[poj] 2891 Strange Way to Express Integers

原题

它是一道假的中国剩余定理，因为模数不互质，所以我们只能ex_gcd将方程逐一合并最后求出满足所有的答案

#include<cstdio>
#include<algorithm>
#include<cstring>
#define N 100010
typedef long long ll;
using namespace std;
ll n,m[N],r[N];

ll exgcd(ll a,ll b,ll &x,ll &y)
{
    if (b==0) return x=1,y=0,a;
    ll r=exgcd(b,a%b,y,x);
    y-=a/b*x;
    return r;
}

ll solve()
{
    ll M=m[1],R=r[1],x,y,d;
    for (int i=2;i<=n;i++)
    {
	d=exgcd(M,m[i],x,y);
	if ((R-r[i])%d!=0) return -1;
	x=(R-r[i])/d*x%m[i];
	R-=x*M;
	M=M/d*m[i];
	R%=M;
    }
    return (R%M+M)%M;
}

int main()
{
    while (scanf("%lld",&n)!=EOF)
    {
	for (int i=1;i<=n;i++)
	    scanf("%lld%lld",&m[i],&r[i]);
	printf("%lld
",solve());
    }
    return 0;
}