Poj

Fibonacci

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

099999999991000000000-1

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:

题意

就是求Fib的第n项后四位

题解：

矩阵快速幂板子 递推构造矩阵需要学习一下

AC代码

#include <cstdio>#include <cstring>#include <algorithm>using namespace std;typedef long long LL;const int mod = 1e4;const int N = 2;struct node {    LL arr[N][N];}p;LL n, k; node mul(node x,node y){    node ans;;    memset(ans.arr,0,sizeof(ans.arr));    for(int i = 0;i < 2; i++) {        for(int j = 0;j < 2; j++) {            for(int k = 0;k < 2; k++) {                ans.arr[i][j] = (ans.arr[i][j]+(x.arr[i][k]*y.arr[k][j])%mod)%mod;            }        }    }    return ans;}node powMod(LL u, node x) {    node ans;    for(int i = 0;i < 2; i++) {        for(int j = 0;j < 2; j++) {            if(i==j) ans.arr[i][j] = 1;            else ans.arr[i][j] = 0;        }    }    while(u) {        if(u&1) ans = mul(ans,x);        x = mul(x,x);        u >>= 1;    }    return ans;}int main(){    int n;    while(~scanf("%d",&n),n!=-1) {        p.arr[0][0] = 1; p.arr[0][1] = 1;        p.arr[1][0] = 1; p.arr[1][1] = 0;        node x = powMod(n,p);        printf("%d\n",x.arr[0][1]);    }return 0;}