 = Random::integer<ll>(1, 1'000'000'000'000ll); + addEdge(a, b, w1); + addEdge(b, a, w2); + }); + + t.start(); + hash_t hash = maxFlow(0, N - 1); + t.stop(); + if (t.time > 2000) cerr << "too slow: " << t.time << FAIL; + cerr << "tested performance: " << t.time << "ms (hash: " << hash << ")" << endl; +} + +int main() { + stress_test(); + performance_test(); +} diff --git a/test/graph/hld.cpp b/test/graph/hld.cpp new file mode 100644 index 0000000..bcd9c8c --- /dev/null +++ b/test/graph/hld.cpp @@ -0,0 +1,83 @@ +#include "../util.h" +#include <graph/hld.cpp> + +struct Seg { // very real segment tree + vector<int> a; + + Seg(int n) : a(n) {} + + void inc(int l, int r) { + for (int i=l; i<r; i++) a[i]++; + } +}; + +void stress_test() { + for (int tries = 0; tries < 100'000; tries++) { + int n = Random::integer<int>(1, 50); + Graph<NoData> g(n); + g.tree(); + + adj.assign(n, {}); + g.forEdges([&](int a, int b){ + adj[a].push_back(b); + adj[b].push_back(a); + }); + + init(Random::integer(0, n)); + + vector<int> a(n); + auto dfs = [&](auto& self, int u, int p, int t) { + if (u == t) { + a[u]++; + return true; + } + for (int v : adj[u]) if (v != p) { + if (self(self, v, u, t)) { + a[u]++; + return true; + } + } + return false; + }; + + Seg seg(n); + + int Q = Random::integer(1, 50); + for (int q=0; q<Q; q++) { + int u = Random::integer(0, n), v = Random::integer(0, n); + for_intervals(u, v, [&](int l, int r) { seg.inc(l, r); }); + dfs(dfs, u, -1, v); + } + for (int i=0; i<n; i++) { + if (seg.a[in[i]] != a[i]) cerr << "WA: expected " << a[i] << " got " << seg.a[in[i]] << FAIL; + } + } + cerr << "tested random tests: " << 100'000 << endl; +} + +constexpr int N = 1'000'000; +void performance_test() { + timer t; + Graph<NoData> g(N); + g.tree(); + adj.assign(N, {}); + g.forEdges([&](int a, int b){ + adj[a].push_back(b); + adj[b].push_back(a); + }); + vector<pair<int, int>> qu(N); + for (auto& [x, y] : qu) x = Random::integer(0, N), y = Random::integer(0, N); + + ll hash = 0; + t.start(); + init(0); + for (auto [x, y] : qu) for_intervals(x, y, [&](int l, int r){ hash += r-l; }); + t.stop(); + if (t.time > 1000) cerr << "too slow: " << t.time << FAIL; + cerr << "tested performance: " << t.time << "ms (hash: " << hash << ")" << endl; +} + +int main() { + stress_test(); + performance_test(); +} diff --git a/test/graph/reroot.cpp b/test/graph/reroot.cpp new file mode 100644 index 0000000..d5043b4 --- /dev/null +++ b/test/graph/reroot.cpp @@ -0,0 +1,59 @@ +#include "../util.h" +#include <graph/reroot.cpp> + +void stress_test() { + for (int tries = 0; tries < 50'000; tries++) { + int n = Random::integer<int>(1, 50); + Graph<NoData> g(n); + g.tree(); + + adj.assign(n, {}); + g.forEdges([&](int a, int b){ + adj[a].emplace_back(b, Random::integer(0, 10)); + adj[b].emplace_back(a, Random::integer(0, 10)); + }); + + Reroot re; + auto ans = re.solve(); + + auto dfs = [&](auto& self, int u, int p) -> ll { + ll val = 0; + for (auto [v, w] : adj[u]) if (v != p) { + val ^= ((v ^ u) + self(self, v, u)) * w % MOD; + } + return u ^ val; + }; + for (int i=0; i<n; i++) { + if (ans[i] != dfs(dfs, i, -1)) { + cerr << "WA expected " << dfs(dfs, i, -1) << " got " << ans[i] << FAIL; + } + } + } + cerr << "tested random 50'000 tests" << endl; +} + +constexpr int N = 1'000'000; +void performance_test() { + timer t; + Graph<NoData> g(N); + g.tree(); + adj.assign(N, {}); + g.forEdges([&](int a, int b){ + adj[a].emplace_back(b, Random::integer(0, (int)1e9)); + adj[b].emplace_back(a, Random::integer(0, (int)1e9)); + }); + + ll hash = 0; + t.start(); + Reroot re; + auto ans = re.solve(); + hash = accumulate(all(ans), 0LL); + t.stop(); + if (t.time > 1000) cerr << "too slow: " << t.time << FAIL; + cerr << "tested performance: " << t.time << "ms (hash: " << hash << ")" << endl; +} + +int main() { + stress_test(); + performance_test(); +} diff --git a/test/graph/reroot.cpp.awk b/test/graph/reroot.cpp.awk new file mode 100644 index 0000000..37ce8c3 --- /dev/null +++ b/test/graph/reroot.cpp.awk @@ -0,0 +1,7 @@ +BEGIN { print "constexpr ll MOD = 1e9 + 7;" } +{ + sub("W w, T x) {\\}", "W w, T x) { return ((v ^ c) + x) * w % MOD; }") + sub("T x, T y) {\\}", "T x, T y) { return x ^ y; }") + sub("int v, T x) {\\}", "int v, T x) { return v ^ x; }") +} +{ print } diff --git a/test/graph/scc.cpp b/test/graph/scc.cpp index 123050f..9ab7051 100644 --- a/test/graph/scc.cpp +++ b/test/graph/scc.cpp @@ -16,18 +16,6 @@ void stress_test() { }); scc(); - vector<bool> tmp(n); - for (int i = 