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【poj3070】Fibonacci (矩阵乘法+快速幂)

2018年04月25日 ⁄ 综合 ⁄ 共 1206字 ⁄ 字号 评论关闭

3.16

#include<iostream>
#include<cstring>
#include<cstdio>
using namespace std;
int a[2][2],b[2][2],n;
void mul(int a[2][2],int b[2][2],int ans[2][2]){
	int t[2][2];
	memset(t,0,sizeof(t));
	for(int i=0;i<=1;i++)
		for(int j=0;j<=1;j++)
			for(int k=0;k<=1;k++)
				t[i][j]=(t[i][j]+a[i][k]*b[k][j])%10000;
	for(int i=0;i<=1;i++)
		for(int j=0;j<=1;j++)
			ans[i][j]=t[i][j];
}
int main(){
	while(scanf("%d",&n)!=EOF){
		a[0][0]=a[0][1]=a[1][0]=b[0][0]=b[1][1]=1;
        b[1][0]=b[0][1]=a[1][1]=0;
		if(n==-1)return 0;
		while(n){
			if(n&1)mul(a,b,b);//b=a*b;
			n>>=1;//n/=2;
			mul(a,a,a);//a*=a;
		}
		printf("%d\n",b[1][0]);
	}
}

8.12

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

inline int read() {
    int x = 0, f = 1;
    char ch = getchar();
    while (ch < '0' || ch > '9') {
        if (ch == '-')f = -1;
        ch = getchar();
    }
    while (ch >= '0' && ch <= '9') {
        x = x * 10 + ch - '0';
        ch = getchar();
    }
    return x*f;
}

struct M {
    int a[2][2];
} a;

inline M operator *(const M &a, const M &b) {
    M res;
    for (int i = 0; i < 2; ++i)
        for (int j = 0; j < 2; ++j) {
            res.a[i][j] = 0;
            for (int k = 0; k < 2; ++k)
                res.a[i][j] = (res.a[i][j] + a.a[i][k] * b.a[k][j]) % 10000;
        }
    return res;
}

inline M operator ^ (M a, int n) {
    M res = a;
    for (--n; n; n >>= 1, a = a * a)
        if (n & 1)res = res * a;
    return res;
}
int n;

int main() {
    while (~scanf("%d", &n)) {
        if (n == -1)return 0;
        if (n == 0) {
            printf("0\n");
            continue;
        }
        a.a[0][0] = a.a[0][1] = a.a[1][0] = 1;
        a.a[1][1] = 0;
        a = a^n;
        printf("%d\n", a.a[1][0]);
    }
}

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