题目1081：递推数列(矩阵二分乘法)

//
//  1081 递推数列.cpp
//  Jobdu
//
//  Created by PengFei_Zheng on 03/05/2017.
//  Copyright © 2017 PengFei_Zheng. All rights reserved.
//

#include <stdio.h>
#include <iostream>
#include <algorithm>
#include <string.h>
#include <cstring>
#include <cmath>
#include <climits>
#define MOD 10000
using namespace std;

int a0, a1, p, q, k;

int metrix[2][2];
/*
*  metrixMul
*
*  | ak   |   | p q |   | ak-1 |
*  |      | = |     | * |      |
*  | ak-1 |   | 1 0 |   | ak-2 |
*
*  metrixPow
*
*  | ak   |   | p q |(k-1)   | a1 |
*  |      | = |     |     *  |    |
*  | ak-1 |   | 1 0 |        | a0 |
*
*/
void metrixMul(int p1[2][2], int p2[2][2]){
int tmp[2][2];
tmp[0][0] = ((p1[0][0]*p2[0][0])%MOD + p1[0][1]*p2[1][0]%MOD)%MOD;
tmp[0][1] = ((p1[0][0]*p2[0][1])%MOD + p1[0][1]*p2[1][1]%MOD)%MOD;
tmp[1][0] = ((p1[1][0]*p2[0][0])%MOD + p1[1][1]*p2[1][0]%MOD)%MOD;
tmp[1][1] = ((p1[1][0]*p2[0][1])%MOD + p1[1][1]*p2[1][1]%MOD)%MOD;
p1[0][0] = tmp[0][0];
p1[0][1] = tmp[0][1];
p1[1][0] = tmp[1][0];
p1[1][1] = tmp[1][1];
}

void metrixPow(int p[2][2], int n){
int tmp[2][2];
tmp[0][0] = p[0][0];
tmp[0][1] = p[0][1];
tmp[1][0] = p[1][0];
tmp[1][1] = p[1][1];

if(n==1) return ;
else if((n&1)==1){//odd
metrixPow(p, n-1);
metrixMul(p, tmp);
}
else{
metrixPow(p,n/2);
metrixMul(p, p);// mind : means metrix p*p
}
}
int main(){
while(scanf("%d %d %d %d %d",&a0,&a1,&p,&q,&k)!=EOF){
if(0==k){
printf("%d\n",a0%MOD);
continue;
}
if(1==k){
printf("%d\n",a1%MOD);
continue;
}
metrix[0][0] = p%MOD;
metrix[0][1] = q%MOD;
metrix[1][0] = 1;
metrix[1][1] = 0;
metrixPow(metrix, k-1);
printf("%d\n",(metrix[0][0]*a1 + metrix[0][1]*a0)%MOD);
}
return 0;
}
/**************************************************************
Problem: 1081
User: zpfbuaa
Language: C++
Result: Accepted
Time:10 ms
Memory:1520 kb
****************************************************************/