Find the Distance Value Between Two Arrays

Problem Description

Given two integer arrays arr1 and arr2, and the integer d, return the distance value between the two arrays. The distance value is defined as the number of elements arr1[i] such that there is not any element arr2[j] where |arr1[i]-arr2[j]| <= d.

Key Insights

• The problem requires comparing elements from two arrays based on their absolute differences.
• A brute-force approach would involve nested loops, which could lead to inefficient solutions for larger arrays.
• Sorting one of the arrays allows for efficient searching of valid distances using binary search.
• The use of binary search reduces the need to compare each element in arr1 against every element in arr2.

Space and Time Complexity

Time Complexity: O(n log n + m log m), where n is the length of arr1 and m is the length of arr2 (due to sorting and binary search). Space Complexity: O(1) for the binary search approach (excluding the input space).

Solution

To solve this problem, we can sort one of the arrays and then use binary search for each element in the other array. The algorithm steps are as follows:

1. Sort arr2.
2. For each element in arr1, use binary search to find the position in arr2 where the corresponding distance condition holds.
3. Count the elements in arr1 that do not have any corresponding elements in arr2 within the distance d.

Code Solutions