【poj3070】Fibonacci

矩乘快速幂入门

题目已经把题解讲得很清楚了

#include<cstdio>
#include<cstring>
#include<cassert>
#include<algorithm>
using namespace std;
#define p 10000
#define N 10
#define ll long long
struct matrix{
    int n,m;
    int mat[N][N];
    matrix(){
        memset(mat,0,sizeof(mat));
    }
    void print(){
        printf("%d\n",mat[0][0]%p);
    }
}m0,trs;
matrix operator *(matrix m1,matrix m2){
    assert(m1.m==m2.n);
    matrix res;
    res.n=m1.n;
    res.m=m2.m;
    for (int i=0;i<m1.n;i++)
        for (int j=0;j<m2.m;j++)
            for (int k=0;k<m1.m;k++)
                res.mat[i][j]+=(ll)m1.mat[i][k]*m2.mat[k][j]%p;
    return res;
}
matrix quickpow(matrix x,int y){
    matrix res;
    res.n=res.m=2;
    res.mat[1][1]=res.mat[0][0]=1;
    while (y){
        if (y&1) res=res*x;
        x=x*x;
        y>>=1;
    }
    return res;
}
int main(){
    ll k;
    scanf("%lld",&k);
    m0.m=2;m0.n=1;
    m0.mat[0][0]=m0.mat[0][1]=1;
    trs.m=trs.n=2;
    trs.mat[1][1]=trs.mat[1][0]=trs.mat[0][1]=1;
    while (k!=-1){
        if (k==0) printf("0\n");
        else (m0*quickpow(trs,k-1)).print();
        scanf("%lld",&k);
    }
    return 0;
}

 PS：

矩乘的简单理解：http://www.ruanyifeng.com/blog/2015/09/matrix-multiplication.html

矩阵拓展：08年国家集训队论文,

http://wenku.baidu.com/link?url=O5_d_kstn_0Ym7zrCiZa1EYPuKlun-K1OHeV42s0pt64JVGvJKSf2gFKyr7hAYEm9SBu52xdUhNkYemH6blJjaaK5fhbIfPjrQuqNAU90EG