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Solution: Count Pairs in Two Arrays

Understand how to count all pairs of indexes (i, j) from two integer arrays where the sum of elements in one is greater than the other. Learn to optimize the solution by sorting a difference array and applying binary search to efficiently find valid pairs, reducing time complexity from quadratic to logarithmic scale.

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 = ...