[Poj] 3070 Fibonacci (matrix multiplication)

Http://poj.org/problem? Id = 3070

Calculate the matrix based on this question and use the quick power.

Bare question

#include <cstdio>#include <cstring>#include <cmath>#include <string>#include <iostream>#include <algorithm>using namespace std;#define rep(i, n) for(int i=0; i<(n); ++i)#define for1(i,a,n) for(int i=(a);i<=(n);++i)#define for2(i,a,n) for(int i=(a);i<(n);++i)#define for3(i,a,n) for(int i=(a);i>=(n);--i)#define for4(i,a,n) for(int i=(a);i>(n);--i)#define CC(i,a) memset(i,a,sizeof(i))#define read(a) a=getint()#define print(a) printf("%d", a)#define dbg(x) cout << #x << " = " << x << endl#define printarr(a, n, m) rep(aaa, n) { rep(bbb, m) cout << a[aaa][bbb]; cout << endl; }inline const int getint() { int r=0, k=1; char c=getchar(); for(; c<‘0‘||c>‘9‘; c=getchar()) if(c==‘-‘) k=-1; for(; c>=‘0‘&&c<=‘9‘; c=getchar()) r=r*10+c-‘0‘; return k*r; }inline const int max(const int &a, const int &b) { return a>b?a:b; }inline const int min(const int &a, const int &b) { return a<b?a:b; }typedef int matrix[2][2];matrix a, b;const int M=10000;int n;inline void mul(matrix a, matrix b, matrix c, const int &la, const int &lb, const int &lc, const int &MOD) {matrix t;rep(i, la) rep(j, lc) {t[i][j]=0;rep(k, lb) t[i][j]=(t[i][j]+(a[i][k]*b[k][j])%MOD)%MOD;}rep(i, la) rep(j, lc) c[i][j]=t[i][j];}int main() {while(~scanf("%d", &n) && n!=-1) {b[0][0]=b[1][1]=1;a[0][0]=a[0][1]=a[1][0]=1;b[0][1]=b[1][0]=a[1][1]=0;while(n) {if(n&1) mul(a, b, b, 2, 2, 2, M);mul(a, a, a, 2, 2, 2, M);n>>=1;}printf("%d\n", b[1][0]);}return 0;}

 

 

 

 

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 in 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

.

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

.

Source

Stanford local 2006

[Poj] 3070 Fibonacci (matrix multiplication)