Solution: Kth Smallest Product of Two Sorted Arrays

Explore how to find the kth smallest product of pairs from two sorted arrays by applying a modified binary search technique. Understand counting methods with binary searches on sorted arrays and manage edge cases like negative and zero values. This lesson equips you with a practical approach to solving large-scale product selection problems efficiently, focusing on time and space optimization.

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Statement
Solution
- Time complexity
- Space complexity

Statement

You are given two sorted $0$ -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 $k^{th}$ smallest product among all such pairs, using $1$ -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:

$1 \leq$ nums1.length, nums2.length $\leq 5 \times 10^4$
$-10^5 \leq$ nums1[i], nums2[j] $\leq 10^5$ ...