Fibonacci--poj3070(矩阵快速幂)

http://poj.org/problem?id=3070

 

 

Description

In the Fibonacci integer sequence, F0 = 0, F1 = 1, and Fn = Fn − 1 + Fn − 2 for n ≥ 2. For example, the first ten terms of the Fibonacci sequence are:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …

An alternative formula for the Fibonacci sequence is

.

Given an integer n, your goal is to compute the last 4 digits of Fn.

Input

The input test file will contain multiple test cases. Each test case consists of a single line containing n (where 0 ≤ n ≤ 1,000,000,000). The end-of-file is denoted by a single line containing the number −1.

Output

For each test case, print the last four digits of Fn. If the last four digits of Fn are all zeros, print ‘0’; otherwise, omit any leading zeros (i.e., print Fn mod 10000).

Sample Input

0
9
999999999
1000000000
-1

Sample Output

0
34
626
6875

Hint

As a reminder, matrix multiplication is associative, and the product of two 2 × 2 matrices is given by

.

Also, note that raising any 2 × 2 matrix to the 0th power gives the identity matrix:

.

 

 

 

这道题就是快速幂http://blog.csdn.net/u013795055/article/details/38599321

还有矩阵相乘   

 

#include <iostream>
#include <stdio.h>
#include <string.h>
#include <algorithm>
#include <math.h>
#include <stdlib.h>
#include <vector>
#include <queue>

using namespace std;
#define memset(a,b) memset(a,b,sizeof(a))
#define N 4
#define INF 0xfffffff
struct node
{
    int a[N][N];
}e;

node mm(node p,node q)
{
    node t;
    for(int i=0;i<2;i++)
    {
        for(int j=0;j<2;j++)
        {
            t.a[i][j]=0;
            for(int k=0;k<2;k++)
            {
                t.a[i][j]=(t.a[i][j]+(p.a[i][k]*q.a[k][j]))%10000;
            }
        }
    }
    return t;
}


node mul(node p,int n)
{

    node q;
    for(int i=0;i<2;i++)
    {
        for(int j=0;j<2;j++)
        {
            q.a[i][j]=(i==j);
        }
    }///这个是为了当n是奇数是第一次跟q相乘是还是原来的p,为了下一次跟下一奇数相乘
while(n) { if(n&1) q=mm(q,p); n=n/2; p=mm(p,p); } return q; } int main() { int n; while(scanf("%d",&n),n!=-1) { e.a[0][0]=1; e.a[0][1]=1; e.a[1][0]=1; e.a[1][1]=0; node b=mul(e,n); printf("%d\n",b.a[0][1]); } return 0; }

 

posted @ 2016-03-15 17:27  啦咯  阅读(785)  评论(0编辑  收藏  举报