786. K-th Smallest Prime Fraction

A sorted list A contains 1, plus some number of primes. Then, for every p < q in the list, we consider the fraction p/q.

What is the K-th smallest fraction considered? Return your answer as an array of ints, where answer[0] = p and answer[1] = q.

Examples:
Input: A = [1, 2, 3, 5], K = 3
Output: [2, 5]
Explanation:
The fractions to be considered in sorted order are:
1/5, 1/3, 2/5, 1/2, 3/5, 2/3.
The third fraction is 2/5.

Input: A = [1, 7], K = 1
Output: [1, 7]

Note:

• A will have length between 2 and 2000.

• Each A[i] will be between 1 and 30000.

• K will be between 1 and A.length * (A.length - 1) / 2.

// Binary Search
vector<int> kthSmallestPrimeFraction(vector<int>& A, int K) {
    double l = 0.0, r = 1.0, mid;
    int p = 0, q = 1, cnt = 0, n = A.size();
    while (true) {
        mid = l + (r - l) / 2.0;
        cnt = 0, p = 0;
        for (int i = 0, j = 0; i < n; ++i) {
            while (j < n && A[i] > mid * A[j]) ++j;
            cnt += (n - j); // [j, n - 1]    
            if (j < n && p * A[j] < q * A[i]) {
                p = A[i];
                q = A[j];
            }
        }
        if (cnt == K) return {p, q};
        else if (cnt < K) l = mid;
        else r = mid;
    }
}