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Grokking the Coding Interview Patterns

Solution: Count Pairs in Two Arrays

Understand how to count pairs of indexes from two integer arrays where the sum of elements from one array exceeds that of the other. Learn to optimize the brute force approach by using a difference array, sorting, and binary search to improve time complexity from quadratic to O(n log n). This lesson helps you master sorting and binary search to solve such pair-counting problems efficiently.

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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 = ...