Codeforces 898 B（拓展欧几里得）

Proper Nutrition

题意:有n元钱，有2种单价不同的商品，是否存在一种购买方式使得钱恰好花光，如果有输入任意一种方式，如果没有输出“NO”

题解：可以使用拓展欧几里得快速求解。

 #include<iostream>
 using namespace std;
 #define ll long long
 ll gcd(ll a, ll b)
 {
     return b? gcd(b, a%b) : a;
 }

 void ex_gcd(ll a, ll b, ll &x, ll &y, ll &d)
 {
     if(!b)
     {
         x = , y = , d = a;
         return ;
     }
     ex_gcd(b, a%b, y, x, d);
     y -= a/b * x;
     return ;
 }
 int main()
 {
     ll m, a, b, x, y;
     cin >> m >> a >> b;
     ll d = gcd(a, b);
     if(m%d)
     {
         cout << "NO\n";
         return ;
     }
     ex_gcd(a, b, x, y, d);
     x *= m/d, y *= m/d;
     a /= d, b /= d;
     if(x< && y <)
     {
         cout << "NO\n";
     }
     else if(x < )
     {
         x = -x;
         ll z;
         if(x%b) z = x/b+; //找到最小的正数x
         else z = x/b;
         x = -x + z * b;
         y = y  -  z*a;
         if(y < )
             cout << "NO\n";
         else cout << "YES\n" << x << ' ' << y << endl;
     }
     else if(y < )
     {
         y = -y;
         ll z;
         if(y%a) z = y/a+;
         else z = y/a;
         y = -y + z*a;
         x = x - z*b;
         if(x < )
             cout << "NO\n";
         else cout << "YES\n" << x << ' ' << y << endl;
     }
     else
         cout << "YES\n" << x << ' ' << y << endl;
     return ;
 }