diff options
Diffstat (limited to 'content/math')
| -rw-r--r-- | content/math/linearRecurrence.cpp | 14 | ||||
| -rw-r--r-- | content/math/math.tex | 7 | ||||
| -rw-r--r-- | content/math/recover.cpp | 13 |
3 files changed, 26 insertions, 8 deletions
diff --git a/content/math/linearRecurrence.cpp b/content/math/linearRecurrence.cpp index c15c25c..ab86f71 100644 --- a/content/math/linearRecurrence.cpp +++ b/content/math/linearRecurrence.cpp @@ -10,21 +10,21 @@ // return c; // } -ll kthTerm(const vector<ll>& f, const vector<ll>& c, ll k){ +ll kthTerm(const vector<ll>& f, const vector<ll>& c, ll k) { int n = sz(c); - vector<ll> q(n+1, 1); - for(int i = 1; i <= n; i++) q[i] = (mod-c[i-1])%mod; + 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{ + do { vector<ll> q2 = q; - for(int i = 1; i <= n; i += 2) q2[i] = (mod - q2[i]) % mod; + 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++){ + 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); + } while (k /= 2); return p[0]; }
\ No newline at end of file diff --git a/content/math/math.tex b/content/math/math.tex index fb66110..4ac6c9e 100644 --- a/content/math/math.tex +++ b/content/math/math.tex @@ -544,6 +544,11 @@ Wenn man $k$ Spiele in den Zuständen $X_1, \ldots, X_k$ hat, dann ist die \text \subsection{Wichtige Zahlen}
\input{math/tables/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}
@@ -552,10 +557,10 @@ Wenn man $k$ Spiele in den Zuständen $X_1, \ldots, X_k$ hat, dann ist die \text \method{pi}{zählt Primzahlen $\leq n$ ($n < N^2$)}{n^{2/3}}
\end{methods}
\sourcecode{math/piLehmer.cpp}
-}
\subsection{Primzahlzählfunktion $\boldsymbol{\pi}$}
\sourcecode{math/piLegendre.cpp}
+}
\begin{algorithm}[optional]{Big Integers}
\sourcecode{math/bigint.cpp}
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; +} |