Kth Smallest Product of Two Sorted Arrays

arraybinary search

Problem Statement

Given two sorted 0-indexed integer arrays nums1 and nums2 as well as an integer k , return the k ^th ( 1-based ) smallest product of nums1[i] * nums2[j] where 0 <= i < nums1.length and 0 <= j < nums2.length .

Examples

Example 1

Input: nums1 = [2,5], nums2 = [3,4], k = 2
Output: 8
The 2 smallest products are:
- nums1[0] * nums2[0] = 2 * 3 = 6
- nums1[0] * nums2[1] = 2 * 4 = 8
The 2 ^nd smallest product is 8.

Example 2

Input: nums1 = [-4,-2,0,3], nums2 = [2,4], k = 6
Output: 0
The 6 smallest products are:
- nums1[0] * nums2[1] = (-4) * 4 = -16
- nums1[0] * nums2[0] = (-4) * 2 = -8
- nums1[1] * nums2[1] = (-2) * 4 = -8
- nums1[1] * nums2[0] = (-2) * 2 = -4
- nums1[2] * nums2[0] = 0 * 2 = 0
- nums1[2] * nums2[1] = 0 * 4 = 0
The 6 ^th smallest product is 0.

Example 3

Input: nums1 = [-2,-1,0,1,2], nums2 = [-3,-1,2,4,5], k = 3
Output: -6
The 3 smallest products are:
- nums1[0] * nums2[4] = (-2) * 5 = -10
- nums1[0] * nums2[3] = (-2) * 4 = -8
- nums1[4] * nums2[0] = 2 * (-3) = -6
The 3 ^rd smallest product is -6.

Constraints

1 <= nums1.length, nums2.length <= 5 * 10 ^4

-10 ^5 <= nums1[i], nums2[j] <= 10 ^5

1 <= k <= nums1.length * nums2.length

nums1 and nums2 are sorted.

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicBinary Search