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Grokking the Coding Interview Patterns in Python

Solution: Count Pairs in Two Arrays

Explore how to efficiently count pairs of indices from two integer arrays where the sum of elements in the first array exceeds that in the second. Understand an optimized approach using difference arrays, sorting, and binary search to reduce time complexity from quadratic to logarithmic scale, helping you solve similar coding interview problems effectively.

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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 ...