Kth Smallest Number in Multiplication Table — LeetCode 668 Python Solution

The problem

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).

Example

Input

m = 3, n = 3, k = 5

Output

3

Explanation

The 5th smallest number is 3.

Python solution

class Solution:
    def findKthNumber(self, m: int, n: int, k: int) -> int:
        left, right = 1, m * n
        while left < right:
            mid = (left + right) >> 1
            cnt = 0
            for i in range(1, m + 1):
                cnt += min(mid // i, n)
            if cnt >= k:
                right = mid
            else:
                left = mid + 1
        return left

Complexity

Pattern: Monotonic Stack

Answer "what is the next greater element" for every position in one pass. LeetCode 668. Kth Smallest Number in Multiplication Table is filed here because the reference solution below belongs to the algorithm family this hub collects, even though its LeetCode tags point elsewhere.

The monotonic stack guide has the Python template for the pattern and the 225 LeetCode problems that use it.

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