Fast Power, matrix multiplication, and rapid power of a Matrix

Fast power usage binary

Complexity log-level

#include <cstdio>#include <iostream>#include <string>#include <bits/stdc++.h>using namespace std;typedef long long ll;typedef unsigned long long ull;int q_power(int a,int b,int c) {    int r=1;    a%=c;    while (b) {        if (b&1) {            r=(r*a)%c;        }        a=(a*a)%c;        b>>=1;    }    return r;}int a,b,c;int main () {    cin>>a>>b>>c;    cout<<q_power(a,b,c);    return 0;}

Attach the matrix's quick power and

Matrix fast idempotent Fibonacci series:

#include<iostream>#include<cstdio>#include<cstring>#include<cmath>#include<algorithm>using namespace std;const int mod = 10000;const int maxn = 35;int N;struct Matrix {    int mat[maxn][maxn];    int x, y;    Matrix() {        memset(mat, 0, sizeof(mat));        for (int i = 1; i <= maxn - 5; i++) mat[i][i] = 1;    }};inline void mat_mul(Matrix a, Matrix b, Matrix &c) {    memset(c.mat, 0, sizeof(c.mat));    c.x = a.x; c.y = b.y;    for (int i = 1; i <= c.x; i++) {        for (int j = 1; j <= c.y; j++) {            for (int k = 1; k <= a.y; k++) {                c.mat[i][j] += (a.mat[i][k] * b.mat[k][j]) % mod;                c.mat[i][j] %= mod;            }        }    }    return ;}inline void mat_pow(Matrix &a, int z) {    Matrix ans, base = a;    ans.x = a.x; ans.y = a.y;    while (z) {        if (z & 1 == 1) mat_mul(ans, base, ans);        mat_mul(base, base, base);        z >>= 1;    }    a = ans;}int main() {    while (cin >> N) {        switch (N) {            case -1: return 0;            case 0: cout << "0" << endl; continue;            case 1: cout << "1" << endl; continue;            case 2: cout << "1" << endl; continue;        }        Matrix A, B;        A.x = 2; A.y = 2;        A.mat[1][1] = 1; A.mat[1][2] = 1;        A.mat[2][1] = 1; A.mat[2][2] = 0;        B.x = 2; B.y = 1;        B.mat[1][1] = 1; B.mat[2][1] = 1;        mat_pow(A, N - 1);        mat_mul(A, B, B);        cout << B.mat[1][1] << endl;    }    return 0;}

By the way

Matrix Multiplication:

/* Assume that A is a matrix of M * P, and B is a matrix of p * n. c = AB (C is the product of matrix A and B) then C is the matrix of M * n */For (INT I = 1; I <= m; ++ I) // the row of a {for (Int J = 1; j <= N; ++ J) // column {for (int K = 1; k <= P; ++ K) of B) // use the formula C {C [I] [J] + = A [I] [k] * B [k] [J] ;}}

# Include <iostream> # include <cmath> # include <cstring> using namespace STD; typedef long ll; const ll mod = 1000000007; /* matrix fast power evaluate Fibonacci series input N output f [N] */struct mat {ll mat [2] [2] ;}; mat operator * (MAT, mat B) // matrix multiplication {mat C; For (INT I = 0; I <2; ++ I) {for (Int J = 0; j <2; ++ J) {C. mat [I] [J] = 0; For (int K = 0; k <2; ++ K) {C. mat [I] [J] = (. mat [I] [k] * B. mat [k] [J]) % mod + C. mat [I] [J]) % mod ;}} return C;} mat operator ^ (MAT a, ll K) // matrix power {mat C; for (INT I = 0; I <2; ++ I) {for (Int J = 0; j <2; ++ J) {C. mat [I] [J] = (I = J); // The unit matrix is initialized} // It is said that the value of any matrix multiplied by the unit matrix will not change to (; K; k> = 1) {If (K & 1) C = C * A; A = A * A;} return C ;}int main () {ll N; while (CIN> N) {mat A;. mat [0] [0] = 1,. mat [0] [1] = 1,. mat [1] [0] = 1,. mat [1] [1] = 0; MAT fn = a ^ N; cout <fn. mat [0] [1] <Endl;} return 0 ;}

 

Fast Power, matrix multiplication, and rapid power of a Matrix