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Solution: Kth Smallest Product of Two Sorted Arrays

Explore the technique of using modified binary search to find the kth smallest product of pairs from two sorted arrays. Understand how to count products efficiently without enumeration and apply binary search on the product values. This lesson teaches how to handle negative values and zeros and solve the problem within time and space constraints.

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Statement

You are given two sorted 00-indexed integer arrays nums1 and nums2, along with an integer k.

Consider all possible products formed by nums1[i] * nums2[j], where i ranges over all valid indices of nums1 and j ranges over all valid indices of nums2. Return the kthk^{th} smallest product among all such pairs, using 11-based indexing.

Note: Both nums1 and nums2 are sorted in non-decreasing order. The arrays may contain negative numbers and zero, so the products can be negative, zero, or positive.

Constraints:

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