668-kth-smallest-number-in-multiplication-table

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Description

Nearly everyone has used the Multiplication Table. The multiplication table of size m x n is an integer matrix mat where mat[i][j] == i * j (1-indexed).

Given three integers m, n, and k, return the kth smallest element in the m x n multiplication table.

 

Example 1:

Input: m = 3, n = 3, k = 5
Output: 3
Explanation: The 5th smallest number is 3.

Example 2:

Input: m = 2, n = 3, k = 6
Output: 6
Explanation: The 6th smallest number is 6.

 

Constraints:

• 1 <= m, n <= 3 * 104
• 1 <= k <= m * n

Solution(Python)

class Solution(object):
    def findKthNumber(self, m, n, k):
        def enough(x):
            count = 0
            for i in range(1, m+1):
                count += min(x // i, n)
            return count >= k

        lo, hi = 1, m * n
        while lo < hi:
            mi = (lo + hi) // 2
            if not enough(mi):
                lo = mi + 1
            else:
                hi = mi
        return lo