0; i < sz(sccs); i++) { - for (int x : sccs[i]) { - if (tmp[x]) cerr << "error: duclicate" << FAIL; - if (idx[x] != i) cerr << "error: inconsistent" << FAIL; - tmp[x] = true; - } - } - for (int i = 0; i < n; i++) { - if (!tmp[i]) cerr << "error: missing" << FAIL; - } - init(n); vector<ll> seen(n); int tmpCounter = 0; diff --git a/test/graph/virtualTree.cpp b/test/graph/virtualTree.cpp new file mode 100644 index 0000000..d256760 --- /dev/null +++ b/test/graph/virtualTree.cpp @@ -0,0 +1,95 @@ +#include "../util.h" +int lca(int u, int v); +#include <graph/virtualTree.cpp> + +vector<int> d, par; +void dfs(int u, vector<vector<int>>& adj, int& counter) { + in[u] = counter++; + for (int v : adj[u]) if (v != par[u]) { + d[v] = d[u]+1; + par[v] = u; + dfs(v, adj, counter); + } + out[u] = counter; +} + +int lca(int u, int v) { + if (d[u] < d[v]) swap(u, v); + while (d[u] > d[v]) u = par[u]; + while (u != v) u = par[u], v = par[v]; + return u; +} + +void init(vector<vector<int>>& adj) { + int n = (int)sz(adj); + d.assign(n, 0); + in = par = out = d; + int counter = 0; + dfs(0, adj, counter); +} + +void stress_test() { + for (int tries = 0; tries < 50'000; tries++) { + int n = Random::integer<int>(1, 50); + Graph<NoData> g(n); + g.tree(); + + vector<vector<int>> adj(n); + g.forEdges([&](int a, int b){ + adj[a].push_back(b); + adj[b].push_back(a); + }); + + init(adj); + vector<int> ind = Random::distinct(Random::integer(1, n+1), 0, n); + auto [idk, tree] = virtualTree(ind); + vector<pair<int, int>> edges; + for (int i=0; i<sz(idk); i++) for (int v : tree[i]) { + edges.emplace_back(idk[i], idk[v]); + } + + vector<pair<int, int>> edges2; + vector<bool> used(n); + for (int u : ind) for (int v : ind) used[lca(u, v)] = true; + auto dfs = [&](auto& self, int u, int p, int last) -> void { + if (used[u]) { + if (last != -1) edges2.emplace_back(last, u); + last = u; + } + for (int v : adj[u]) if (v != p) self(self, v, u, last); + }; + dfs(dfs, 0, -1, -1); + + sort(all(edges)), sort(all(edges2)); + if (edges != edges2) cerr << "WA edge list does not match" << FAIL; + } + cerr << "tested random 50'000 tests" << endl; +} + +constexpr int N = 1'000'000; +void performance_test() { + timer t; + Graph<NoData> g(N); + g.tree(); + vector<vector<int>> adj(N); + g.forEdges([&](int a, int b){ + adj[a].push_back(b); + adj[b].push_back(a); + }); + + init(adj); + vector<int> ind = Random::distinct(N/2, 0, N); + + ll hash = 0; + t.start(); + auto [idk, tree] = virtualTree(ind); + hash = accumulate(all(idk), 0LL); + t.stop(); + if (t.time > 1000) cerr << "too slow: " << t.time << FAIL; + cerr << "tested performance: " << t.time << "ms (hash: " << hash << ")" << endl; +} + +int main() { + stress_test(); + performance_test(); +} diff --git a/test/graph/virtualTree.cpp.awk b/test/graph/virtualTree.cpp.awk new file mode 100644 index 0000000..fe4bc62 --- /dev/null +++ b/test/graph/virtualTree.cpp.awk @@ -0,0 +1,7 @@ +/\/\/ v/ { + print "return {ind, tree};" +} +{ + sub("void", "pair<vector<int>, vector<vector<int>>>") +} +{ print } diff --git a/test/math/divSum.cpp b/test/math/divSum.cpp new file mode 100644 index 0000000..1f82387 --- /dev/null +++ b/test/math/divSum.cpp @@ -0,0 +1,48 @@ +#include "../util.h" +#include <math/divSum.cpp> + +ll naive(ll n, ll m, ll a, ll b){ + ll ans = 0; + for(ll i = 0; i < n; i++){ + ans += (a*i+b)/m; + } + return ans; +} + +void stress_test() { + ll queries = 0; + for (ll i = 0; i < 10'000; i++) { + int n = Random::integer<int>(1, 100); + int m = Random::integer<int>(1, 100); + int a = Random::integer<int>(0, 100); + int b = Random::integer<int>(0, 100); + ll expected = naive(n, m, a, b); + ll got = divSum(n, m, a, b); + if (got != expected) cerr << "got: " << got << ", expected: " << expected << FAIL; + queries++; + } + cerr << "tested queries: " << queries << endl; +} + +constexpr int N = 1'000'000; +void performance_test() { + timer t; + hash_t hash = 0; + for (int operations = 0; operations < N; operations++) { + ll n = Random::integer<ll>(1, 1'000'000'000); + ll m = Random::integer<ll>(1, 1'000'000'000); + ll a = Random::integer<ll>(0, 1'000'000'000); + ll b = Random::integer<ll>(0, 1'000'000'000); + t.start(); + hash += divSum(n, m, a, b); + t.stop(); + } + if (t.time > 750) cerr << "too slow: " << t.time << FAIL; + cerr << "tested performance: " << t.time << "ms (hash: " << hash << ")" << endl; +} + +int main() { + stress_test(); + performance_test(); +} + diff --git a/test/math/gauss.cpp b/test/math/gauss.cpp index 37bacce..6e4759d 