Time Limit: 1000MS | Memory Limit: 65536K | |
Total Submissions: 17171 | Accepted: 11999 |
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
0346266875
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
#include#include #include #include using namespace std;typedef long long ll;const int mod=10000;typedef vector vec;typedef vector mat;mat mul(mat &a,mat &b){ mat c(a.size(),vec(b[0].size())); for(int i=0;i<2;i++) for(int j=0;j<2;j++) for(int k=0;k<2;k++){ c[i][j]+=a[i][k]*b[k][j]; c[i][j]%=mod; } return c;}mat Pow(mat a,ll n){ mat res(a.size(),vec(a.size())); for(int i=0;i >n&&n!=-1) { cout< <