1. 程式人生 > >矩陣運算,矩陣快速冪,模板

矩陣運算,矩陣快速冪,模板

#include<cstdio>
#include<algorithm>
#include<cstring>
#include<iostream>
using namespace std;

#define MOD 1000000007
struct Mat{
    int n,m;   //行列
    int mat[19][19];
};
Mat operator *(Mat a, Mat b) {  //矩陣相乘  
	Mat c;
	memset(c.mat, 0, sizeof(c.mat));
	c.n = a.n, c.m = b.m;
	for (int i = 1; i <= a.n; i++) {
		for (int j = 1; j <= b.m; j++) {
			for (int k = 1; k <= a.m; k++) {
				c.mat[i][j] += (a.mat[i][k] * b.mat[k][j]) % MOD;
				c.mat[i][j] = (c.mat[i][j] % MOD + MOD) % MOD;
			}
		}
	}
	return c;
}
Mat operator +(Mat a, Mat b) { //矩陣相加  
	Mat c;
	memset(c.mat, 0, sizeof(c.mat));
	c.n = a.n, c.m = a.m;
	for (int i = 1; i <= a.n; i++) {
		for (int j = 1; j <= a.m; j++) {
			c.mat[i][j] = (a.mat[i][j] + b.mat[i][j]) % MOD;
		}
	}
	return c;
}
Mat operator ^(Mat a,int k){   //矩陣冪
    Mat c;
    memset(c.mat,0,sizeof(c.mat));
    c.n = a.n,c.m = a.n;
    for(int i=1;i<=a.n;i++)c.mat[i][i] = 1;
    while(k){
        if(k&1){
            c = c*a;
        }
        a = a*a;
        k>>=1;
    }
    return c;
}
void out(Mat a){      //輸出矩陣
    for(int i=1;i<=a.n;i++){
        for(int j=1;j<=a.m;j++){
            printf(j==a.m? "%d\n":"%d ",a.mat[i][j]);
        }
    }
}
int main(){
    Mat d;
    d.n=3,d.m=3;
    for(int i=1;i<=d.n;i++){
        for(int j=1;j<=d.m;j++){
            scanf("%d",&d.mat[i][j]);
        }
    }
    d=d^2;
    out(d);
}