Poj3070 -- Fibonacci (Fast Power of matrix)

Fibonacci

Time limit:1000 ms		Memory limit:65536 K
Total submissions:9650		Accepted:6856

Description

In the Fibonacci integer sequence,F0 = 0,F1 = 1, andFN=FN? 1 +FN? 2N≥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 integerN, Your goal is to compute the last 4 digitsFN.

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 digitsFN. If the last four digitsFNAre all zeros, print '0'; otherwise, omit any leading zeros (I. e., printFNMoD 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 is written in the same way as a normal fast power. The difference is that you need to calculate the Matrix Multiplication. As long as you write the multiplication of the matrix, it is no longer difficult.

#include <cstdio>#include <cstring>#include <algorithm>using namespace std;#define LL long longstruct node{    LL s11 , s12 , s21 , s22 ;};node f(node a,node b){    node p ;    p.s11 = (a.s11*b.s11 + a.s12*b.s21)%10000 ;    p.s12 = (a.s11*b.s12 + a.s12*b.s22)%10000 ;    p.s21 = (a.s21*b.s11 + a.s22*b.s21)%10000 ;    p.s22 = (a.s21*b.s12 + a.s22*b.s22)%10000 ;    return p ;}node pow(node p,int n){    node q ;    q.s11 = q.s22 = 1 ;    q.s12 = q.s21 = 0 ;    if(n == 0)        return q ;    q = pow(p,n/2);    q = f(q,q);    if( n%2 )        q = f(q,p);    return q ;}int main(){    int n ;    node p ;    while(scanf("%d", &n) && n != -1)    {        p.s11 = p.s12 = p.s21 = 1 ;        p.s22 = 0 ;        p = pow(p,n);        printf("%d\n", p.s12);    }    return 0;}

Poj3070 -- Fibonacci (Fast Power of matrix)