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Grokking the Coding Interview Patterns

Solution: Count Pairs in Two Arrays

Explore how to count pairs (i, j) where the sum of elements in one array exceeds that in another. Understand the use of a difference array, sorting, and binary search to optimize the solution from a brute force approach to O(n log n) time complexity.

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Statement

You are given two positive integer arrays, nums1 and nums2, both of length nn. Your task is to count and return the number of pairs of indexes (i,j)(i, j) where:

  • i<ji < j , and

  • nums1[i]+nums1[j]>nums2[i]+nums2[j]\text{nums1}[i] + \text{nums1}[j] > \text{nums2}[i] + \text{nums2}[j]

In simpler terms, the sum of two elements from nums1 must be greater than that of the corresponding elements from nums2.

Constraints:

  • n=n = ...