Advantage Shuffle

Problem Description

You are given two integer arrays nums1 and nums2 both of the same length. The advantage of nums1 with respect to nums2 is the number of indices i for which nums1[i] > nums2[i]. Return any permutation of nums1 that maximizes its advantage with respect to nums2.

Key Insights

• The goal is to rearrange nums1 such that as many elements as possible are greater than the corresponding elements in nums2.
• Sorting both arrays allows for a systematic comparison and pairing of elements.
• A greedy approach can be used to match the smallest available element in nums1 that is greater than the current element in nums2, while placing smaller elements in positions of nums2 where they are not advantageous.

Space and Time Complexity

Time Complexity: O(n log n) - due to sorting both arrays.
Space Complexity: O(n) - for storing the result and auxiliary data structures.

Solution

To solve the problem, we can use a greedy algorithm combined with sorting. The steps are as follows:

1. Sort both nums1 and nums2.
2. Use a two-pointer technique to traverse both sorted arrays.
3. For each element in nums2, find the smallest element in nums1 that is greater than it. If such an element is found, it is placed in the result; otherwise, place the smallest remaining element from nums1.
4. This ensures we maximize the advantage by always attempting to use the smallest possible element in nums1 that can still win against an element in nums2.

Code Solutions