2013
11-12

# Fibonacci

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.

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.

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).

0
9
999999999
1000000000
-1

0
34
626
6875

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:

.

import java.io.BufferedReader;
import java.io.IOException;

public class Main {

public static void main(String[] args) throws IOException {
System.in));
int[] f = new int[15000];
f[0] = 0;
f[1] = 1;
f[2] = 1;
for (int i = 2; i < f.length - 1; i++) {
f[i + 1] = (f[i - 1] + f[i]) % 10000;
}
int i;
}