[蓝桥杯训练系统] ALGO-199 奇异的虫群 （矩阵快速幂） Apare_xzc

---

---

题面：

---

分析：

就是求斐波那契数列第n项

可用矩阵快速幂

A1 = 1   B1 = 1
A2 = 2   B2 = 1
A3 = 3   B3=  2
A4 = 5   B4 = 3
A5 = 8   B5 = 5
...
A[i+1] = A[i]+B[i]
B[i+1] = A[i]

矩阵递推式如下：

| A[i+1]  |        =      |1  1|     *      |  A[i]  |
| B[i+1]  |               |1  0|            |  B[i]  |

---

我的AC代码

#include <bits/stdc++.h>
using namespace std;
#define LL long long
const int N = 5;
const int mod = 1000000007;
LL arr[N][N];
void Mul(LL a[N][N],LL b[N][N],int n) /// a(n,n) = a(n,n) * b(n,n)
{
	LL c[N][N] = {0};
	for(int row=0; row<n; ++row)
		for(int col=0; col<n; ++col)
			for(int k=0;k<n;++k)
				c[row][col] = (a[row][k]*b[k][col]%mod+c[row][col])%mod;
	for(int i=0; i<n; ++i)
		for(int j=0; j<n; ++j)
			a[i][j] = c[i][j];
} 
void solve(LL a[N][N],int n,LL m)
{
	LL ans[N][N] = {0};
	for(int i=0; i<n; ++i) ans[i][i] = 1;
	while(m>0)
	{
		if(m&1) Mul(ans,a,n);
		Mul(a,a,n);
		m >>= 1;
	}
	printf("%lld\n",ans[0][0]); 
}
int main()
{
	LL m;
	while(cin>>m)
	{
		arr[0][0] = arr[0][1] = arr[1][0] = 1;
		arr[1][1] = 0;
		solve(arr,2,m);
	}
	return 0;
}

---

---

矩阵快速幂入门水题
xzc
2020.1.13 16:09

---