矩阵快速幂模版

其实大致的步骤和正数快速幂是一样的，只不过它是矩阵。

#include <stdio.h>
#include <iostream>
#include <algorithm>
#include <string.h>
#include <stdlib.h>
#include <math.h>
#include <queue>
#include <set>

#define INF 0x3f3f3f3f
#define pii pair<int,int>
#define LL long long
using namespace std;
typedef unsigned long long ull;
const int mod = 1000000009;
const int N = 10;

LL tmp[N][N],res[N][N];

void multi(LL a[][N],LL b[][N],int n){
    memset(tmp,0, sizeof(tmp));
    for (LL i=0;i<n;i++){
        for (LL j=0;j<n;j++){
            for (LL k=0;k<n;k++){
                tmp[i][j] += (a[i][k]*b[k][j]) % mod;
            }
            tmp[i][j] = tmp[i][j] % mod;
        }
    }
    for (LL i=0;i<n;i++){
        for (LL j=0;j<n;j++)
            a[i][j] = tmp[i][j];
    }
}

void Pow(LL a[][N],LL m,int n){
    memset(res,0, sizeof(res));
    for (LL i=0;i<n;i++){
        res[i][i] = 1;
    }
    while (m){
        if (m & 1){
            multi(res,a,n);
        }
        multi(a,a,n);
        m >>= 1;
    }
}
LL a[N][N];

int main(){
    LL m;
    int n;
    while (~scanf("%lld",&m)){
        n = 2;
        a[0][0] = a[0][1] = a[1][0] = 1;
        a[1][1] = 0;
        Pow(a,m-1,n);
        printf("%lld
",res[0][0]%mod);
    }
    return 0;
}