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Grokking the Coding Interview Patterns in Python

Solution: Count Pairs in Two Arrays

Explore how to count pairs of indices in two integer arrays where the sum of pairs in one array exceeds the other. Learn to optimize from brute force O(n²) to O(n log n) using sorting, difference arrays, and binary search. This lesson builds your ability to apply sorting and search techniques for efficient pair comparison.

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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 = ...