51nod 1079 中国剩余定理模板

中国剩余定理就是同余方程组除数为质数的特殊情况

我直接用同余方程组解了。

记得exgcd后x要更新

还有先更新b1再更新m1，顺序不能错！！（不然会影响到b1的更新）

#include<cstdio>
#include<cctype>
#define REP(i, a, b) for(int i = (a); i < (b); i++)
#define _for(i, a, b) for(int i = (a); i <= (b); i++)
using namespace std;

typedef long long ll;
void exgcd(ll a, ll b, ll& d, ll& x, ll& y)
{
	if(!b) { d = a; x = 1; y = 0; }
	else { exgcd(b, a % b, d, y, x); y -= x * (a / b); }
}

void read(ll& x)
{
	ll f = 1; x = 0; char ch = getchar();
	while(!isdigit(ch)) { if(ch == '-1') f = -1; ch = getchar(); }
	while(isdigit(ch)) { x = x * 10 + ch - '0'; ch = getchar(); }
	x *= f;
}

int main()
{
	ll n, m1, b1, m2, b2;
	read(n); read(m1); read(b1);
	_for(i, 2, n)
	{
		read(m2); read(b2);
		ll A = m1, B = m2, K = b2 - b1, d, x, y;
		exgcd(A, B, d, x, y);
		x = (x * (K / d) % (B / d) + (B / d)) % (B / d);
		b1 = m1 * x + b1;
		m1 = m1 / d * m2; 
	}
	printf("%lld
", b1);
	return 0;
}