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Solution: Kth Smallest Number in Multiplication Table

Discover how to find the kth smallest number in an m by n multiplication table by leveraging the table’s ordered properties and binary search. This lesson teaches you a method to count elements efficiently and identify the desired value without explicitly constructing the full table, optimizing both time and space complexity.

Statement

You are given a multiplication table of size m×\timesn, where each element at position mat[i][j] is calculated as i×ji \times j (with 1-based indexing).

Your task is to find the kthk^{th} smallest element in this table, given the m, n, and k values.

Constraints:

  • 11 \leq m, n 3×104\leq 3 \times 10^4

  • 11 \leq k \leq m ×\timesn

Solution

We need to find the kth ...