100644 --- a/test/math/gauss.cpp +++ b/test/math/gauss.cpp @@ -14,7 +14,7 @@ vector<vector<double>> inverseMat(const vector<vector<double>>& m) { mat[i].resize(2*n); mat[i][n+i] = 1; } - gauss(n);//the unique cetc. checks are not usefull since we dont solve an lgs... + gauss(n); //the unique cetc. checks are not usefull since we dont solve an lgs... vector<vector<double>> res(m); for (int i = 0; i < n; i++) { res[i] = vector<double>(mat[i].begin() + n, mat[i].end()); diff --git a/test/math/inversionsMerge.cpp b/test/math/inversionsMerge.cpp index 85ab0d2..acdc555 100644 --- a/test/math/inversionsMerge.cpp +++ b/test/math/inversionsMerge.cpp @@ -16,7 +16,7 @@ void stress_test() { for (ll i = 0; i < 100'000; i++) { int n = Random::integer<int>(1, 100); vector<ll> v(n); - for (ll j = 0; j < n; j++) v[j] = (j-10) * 100000 + Random::integer<ll>(0, 10000);//values must be unique ): + for (ll j = 0; j < n; j++) v[j] = (j-10) * 100000 + Random::integer<ll>(0, 10000); //values must be unique ): shuffle(all(v), Random::rng); ll expected = naive(v); ll got = mergeSort(v); diff --git a/test/math/linearRecurrence.cpp b/test/math/linearRecurrence.cpp index 21a8a7c..8640980 100644 --- a/test/math/linearRecurrence.cpp +++ b/test/math/linearRecurrence.cpp @@ -1,6 +1,11 @@ #include "../util.h" +vector<ll> mul(const vector<ll>& a, const vector<ll>& b); #include <math/linearRecurrence.cpp> +vector<ll> mul(const vector<ll>& a, const vector<ll>& b) { + return mulSlow(a, b); +} + struct RandomRecurence { vector<ll> f, c, cache; RandomRecurence(int n) : f(Random::integers<ll>(n, 0, mod)), c(Random::integers<ll>(n, 0, mod)), cache(f) {} diff --git a/test/math/linearRecurrence.cpp.awk b/test/math/linearRecurrence.cpp.awk new file mode 100644 index 0000000..902fd4b --- /dev/null +++ b/test/math/linearRecurrence.cpp.awk @@ -0,0 +1,4 @@ +/vector<ll> mul/ { + sub(/mul/, "mulSlow") +} +{ print } diff --git a/test/math/linearRecurrenceNTT.cpp b/test/math/linearRecurrenceNTT.cpp new file mode 100644 index 0000000..e03c27e --- /dev/null +++ b/test/math/linearRecurrenceNTT.cpp @@ -0,0 +1,60 @@ +#include "../util.h" +#include <math/modPowIterativ.cpp> +#include <math/transforms/ntt.cpp> +#include <math/transforms/multiplyNTT.cpp> +#define mod mod2 +#include <math/linearRecurrence.cpp> +#undef mod +static_assert(mod == mod2); + +struct RandomRecurence { + vector<ll> f, c, cache; + RandomRecurence(int n) : f(Random::integers<ll>(n, 0, mod)), c(Random::integers<ll>(n, 0, mod)), cache(f) {} + + ll operator()(ll k){ + while (sz(cache) <= k) { + ll cur = 0; + for (ll i = 0; i < sz(c); i++) { + cur += (c[i] * cache[sz(cache) - i - 1]) % mod; + } + cur %= mod; + cache.push_back(cur); + } + return cache[k]; + } +}; + +void stress_test() { + int queries = 0; + for (int i = 0; i < 1'000; i++) { + int n = Random::integer<int>(1, 10); + RandomRecurence f(n); + for (int j = 0; j < 100; j++) { + ll k = Random::integer<ll>(0, 1000); + + ll got = kthTerm(f.f, f.c, k); + ll expected = f(k); + + if (got != expected) cerr << "got: " << got << ", expected: " << expected << FAIL; + queries++; + } + } + cerr << "tested random queries: " << queries << endl; +} + +constexpr int N = 100'000; +void performance_test() { + timer t; + RandomRecurence f(N); + t.start(); + hash_t hash = kthTerm(f.f, f.c, 1e18); + t.stop(); + if (t.time > 8000) cerr << "too slow: " << t.time << FAIL; + cerr << "tested performance: " << t.time << "ms (hash: " << hash << ")" << endl; +} + +int main() { + stress_test(); + performance_test(); +} + diff --git a/test/math/linearRecurrenceOld.cpp b/test/math/linearRecurrenceOld.cpp new file mode 100644 index 0000000..dab2256 --- /dev/null +++ b/test/math/linearRecurrenceOld.cpp @@ -0,0 +1,54 @@ +#include "../util.h" +#include <math/linearRecurrenceOld.cpp> + +struct RandomRecurence { + vector<ll> f, c, cache; + RandomRecurence(int n) : f(Random::integers<ll>(n, 0, mod)), c(Random::integers<ll>(n, 0, mod)), cache(f) {} + + ll operator()(ll k){ + while (sz(cache) <= k) { + ll cur = 0; + for (ll i = 0; i < sz(c); i++) { + cur += (c[i] * cache[sz(cache) - i - 1]) % mod; + } + cur %= mod; + cache.push_back(cur); + } + return cache[k]; + } +}; + +void stress_test() { + int queries = 0; + for (int i = 0; i < 10'000; i++) { + int n = Random::integer<int>(1, 10); + RandomRecurence f(n); + for (int j = 0; j < 100; j++) { + ll k = Random::integer<ll>(0, 1000); + + ll got = kthTerm(f.f, f.c, k); + ll expected = f(k); + + if (got != expected) cerr << "got: " << got << ", expected: " << expected << FAIL; + queries++; + } + } + cerr << "tested random queries: " << queries << endl; +} + +constexpr int N = 1'000; +void performance_test() { + timer t; + RandomRecurence f(N); + t.start(); + hash_t hash = kthTerm(f.f, f.c, 1e18); + t.stop(); + if (t.time > 500) cerr << "too slow: " << t.time << FAIL; + cerr << "tested performance: " << t.time << "ms (hash: " << hash << ")" << endl; +} + +int main() { + stress_test(); + performance_test(); +} + diff --git a/test/math/minMod.cpp b/test/math/minMod.cpp new file mode 100644 index 0000000..e49da11 --- /dev/null +++ b/test/math/minMod.cpp @@ -0,0 +1,92 @@ +#include "../util.h" +#include <math/shortModInv.cpp> +#include <math/minMod.cpp> + +ll naiveMinMod(ll n, ll m, ll a, ll b){ + ll ans = m; + for(ll i = 0; i < n; i++){ + ans = min(ans, (a*i+b)%m); + } + return ans; +} + +ll naiveFirstVal(ll a, ll m, ll l, ll r){ + for(ll i = 0; i < m; i++){ + ll v = a*i % m; + if(l <= v && v <= r) return v; + } + return -1; +} + +void stress_test_minMod() { + ll queries = 0; + for (ll i = 0; i < 10'000; i++) { + int n = Random::integer<int>(1, 100); + int m = Random::integer<int>(1, 100); + int a = Random::integer<int>(0, m); + int b = Random::integer<int>(0, m); + ll expected = naiveMinMod(n, m, a, b); + ll got = minMod(n, m, a, b); + if (got != expected) cerr << "got: " << got << ", expected: " << expected << FAIL; + queries++; + } + cerr << "tested queries: " << queries << endl; +} + +void stress_test_firstVal() { + ll queries = 0; + for (ll i = 0; i < 10'000; i++) { + int m = Random::integer<int>(1, 100); + int a = Random::integer<int>(0, m); + int l = Random::integer<int>(0, m); + int r = Random::integer<int>(0, m); + if(l > r) swap(l, r); + ll expected = naiveFirstVal(a, m, l, r); + ll got = firstVal(a, m, l, r); + if (got != expected) cerr << a << " " << m << " " << l << " " << r << "got: " << got << ", expected: " << expected << FAIL; + queries++; + } + cerr << "tested queries: " << queries << endl; +} + +constexpr int N = 1'000'000; +void performance_test_minMod() { + timer t; + hash_t hash = 0; + for (int operations = 0; operations < N; operations++) { + ll n = Random::integer<ll>(1, 1'000'000'000); + ll m = Random::integer<ll>(1, 1'000'000'000); + ll a = Random::integer<ll>(0, m); + ll b = Random::integer<ll>(0, m); + t.start(); + hash += minMod(n, m, a, b); + t.stop(); + } + if (t.time > 750) cerr << "too slow: " << t.time << FAIL; + cerr << "tested performance: " << t.time << "ms (hash: " << hash << ")" << endl; +} + +void performance_test_firstVal() { + timer t; + hash_t hash = 0; + for (int operations = 0; operations < N; operations++) { + ll m = Random::integer<ll>(1, 1'000'000'000); + ll a = Random::integer<ll>(1, m); + ll l = Random::integer<ll>(0, m); + ll r = Random::integer<ll>(0, m); + if(l > r) swap(l, r); + t.start(); + hash += firstVal(a, m, l, r); + t.stop(); + } + if (t.time > 750) cerr << "too slow: " << t.time << FAIL; + cerr << "tested performance: " << t.time << "ms (hash: " << hash << ")" << endl; +} + +int main() { + stress_test_minMod(); + stress_test_firstVal(); + performance_test_minMod(); + performance_test_firstVal(); +} + diff --git a/test/math/polynomial.cpp b/test/math/polynomial.cpp new file mode 100644 index 0000000..f4a9486 --- /dev/null +++ b/test/math/polynomial.cpp @@ -0,0 +1,153 @@ +#include "../util.h" +#include <math/shortModInv.cpp> +constexpr ll mod = 1'394'633'899; +#include <math/polynomial.cpp> + +poly randomPoly(int deg) { + poly p; + p.data = Random::integers<ll>(deg + 1, 0, mod); + return p; +} + +ll eval(const vector<ll>& p, ll x) { + ll res = 0; + for (ll i = 0, j = 1; i < sz(p); i++, j = (j * x) % mod) { + res += j * p[i]; + res %= mod; + } + return res; +} + +void test_eval() { + int queries = 0; + for (int tries = 0; tries < 100'000; tries++) { + int deg = Random::integer<int>(1, 30); + vector<ll> tmp = Random::integers<ll>(deg + 1, 0, mod); + poly p(deg); + for (int i = 0; i <= deg; i++) p[i] = tmp[i]; + + for (int i = 0; i <= deg + 7; i++) { + ll x = Random::integer<ll>(0, mod); + + ll got = p(x); + ll expected = eval(tmp, x); + + if (got != expected) cerr << "got: " << got << ", expected: " << expected << FAIL; + } + queries += deg + 1; + } + cerr << "tested eval: " << queries << endl; +} + +void test_add() { + int queries = 0; + for (int tries = 0; tries < 100'000; tries++) { + int n = Random::integer<int>(1, 30); + int m = Random::integer<int>(1, 30); + auto a = randomPoly(n); + auto b = randomPoly(m); + + auto