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authorLucas Schwebler <lucas.schwebler@gmail.com>2024-03-13 22:21:49 +0100
committerLucas Schwebler <lucas.schwebler@gmail.com>2024-03-13 22:21:49 +0100
commit36e9961fe1f3a63693c86da020cf2c38893170b9 (patch)
tree2cfa331cb274f8858f9dcdbc9b9af147c01b1797 /math
parentb9b46fb67aeb45baa83e91c699bd3fae0f4fe4af (diff)
new crt
Diffstat (limited to 'math')
-rw-r--r--math/chineseRemainder.cpp47
1 files changed, 13 insertions, 34 deletions
diff --git a/math/chineseRemainder.cpp b/math/chineseRemainder.cpp
index 623f94b..a1aa480 100644
--- a/math/chineseRemainder.cpp
+++ b/math/chineseRemainder.cpp
@@ -1,35 +1,14 @@
-// Laufzeit: O(n * log(n)), n := Anzahl der Kongruenzen. Nur für
-// teilerfremde Moduli. Berechnet das kleinste, nicht negative x,
-// das alle Kongruenzen simultan löst. Alle Lösungen sind
-// kongruent zum kgV der Moduli (Produkt, da teilerfremd).
-struct ChineseRemainder {
- using lll = __int128;
- vector<lll> lhs, rhs, mods, inv;
- lll M; // Produkt über die Moduli. Kann leicht überlaufen.
+struct CRT{
+ using lll = __int128_t;
+ lll M = 1, sol = 0; // Solution unique modulo M
+ bool hasSol = true;
- ll g(const vector<lll> &vec) {
- lll res = 0;
- for (int i = 0; i < sz(vec); i++) {
- res += (vec[i] * inv[i]) % M;
- res %= M;
- }
- return res;
- }
-
- // Fügt Kongruenz l * x = r (mod m) hinzu.
- void addEquation(ll l, ll r, ll m) {
- lhs.push_back(l);
- rhs.push_back(r);
- mods.push_back(m);
- }
-
- ll solve() { // Löst das System.
- M = accumulate(all(mods), lll(1), multiplies<lll>());
- inv.resize(sz(lhs));
- for (int i = 0; i < sz(lhs); i++) {
- lll x = (M / mods[i]) % mods[i];
- inv[i] = (multInv(x, mods[i]) * (M / mods[i]));
- }
- return (multInv(g(lhs), M) * g(rhs)) % M;
- }
-};
+ // Adds congruence x = a (mod m)
+ void add(ll a, ll m){
+ ll s, t, d = extendedEuclid(M, m, s, t);
+ if((a - sol) % d != 0) hasSol = false;
+ lll z = M/d * s;
+ M *= m/d;
+ sol = (z % M * (a-sol) % M + sol + M) % M;
+ }
+}; \ No newline at end of file