POJ 2891 Strange Way to Express Integers 中国剩余定理

Posted 2020-09-18 zhchoutai

裸题，上模版，，嘿嘿

#include<stdio.h>
#include<string.h>
#include<iostream>
#include<algorithm>
#include<math.h>
#include<set>
#include<queue>
#include<vector>
#include<map>
using namespace std;
#define ll __int64
ll gcd(ll a, ll b) {
	return b == 0 ?
 a : gcd(b, a%b);
}
//求一组解(x,y)使得 ax+by = gcd(a,b), 且|x|+|y|最小(注意求出的 x,y 可能为0或负数)。
//以下代码中d = gcd(a,b)
//能够扩展成求等式 ax+by = c,但c必须是d的倍数才有解,即 (c%gcd(a,b))==0
void extend_gcd (ll a , ll b , ll& d, ll &x , ll &y) {  
	if(!b){d = a; x = 1; y = 0;}
	else {extend_gcd(b, a%b, d, y, x); y-=x*(a/b);}
}
ll inv(ll a, ll n) { //计算%n下 a的逆。假设不存在逆return -1;
	ll d, x, y;
	extend_gcd(a, n, d, x, y);
	return d == 1 ? (x+n)%n : -1;
}
ll work(ll l, ll r, ll *m, ll *a){ //下标[l,r] 方程x%m=a;
	ll lcm = 1;
	for(ll i = l; i <= r; i++)lcm = lcm/gcd(lcm,m[i])*m[i];
	for(ll i = l+1; i <= r; i++) {
		ll A = m[l], B = m[i], d, k1, k2, c = a[i]-a[l];
		extend_gcd(A,B,d,k1,k2);
		if(c%d)return -1;
		ll mod = m[i]/d;
		ll K = ((k1*c/d)%mod+mod)%mod;
		a[l] = m[l]*K + a[l];
		m[l] = m[l]*m[i]/d;
	}
	if(a[l]==0)return lcm;
	return a[l];
}
#define N 10005
ll n[N],b[N],len;
int main(){  
	ll len;
	while(cin>>len){
		for(ll i = 1; i <= len; i++) cin>>n[i]>>b[i];
		cout<<work(1,len,n,b)<<endl;  
	}
	return 0;  
}