51nod 1242 斐波那契数列第N项

传送门--斐波那契数列第N项

矩阵连乘

快速幂取模

#include<iostream>#include<cstdio>using namespace std;const int maxn=2;struct Matrix{   long long int m[maxn][maxn];};long long int n;Matrix P={1,1,          1,0};Matrix I={1,0,          0,1};Matrix Matrixmul(Matrix a,Matrix b){    int i,j,k;    Matrix c;    for(int i=0;i<maxn;i++)    {        for(int j=0;j<maxn;j++)        {            c.m[i][j]=0;            for(int k=0;k<maxn;k++)            {                c.m[i][j]=c.m[i][j]+(a.m[i][k]*b.m[k][j])% 1000000009;            }            c.m[i][j]%= 1000000009;        }    }    return c;}Matrix quickpow(long long int n){    Matrix m=P,b=I;    while(n>=1)    {        if(n&1)        {            b=Matrixmul(b,m);        }        n=n>>1;        m=Matrixmul(m,m);    }    return b;}int main(){    while(scanf("%lld",&n)!=-1)    {        if(n==0)        printf("0\n");        else if(n==-1)            break;        else{   Matrix x=quickpow(n-2);        printf("%lld\n",(x.m[0][0]+x.m[0][1])% 1000000009);}    }    return 0;}