【矩阵乘法】斐波那契数列

链接

YbtOJ 6-1-2

题目描述

求斐波那契数列第n项
答案取模1e9+7

思路

矩阵乘法直接求就好了

代码

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>
#define ll long long

using namespace std;

const ll mo = 1e9 + 7;
ll n;

struct matrix
{
    
    
	ll n, m;
	ll a[15][15]; 	
}a, ans, c;

matrix operator *(matrix a, matrix b)
{
    
    
	c.n = a.n; c.m = b.m;
	for(int i = 1; i <= c.n; ++i)
	for(int j = 1; j <= c.m; ++j)
		c.a[i][j] = 0;
	for(int k = 1; k <= a.m; ++k)
	for(int i = 1; i <= c.n; ++i)
	for(int j = 1; j <= c.m; ++j)
		c.a[i][j] = ((a.a[i][k] * b.a[k][j]) % mo + c.a[i][j]) % mo;
	return c;
}

ll ksm(ll k)
{
    
    
	while(k)
	{
    
    
		if(k & 1) ans = ans * a;
		a = a * a;
		k >>= 1;
	}
}

int main()
{
    
    
	scanf("%lld", &n);
	if(n <= 2) {
    
    
		printf("1");
		return 0;
	}
	a.n = 2; a.m = 2;
	ans.n = 1; ans.m = 2;
	a.a[1][1] = a.a[1][2] = a.a[2][1] = 1;
	ans.a[1][1] = ans.a[1][2] = 1;
	ksm(n - 2);
	printf("%d", ans.a[1][1] % mo);
	return 0;
}