c = a; + c += b; + + if (sz(c) > sz(a) && sz(c) > sz(b)) cerr << "error: wrong degree" << FAIL; + + for (int i = 0; i <= n + m + 7; i++) { + ll x = Random::integer<ll>(0, mod); + + ll got = c(x); + ll expected = (a(x) + b(x)) % mod; + + if (got != expected) cerr << "got: " << got << ", expected: " << expected << FAIL; + } + queries += n + m; + } + cerr << "tested add: " << queries << endl; +} + +void test_mul() { + int queries = 0; + for (int tries = 0; tries < 100'000; tries++) { + int n = Random::integer<int>(1, 30); + int m = Random::integer<int>(1, 30); + auto a = randomPoly(n); + auto b = randomPoly(m); + + auto c = a * b; + if (sz(c) > sz(a) + sz(b) - 1) cerr << "error: wrong degree" << FAIL; + + for (int i = 0; i <= n + m + 7; i++) { + ll x = Random::integer<ll>(0, mod); + + ll got = c(x); + ll expected = (a(x) * b(x)) % mod; + + if (got != expected) cerr << "got: " << got << ", expected: " << expected << FAIL; + } + queries += n + m; + } + cerr << "tested mul: " << queries << endl; +} + +void test_shift() { + int queries = 0; + for (int tries = 0; tries < 100'000; tries++) { + int n = Random::integer<int>(1, 30); + int m = Random::integer<int>(1, 30); + auto a = randomPoly(n); + + auto b = a << m; + if (sz(b) > sz(a)) cerr << sz(a) << " " << sz(b) << endl; + if (sz(b) > sz(a)) cerr << "error: wrong degree" << FAIL; + + for (int i = 0; i <= n + 7; i++) { + ll x = Random::integer<ll>(0, mod); + + ll got = b(x); + ll expected = a((x + m) % mod); + + if (got != expected) { + for (ll y : b.data) cerr << y << " "; + cerr << endl; + } + if (got != expected) cerr << "got: " << got << ", expected: " << expected << FAIL; + } + queries += n; + } + cerr << "tested shift: " << queries << endl; +} + +void test_divmod() { + int queries = 0; + for (int tries = 0; tries < 100'000; tries++) { + int n = Random::integer<int>(1, 30); + int m = Random::integer<int>(1, 30); + auto a = randomPoly(n); + auto b = randomPoly(m); + + auto [div, rem] = a.divmod(b); + if (sz(rem) > sz(b)) cerr << "error: wrong degree (rem)" << FAIL; + if (sz(div) > 1 + max<ll>(0, sz(a) - sz(b))) cerr << "error: wrong degree (div)" << FAIL; + + for (int i = 0; i <= n + m; i++) { + ll x = Random::integer<ll>(0, mod); + ll d = multInv(b(x), mod); + + ll got = (div(x) + rem(x) * d) % mod; + ll expected = (a(x) * d) % mod; + + if (got != expected) cerr << "got: " << got << ", expected: " << expected << FAIL; + } + queries += n + m; + } + cerr << "tested divmod: " << queries << endl; +} + +int main() { + test_eval(); + test_add(); + test_mul(); + test_shift(); + test_divmod(); +} + diff --git a/test/math/recover.cpp b/test/math/recover.cpp new file mode 100644 index 0000000..6f89e5a --- /dev/null +++ b/test/math/recover.cpp @@ -0,0 +1,44 @@ +#include "../util.h" +#include <math/recover.cpp> +#include <math/shortModInv.cpp> + +void stress_test() { + ll queries = 0; + timer t; + for (int i = 0; i < 500; i++) { + ll p = Random::prime<ll>(10000); + for (ll j = 0; 2*j*j < p; j++) { + for (ll b = 1; 2*b*b < p; b++) { + if (gcd(j, b) != 1) continue; + for (ll a : {-j, j}) { + ll c = a * multInv(b, p); + + t.start(); + auto [x, y] = recover(c, p); + t.stop(); + + if (a != x || b != y) cerr << "got: " << x << "/" << y << ", expected: " << a << "/" << b << FAIL; + queries++; + } + } + } + for (ll c = 0; c < p; c++) { + t.start(); + auto [x, y] = recover(c, p); + t.stop(); + + if (y < 0) continue; + if (y == 0) cerr << "error: y=0" << FAIL; + ll got = (((x * multInv(y, p)) % p) + p) % p; + if (got != c) cerr << "got: " << got << ", expected: " << c << FAIL; + queries++; + } + } + cerr << "tested random queries: " << queries << endl; + if (t.time > 500) cerr << "too slow: " << t.time << FAIL; + cerr << "tested performance: " << t.time << "ms" << endl; +} + +int main() { + stress_test(); +} diff --git a/test/math/rho.cpp b/test/math/rho.cpp index 5e4792a..941524b 100644 --- a/test/math/rho.cpp +++ b/test/math/rho.cpp @@ -96,17 +96,25 @@ void stress_test() { cerr << "stress tested: " << t.time << "ms" << endl; } -constexpr int N = 2'000; +ll randomHard(ll lim) { + ll root2 = sqrt(lim); + ll root3 = cbrt(lim); + ll a = Random::prime<ll>(root2 / 2 - root3, root2 / 2 + root3); + ll b = Random::prime<ll>(lim / a - root3, lim / a); + return a * b; +} + +constexpr int N = 200; void performance_test() { timer t; hash_t hash = 0; for (int operations = 0; operations < N; operations++) { - ll x = Random::integer<ll>(1e18 / 2, 1e18); + ll x = randomHard(1e18); t.start(); hash += factor(x).size(); t.stop(); } - if (t.time > 500) cerr << "too slow: " << t.time << FAIL; + if (t.time > 750) cerr << "too slow: " << t.time << FAIL; cerr << "tested performance: " << t.time << "ms (hash: " << hash << ")" << endl; } diff --git a/test/math/transforms/seriesOperations.cpp b/test/math/transforms/seriesOperations.cpp new file mode 100644 index 0000000..ee30e00 --- /dev/null +++ b/test/math/transforms/seriesOperations.cpp @@ -0,0 +1,145 @@ +#include "../../util.h" +#include <math/modPowIterativ.cpp> +#include <math/transforms/ntt.cpp> +#include <math/transforms/multiplyNTT.cpp> +#pragma GCC diagnostic ignored "-Wunused-variable" +#include <math/transforms/seriesOperations.cpp> + +namespace reference {//checked against yosupo + vector<ll> poly_inv(vector<ll> a, int n){ + vector<ll> q = {powMod(a[0], mod-2, mod)}; + for(int len = 1; len < n; len *= 2){ + vector<ll> a2 = a, q2 = q; + a2.resize(2*len), q2.resize(2*len); + ntt(q2); + for(int j = 0; j < 2; j++){ + ntt(a2); + for(int i = 0; i < 2*len; i++) a2[i] = a2[i] * q2[i] % mod; + ntt(a2, true); + for(int i = 0; i < len; i++) a2[i] = 0; + } + for(int i = len; i < min(n, 2*len); i++) q.push_back((mod - a2[i]) % mod); + } + return q; + } + + vector<ll> poly_deriv(vector<ll> a){ + for(int i = 0; i < sz(a)-1; i++) + a[i] = a[i+1] * (i+1) % mod; + a.pop_back(); + return a; + } + + vector<ll> poly_integr(vector<ll> a){ + if(a.empty()) return {0}; + a.push_back(a.back() * powMod(sz(a), mod-2, mod) % mod); + for(int i = sz(a)-2; i > 0; i--) + a[i] = a[i-1] * powMod(i, mod-2, mod) % mod; + a[0] = 0; + return a; + } + + vector<ll> poly_log(vector<ll> a, int n){ + a = mul(poly_deriv(a), poly_inv(a, n)); + a.resize(n-1); + a = poly_integr(a); + return a; + } + + vector<ll> poly_exp(vector<ll> a, int n){ + vector<ll> q = {1}; + for(int len = 1; len < n; len *= 2){ + vector<ll> p = poly_log(q, 2*len); + for(int i = 0; i < 2*len; i++) + p[i] = (mod - p[i] + (i < sz(a) ? a[i] : 0)) % mod; + vector<ll> q2 = q; + q2.resize(2*len); + ntt(p), ntt(q2); + for(int i = 0; i < 2*len; i++) p[i] = p[i] * q2[i] % mod; + ntt(p, true); + for(int i = len; i < min(n, 2*len); i++) q.push_back(p[i]); + } + return q; + } +} + +void test_inv() { + ll queries = 0; + for (ll i = 0; i < 50'000; i++) { + int n = Random::integer<int>(1, 100); + int m = Random::integer<int>(1, 100); + vector<ll> a = Random::integers<ll>(n, 0, mod); + + auto got = poly_inv(a, m); + auto expected = reference::poly_inv(a, m); + if (got != expected) cerr << "error" << FAIL; + queries += n; + } + cerr << "tested inv: " << queries << endl; +} + +void test_deriv() { + ll queries = 0; + for (ll i = 0; i < 50'000; i++) { + int n = Random::integer<int>(1, 100); + vector<ll> a = Random::integers<ll>(n, 0, mod); + + auto got = poly_deriv(a); + auto expected = reference::poly_deriv(a); + if (got != expected) cerr << "error" << FAIL; + queries += n; + } + cerr << "tested deriv: " << queries << endl; +} + +void test_integr() { + ll queries = 0; + for (ll i = 0; i < 50'000; i++) { + int n = Random::integer<int>(1, 100); + vector<ll> a = Random::integers<ll>(n, 0, mod); + + auto got = poly_deriv(a); + auto expected = reference::poly_deriv(a); + if (got != expected) cerr << "error" << FAIL; + queries += n; + } + cerr << "tested integr: " << queries << endl; +} + +void test_log() { + ll queries = 0; + for (ll i = 0; i < 50'000; i++) { + int n = Random::integer<int>(1, 100); + int m = Random::integer<int>(1, 100); + vector<ll> a = Random::integers<ll>(n, 0, mod); + + auto got = poly_log(a, m); + auto expected = reference::poly_log(a, m); + if (got != expected) cerr << "error" << FAIL; + queries += n; + } + cerr << "tested log: " << queries << endl; +} + +void test_exp() { + ll queries = 0; + for (ll i = 0; i < 50'000; i++) { + int n = Random::integer<int>(1, 100); + int m = Random::integer<int>(1, 100); + vector<ll> a = Random::integers<ll>(n, 0, mod); + + auto got = poly_exp(a, m); + auto expected = reference::poly_exp(a, m); + if (got != expected) cerr << "error" << FAIL; + queries += n; + } + cerr << "tested exp: " << queries << endl; +} + +int main() { + test_inv(); + test_deriv(); + test_integr(); + test_log(); + test_exp(); +} diff --git a/test/missing.ignore b/test/missing.ignore index 0f6956f..c5f97bc 100644 --- a/test/missing.ignore +++ b/test/missing.ignore @@ -1,6 +1,4 @@ -datastructures/stlRope.cpp -other/bitOps.cpp -other/pbs.cpp +datastructures/pbds.cpp other/pragmas.cpp other/stuff.cpp other/timed.cpp diff --git a/test/other/bitOps.cpp