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Grokking the Coding Interview Patterns

Solution: Count Pairs in Two Arrays

Explore how to count index pairs in two integer arrays where the sum of elements in one array exceeds the other. Understand how to optimize from a brute force approach to an O(n log n) solution by using a difference array, sorting, and binary search techniques to efficiently identify valid pairs.

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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 = ...