矩陣快速冪 (模板)
阿新 • • 發佈:2018-11-11
#include<iostream> #include<cstdio> #include<cstring> using namespace std; const int maxn = 2; const int mod = 10000; //矩陣結構體 struct Matrix{ int a[maxn][maxn]; void init(){ //初始化為單位矩陣 memset(a, 0, sizeof(a)); for(int i=0;i<maxn;++i){ a[i][i] = 1; } } }; //矩陣乘法 Matrix mul(Matrix a, Matrix b){ Matrix ans; for(int i=0;i<maxn;++i){ for(int j=0;j<maxn;++j){ ans.a[i][j] = 0; for(int k=0;k<maxn;++k){ ans.a[i][j] += a.a[i][k] * b.a[k][j]; ans.a[i][j] %= mod; } } } return ans; } //矩陣快速冪 Matrix qpow(Matrix a, int n){ Matrix ans; ans.init(); while(n){ if(n&1) ans = mul(ans, a); a = mul(a, a); n /= 2; } return ans; } void output(Matrix a){ for(int i=0;i<maxn;++i){ for(int j=0;j<maxn;++j){ cout << a.a[i][j] << " "; } cout << endl; } } int main(){ Matrix a; a.a[0][0] = 1; a.a[0][1] = 1; a.a[1][0] = 1; a.a[1][1] = 0; Matrix ans = qpow(a, 10); cout << "f(12) = [f(2), f(1)] = [1, 1] * a^10 = " << ans.a[0][0] + ans.a[1][0]; return 0; }