Strange Way to Express Integers - poj2891 - 中国剩余定理(不互质)

Strange Way to Express Integers

Time Limit: 1000MS   Memory Limit: 131072K
Total Submissions: 20313   Accepted: 6858

Description

Elina is reading a book written by Rujia Liu, which introduces a strange way to express non-negative integers. The way is described as following:

Choose k different positive integers a1, a2, …, ak. For some non-negative m, divide it by every ai (1 ≤ i ≤ k) to find the remainder ri. If a1, a2, …, ak are properly chosen, m can be determined, then the pairs (airi) can be used to express m.

“It is easy to calculate the pairs from m, ” said Elina. “But how can I find m from the pairs?”

Since Elina is new to programming, this problem is too difficult for her. Can you help her?

Input

The input contains multiple test cases. Each test cases consists of some lines.

  • Line 1: Contains the integer k.
  • Lines 2 ~ k + 1: Each contains a pair of integers airi (1 ≤ i ≤ k).

Output

Output the non-negative integer m on a separate line for each test case. If there are multiple possible values, output the smallest one. If there are no possible values, output -1.

Sample Input

2
8 7
11 9

Sample Output

31

Hint

All integers in the input and the output are non-negative and can be represented by 64-bit integral types.

Source

POJ Monthly--2006.07.30, Static

思路:

中国剩余定理的模板题,最近刚学~

学习博客:

https://blog.csdn.net/litble/article/details/75807726

https://blog.csdn.net/Dafang_Xu/article/details/50818919

https://blog.csdn.net/HownoneHe/article/details/52186204

代码如下:

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>
#include<queue>
#include<vector>
using namespace std;
#define ll long long
const int N=1e+5;
ll n,m[N],a[N];

ll extgcd(ll a,ll b,ll &x,ll &y){
	int d=a;
	if(b!=0){
		d=extgcd(b,a%b,y,x);
		y-=(a/b)*x;
	}
	else {x=1;y=0;}
	return d;
}

ll work(){
	ll M=m[1],A=a[1],t,d,x,y;
	for(int i=2;i<=n;i++){
		d=extgcd(M,m[i],x,y);
		if((a[i]-A)%d)return -1;
		x*=(a[i]-A)/d;t=m[i]/d;x=(x%t+t)%t;
		A=M*x+A,M=M*m[i]/d;A%=M;
	}
	return A=(A%M+M)%M;
}

int main(){
    while(scanf("%lld",&n)!=EOF){
    	for(int i=1;i<=n;i++){
    	    scanf("%d%d",&m[i],&a[i]);
	}
	printf("%lld\n",work());
    }
}

猜你喜欢

转载自blog.csdn.net/m0_37579232/article/details/82113380