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Solution: Count Pairs in Two Arrays

Explore how to count index pairs in two arrays where the sum of elements in one array is greater than the other. Learn to optimize the brute force approach by using a difference array, sorting, and binary search to efficiently find valid pairs. Understand the tradeoffs in time and space complexity to apply these techniques in coding interviews.

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 = ...