b/test/other/bitOps.cpp new file mode 100644 index 0000000..44f6297 --- /dev/null +++ b/test/other/bitOps.cpp @@ -0,0 +1,59 @@ +#include "../util.h" +#include <other/bitOps.cpp> + +void test_subsets() { + int queries = 0; + for (int i = 0; i < 1000'000; i++) { + int mask = 0; + int limBits = Random::integer<int>(1, 15); + for (int j = 0; j < limBits; j++) { + mask |= 1 << Random::integer<int>(0, 31); + } + + int expeced = 1 << __builtin_popcount(mask); + int last = -1; + int seen = 1; + subsets(mask, [&](int active){ + if (active <= 0) cerr << "error active: " << active << FAIL; + if (last >= 0 && active >= last) cerr << "error active: " << active << ", last: " << last << FAIL; + last = active; + seen++; + }); + if (expeced != seen) cerr << "got: " << seen << ", expeced: " << expeced << FAIL; + queries++; + } + cerr << "tested subsets queries: " << queries << endl; +} + +ll naive(ll x) { + vector<ll> bits; + for (ll i = 0; i < 64; i++) { + bits.push_back(x & 1); + x >>= 1; + } + reverse(all(bits)); + next_permutation(all(bits)); + reverse(all(bits)); + x = 0; + for (ll i = 0, j = 1; i < 64; i++, j <<= 1) { + if (bits[i] != 0) x |= j; + } + return x; +} + +void test_nextPerm() { + int queries = 0; + for (int i = 0; i < 1000'000; i++) { + ll x = 4;//Random::integer<ll>(1, LL::INF); + ll got = nextPerm(x); + ll expeced = naive(x); + if (got != expeced) cerr << x << ": got: " << got << ", expeced: " << expeced << FAIL; + queries++; + } + cerr << "tested nextPerm queries: " << queries << endl; +} + +int main() { + test_subsets(); + test_nextPerm(); +}
\ No newline at end of file diff --git a/test/other/bitOps.cpp.awk b/test/other/bitOps.cpp.awk new file mode 100644 index 0000000..f1abcfb --- /dev/null +++ b/test/other/bitOps.cpp.awk @@ -0,0 +1,9 @@ +/for \(int subset/ { + print "template<typename F>" + print "void subsets(int bitmask, F&& f) {" +} +/\/\/ Nächste Permutation/ { + print " {f(subset);}" + print "}" +} +{ print } diff --git a/test/other/divideAndConquer.cpp b/test/other/divideAndConquer.cpp index a6fda9d..6d1b444 100644 --- a/test/other/divideAndConquer.cpp +++ b/test/other/divideAndConquer.cpp @@ -1,5 +1,5 @@ #include "../util.h" -constexpr ll inf = LL::INF; +constexpr ll INF = LL::INF; #include <other/divideAndConquer.cpp> vector<vector<ll>> gen(int n) { @@ -43,7 +43,7 @@ vector<vector<ll>> genQuick(int n) { } /*ll naive(int n, int m) { - vector<vector<ll>> state(m+1, vector<ll>(n+1, inf)); + vector<vector<ll>> state(m+1, vector<ll>(n+1, INF)); state[0][0] = 0; for (int i = 1; i <= m; i++) { for (int j = 1; j <= n; j++) { @@ -56,9 +56,9 @@ vector<vector<ll>> genQuick(int n) { }*/ vector<ll> naive(int n) { - vector<vector<ll>> state(n+1, vector<ll>(n+1, inf)); + vector<vector<ll>> state(n+1, vector<ll>(n+1, INF)); state[0][0] = 0; - vector<ll> res(n+1, inf); + vector<ll> res(n+1, INF); for (int i = 1; i <= n; i++) { for (int j = 1; j <= n; j++) { for (int k = 1; k <= j; k++) { diff --git a/test/other/fastSubsetSum.cpp b/test/other/fastSubsetSum.cpp new file mode 100644 index 0000000..c61b1ea --- /dev/null +++ b/test/other/fastSubsetSum.cpp @@ -0,0 +1,49 @@ +#include "../util.h" +#include <other/fastSubsetSum.cpp> + +int subsetSum(vector<int> w, int t){ + vector<bool> dp(t+1); + dp[0] = true; + for(int x : w){ + for(int i = t; i >= x; i--){ + dp[i] = dp[i] || dp[i-x]; + } + } + int ma = 0; + for(int i = 0; i <= t; i++){ + if(dp[i]) ma = i; + } + return ma; +} + +void stress_test() { + int queries = 0; + for (int test = 0; test < 10'000; test++) { + int n = Random::integer<int>(1, 20); + int t = Random::integer<int>(1, 500); + vector<int> w = Random::integers<int>(n, 0, 50); + int got = fastSubsetSum(w, t); + int expected = subsetSum(w, t); + if(got != expected) cerr << "got: " << got << " expected: " << expected << FAIL; + queries++; + } + cerr << "tested queries: " << queries << endl; +} + +void performance_test() { + timer t; + int n = 10'000, a = 10'000; + vector<int> w = Random::integers<int>(n, 0, a); + int target = 10'000'000; + t.start(); + hash_t hash = fastSubsetSum(w, target); + t.stop(); + if (t.time > 750) cerr << "too slow: " << t.time << FAIL; + cerr << "tested performance: " << t.time << "ms (hash: " << hash << ")" << endl; +} + +int main() { + stress_test(); + performance_test(); +} + diff --git a/test/other/josephus2.cpp b/test/other/josephus2.cpp index d28fe0d..85a9d28 100644 --- a/test/other/josephus2.cpp +++ b/test/other/josephus2.cpp @@ -31,7 +31,7 @@ void performance_test() { hash += rotateLeft(1'000'000'000'000'000'000ll + i); } t.stop(); - if (t.time > 500) cerr << "too slow: " << t.time << FAIL; + if (t.time > 750) cerr << "too slow: " << t.time << FAIL; cerr << "tested performance: " << t.time << "ms (hash: " << hash << ")" << endl; } diff --git a/test/other/knuth.cpp b/test/other/knuth.cpp index d469ceb..aaf5059 100644 --- a/test/other/knuth.cpp +++ b/test/other/knuth.cpp @@ -1,5 +1,5 @@ #include "../util.h" -constexpr ll inf = LL::INF; +constexpr ll INF = LL::INF; #include <other/knuth.cpp> vector<vector<ll>> gen(int n) { @@ -43,7 +43,7 @@ vector<vector<ll>> genQuick(int n) { } /*ll naive(int n, int m, const vector<vector<ll>>& C) { - vector<vector<ll>> state(m+1, vector<ll>(n+1, inf)); + vector<vector<ll>> state(m+1, vector<ll>(n+1, INF)); state[0][0] = 0; for (int i = 1; i <= m; i++) { for (int j = 1; j <= n; j++) { @@ -56,9 +56,9 @@ vector<vector<ll>> genQuick(int n) { }*/ vector<ll> naive(int n, const vector<vector<ll>>& C) { - vector<vector<ll>> state(n+1, vector<ll>(n+1, inf)); + vector<vector<ll>> state(n+1, vector<ll>(n+1, INF)); state[0][0] = 0; - vector<ll> res(n+1, inf); + vector<ll> res(n+1, INF); for (int i = 1; i <= n; i++) { for (int j = 1; j <= n; j++) { for (int k = 1; k <= j; k++) { diff --git a/test/other/pbs.cpp b/test/other/pbs.cpp new file mode 100644 index 0000000..ba3b9d0 --- /dev/null +++ b/test/other/pbs.cpp @@ -0,0 +1,103 @@ +#include "../util.h" + +struct Union { + vector<int> a; + + Union(int n) : a(n, -1) {} + + int find(int i) { + return a[i] < 0 ? i : a[i] = find(a[i]); + } + + void join(int i, int j) { + i = find(i), j = find(j); + if (i == j) return; + a[j] = i; + } + + bool same(int i, int j) { + return find(i) == find(j); + } +}; + +int n; +Union un(0); +void reset() { + un = Union(n); +} + +vector<pair<int, int>> edges; +void do_step(int i) { + auto [u, v] = edges[i]; + un.join(u, v); +} + +vector<pair<int, int>> queries; +bool test(int i) { + auto [u, v] = queries[i]; + return un.same(u, v); +} + +#include <other/pbs.cpp> +void stress_test() { + for (int it = 0; it < 100'000; it++) { + n = Random::integer(2, 31); + int Q = Random::integer(2, 31); + int MAX_OPERATIONS = n-1; + + edges.clear(); + for (int i=1; i<n; i++) { + edges.emplace_back(Random::integer(0, i), i); + } + shuffle(all(edges), Random::rng); + queries.clear(); + for (int i=0; i<Q; i++) { + auto x = Random::distinct(2, n); + queries.emplace_back(x[0], x[1]); + } + vector<int> ans = pbs(Q, MAX_OPERATIONS); + + vector<int> correct(Q, -1); + Union un2(n); + for (int j=0; j<MAX_OPERATIONS; j++) { + un2.join(edges[j].first, edges[j].second); + for (int k=0; k<Q; k++) if (correct[k] == -1) { + if (un2.same(queries[k].first, queries[k].second)) { + correct[k] = j; + } + } + } + + if (ans != correct) cerr << "Failed stress test" << FAIL; + } +} + +void performance_test() { + n = 300'000; + constexpr int Q = 300'000; + int MAX_OPERATIONS = n-1; + edges.clear(); + for (int i=1; i<n; i++) { + edges.emplace_back(Random::integer(0, i), i); + } + shuffle(all(edges), Random::rng); + queries.clear(); + for (int i=0; i<Q; i++) { + auto x = Random::distinct(2, n); + queries.emplace_back(x[0], x[1]); + } + + timer t; + t.start(); + vector<int> ans = pbs(Q, MAX_OPERATIONS); + t.stop(); + ll hash = accumulate(all(ans), 0LL); + + if (t.time > 700) cerr << "too slow: " << t.time << FAIL; + cerr << "tested performance: " << t.time << "ms (hash: " << hash << ")" << endl; +} + +int main() { + stress_test(); + performance_test(); +} diff --git a/test/other/pbs.cpp.awk b/test/other/pbs.cpp.awk new file mode 100644 index 0000000..3084ebd --- /dev/null +++ b/test/other/pbs.cpp.awk @@ -0,0 +1,8 @@ +BEGIN { print "vector<int> pbs(int Q, int MAX_OPERATIONS) {" } +{ + sub(/\/\* requirement already fulfilled \*\//, "test(i)") + sub(/\/\/ simulation step/, "do_step(step);") + sub(/\/\/ reset simulation/, "reset();") +} +{ print } +END { print "return high; }" } diff --git a/test/util.h b/test/util.h index ac0ea74..e123fc2 100644 --- a/test/util.h +++ b/test/util.h @@ -24,7 +24,11 @@ namespace details { } namespace Random { - mt19937_64 rng(3141592653589793238ll); + #ifdef SEED + mt19937_64 rng(SEED); + #else + mt19937_64 rng(3141592653589793238ll); + #endif template<typename T = ll> T integer(T l, T r) { return uniform_int_distribution<T>(l, r-1)(rng); @@ -182,7 +186,7 @@ namespace detail { double t = chrono::duration_cast<chrono::duration<double, milli>>(end - start) .count(); - return 50/t; + return 30/t; } double speed = benchmark(); |