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Solution: Count Pairs in Two Arrays

Explore how to count pairs (i, j) in two arrays such that the sum of elements from the first array is greater than the sum of corresponding elements from the second array. Understand how to optimize the brute force approach by using a difference array, sorting, and binary search to achieve an efficient O(n log n) solution.

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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 = ...