斐波那契

#include<cstdlib>
#include<cstring>
#include<iostream>

using namespace std;

struct matrix
{
	int n,m;
	int a[3][3];
	matrix()
	{
		n=m=0;
		memset(a,0,sizeof(a));	
	} 
}A,B;

matrix operator*(const matrix &x,const matrix &y)
{//O(n^3)
	//matrix z;
	z.n = x.n;z.m = y.m;
	for (int i=1;i<=z.n;i++)
		for (int k=1;k<=x.m;k++)
			for (int j=1;j<=z.m;j++)
				z.a[i][j] = z.a[i][j] + x.a[i][k] * y.a[k][j];
	return z;
}

matrix ksm(matrix a,int b)//计算a^b
{
	if (b==0)
	{
		matrix c;
		c.n=c.m=a.n;
		for (int i=1;i<=c.n;i++)
			c.a[i][i]=1;
		return c;
	}
	matrix c = ksm(a,b/2);//c=a^(b/2)
	c=c*c;
	if (b&1) c=c*a;
	return c;
} 

int main()
{
	A.n=1;A.m=2;
	A.a[1][1]=0;A.a[1][2]=1;
	
	B.n=2;B.m=2;
	B.a[1][1]=0;B.a[1][2]=1;
	B.a[2][1]=1;B.a[2][2]=1;
	
	C = A * ksm(B,n);
	cout << C.a[1][1] << "\n";
	
	return 0;
}