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Grokking the Coding Interview Patterns in C++

Solution: Count Pairs in Two Arrays

Understand how to efficiently count pairs of indices where the sum of elements in one array exceeds that in another. Explore using a difference array, sorting, and binary search to optimize the solution beyond brute force, reducing complexity to O(n log n). This lesson guides you through the implementation details and analysis.

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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 = nums1.length == nums2.length

  • 1≤n≤1031 \leq n \leq 10^3 ...