Maximum Strong Pair XOR II

Problem Description

You are given a 0-indexed integer array nums. A pair of integers x and y is called a strong pair if it satisfies the condition: |x - y| <= min(x, y). You need to select two integers from nums such that they form a strong pair and their bitwise XOR is the maximum among all strong pairs in the array. Return the maximum XOR value out of all possible strong pairs in the array nums. Note that you can pick the same integer twice to form a pair.

Key Insights

• A strong pair (x, y) must satisfy the condition |x - y| <= min(x, y).
• This condition implies that the values of x and y must be relatively close to each other, particularly when both values are large.
• The XOR operation can produce high values when the binary representations of the numbers differ significantly.
• We can utilize bit manipulation to find pairs efficiently, considering both the strong pair condition and maximizing the XOR value.

Space and Time Complexity

Time Complexity: O(n^2) in the worst case, but can be optimized to O(n log n) using sorting and a careful selection of pairs.
Space Complexity: O(n) for storing the sorted list or any additional data structures.

Solution

To solve the problem, we can follow these steps:

1. Sort the array nums. This allows us to easily find strong pairs that meet the criteria.
2. Iterate through the sorted array and check each possible pair (nums[i], nums[j]) where j >= i.
3. For each pair, check if it satisfies the strong pair condition.
4. If it does, calculate the XOR of the pair and update the maximum XOR found.
5. Return the maximum XOR after checking all valid pairs.

The main data structure used here is a sorted array, and the algorithm involves a nested loop to check pairs efficiently.

Code Solutions