Codeforces Round #412 C. Success Rate
C. Success Rate
You are an experienced Codeforces user. Today you found out that during your activity on Codeforces you have made ysubmissions, out of which x have been successful. Thus, your current success rate on Codeforces is equal to x / y.
Your favorite rational number in the [0;1] range is p / q. Now you wonder: what is the smallest number of submissions you have to make if you want your success rate to be p / q?
The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of test cases.
Each of the next t lines contains four integers x, y, p and q (0 ≤ x ≤ y ≤ 109; 0 ≤ p ≤ q ≤ 109; y > 0; q > 0).
It is guaranteed that p / q is an irreducible fraction.
Hacks. For hacks, an additional constraint of t ≤ 5 must be met.
For each test case, output a single integer equal to the smallest number of submissions you have to make if you want your success rate to be equal to your favorite rational number, or -1 if this is impossible to achieve.
4
10
0
-1
In the first example, you have to make 4 successful submissions. Your success rate will be equal to 7 / 14, or 1 / 2.
In the second example, you have to make 2 successful and 8 unsuccessful submissions. Your success rate will be equal to9 / 24, or 3 / 8.
In the third example, there is no need to make any new submissions. Your success rate is already equal to 20 / 70, or 2 / 7.
In the fourth example, the only unsuccessful submission breaks your hopes of having the success rate equal to 1.
解题思路:
这道题题意比较好懂,就不说了,为了方便理解我们可以用 (x+a)/(y+b) = p/q 来表示其核心思想,其中a 为做对的题目,b为做的题目,则有x+a = k*p,y+b = k*q.且有0<=a<=b,两式合并可得k>=x/p,k>=(y-x)/(q-p), 则如要满足两个等式,k应取其中较大的值(注意:若取得的k为小数,我们需要的是最小整数解,加1),最后注意一下特殊情况 p = 0,p = q.
实现代码:
#include <bits/stdc++.h> using namespace std; int main() { long long n, x, y, p, q, k; cin >> n; for (int i = 0; i < n; i++) { cin >> x >> y >> p >> q; if (p == 0) { if (x == 0) cout << 0 << endl; else cout << -1 << endl; } else if (p == q) { if (x == y) cout << 0 << endl; else cout << -1 << endl; } else { long long k1 = (y-x)/(q-p) + (((y-x)%(q-p)) ? 1 : 0); long long k2 = x/p + ((x%p) ? 1 : 0); k = max(k1,k2); cout << k*q-y << endl; } } return 0; }