POJ 2891 Strange Way to Express Integers

模线性同余方程组的求解

#include <cstdio>
#include <cstring>

using namespace std;
const int N = 1005;

#define ll long long
ll a[N] , b[N];

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

ll mod_line(int n)
{
    ll r = b[0] , lcm = a[0] , x , y;
    for(int i = 1 ; i<n ; i++)
    {
        ll del = b[i] - r;
        ll g = ex_gcd(lcm , x , a[i] , y);
        if(del % g != 0) return -1;
        ll Mod = a[i] / g;
        x = ((x*del/g % Mod) + Mod)%Mod;
        r = r + lcm*x;
        lcm = lcm*a[i]/g;
        r %= lcm;
    }
    return r;
}

int main()
{
   // freopen("a.in" , "r" , stdin);
    int n;
    while(scanf("%d" , &n) == 1)
    {
        for(int i= 0 ; i<n ; i++)
            scanf("%I64d%I64d" , a+i , b+i);
        printf("%I64d
" , mod_line(n));
    }
    return 0;
}