668. Kth Smallest Number in Multiplication Table

Nearly every one have used the Multiplication Table. But could you find out the k-th smallest number quickly from the multiplication table?

Given the height m and the length n of a m * n Multiplication Table, and a positive integer k, you need to return the k-th smallest number in this table.

Example 1:

Input: m = 3, n = 3, k = 5
Output: 
Explanation: 
The Multiplication Table:
1	2	3
2	4	6
3	6	9

The 5-th smallest number is 3 (1, 2, 2, 3, 3).

Example 2:

Input: m = 2, n = 3, k = 6
Output: 
Explanation: 
The Multiplication Table:
1	2	3
2	4	6

The 6-th smallest number is 6 (1, 2, 2, 3, 4, 6).

Note:

1. The m and n will be in the range [1, 30000].

2. The k will be in the range [1, m * n]

// Binary Search
int findKthNumber(int m, int n, int k) { // time: O(m * log(m * n)); space: O(1)
    int l = 1, r = m * n + 1;
    while (l < r) {
        int mid = l + (r - l) / 2, cnt = 0;
        for (int i = 1; i <= m; ++i) {
            cnt += min(n, mid / i);
        }
        if (cnt < k) l = mid + 1;
        else r = mid;
    }
    return l;
}