POJ 3070 Fibonacci【矩阵连乘】

Fibonacci

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 6881		Accepted: 4873

Description

In the Fibonacci integer sequence, F₀ = 0, F₁ = 1, and F_n = F_{n − 1} + F_{n − 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 F_n.

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 F_n. If the last four digits of F_n are all zeros, print ‘0’; otherwise, omit any leading zeros (i.e., print F_n 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:

.

Source

Stanford Local 2006

3070

Accepted

132K

0MS

C++

1162B

2013-04-09 21:17:22

#include<cstdio>

const int mod = 10000;

struct Matrix
{
    __int64 a11, a12, a21, a22;
}matrix;

Matrix mull(Matrix a, Matrix b)
{
    Matrix c;
    c.a11 = a.a11*b.a11+a.a12*b.a21;
    c.a12 = a.a11*b.a12+a.a12*b.a22;
    c.a21 = a.a21*b.a11+a.a22*b.a21;
    c.a22 = a.a21*b.a12+a.a22*b.a22;

    c.a11 %= mod;
    c.a12 %= mod;
    c.a21 %= mod;
    c.a22 %= mod;

    return c;
}


Matrix find(Matrix m, __int64 n)
{
    Matrix b;
    b.a11 = 1; b.a12 = 0;
    b.a21 = 0; b.a22 = 1;
    while(n > 0)
    {
        if(n&1)
        {
            b = mull(b, m);
        }
        n = n>>1;

        m = mull(m, m);

    }
    return b;
}
int main()
{
    __int64 n;
    while(scanf("%I64d", &n) != EOF)
    {
        if(n == -1) break;
        else if(n == 0)
        {
           printf("0\n");
           continue;
        }

        __int64 a11, a12, a21, a22;
        Matrix m, ans;
        m.a11 = 1;
        m.a12 = 1;
        m.a21 = 1;
        m.a22 = 0;

        ans = find(m, n);

        __int64 result = ans.a12%10000;
        printf("%I64d\n", result);
    }
    return 0;
}