Maximum Strong Pair XOR II

Maximum Strong Pair XOR II

1. What is this problem about?

Maximum Strong Pair XOR II is a more advanced version of the strong pair problem. Like its predecessor, it requires finding the maximum bitwise XOR value from a pair of integers (x, y) in an array that satisfies the "strong" condition: |x - y| <= min(x, y). However, this "HARD" version typically involves much larger input arrays, meaning a simple brute-force approach will be too slow. You must find a way to efficiently query for the best XOR partner for each number while respecting the sliding numerical window defined by the strong pair rule.

2. Why is this asked in interviews?

This is a high-level "Maximum Strong Pair XOR II interview question" because it separates candidates who know basic algorithms from those who can implement complex data structures under pressure. Companies like ZScaler use it to test mastery over Tries (Prefix Trees) and the sliding window technique. It demonstrates your ability to optimize bitwise queries and manage a dynamic set of candidates (numbers currently in the "strong" range) as you iterate through a sorted dataset.

3. Algorithmic pattern used

The "Array, Hash Table, Trie, Sliding Window, Bit Manipulation interview pattern" is essential here. First, sorting the array is crucial as it allows you to transform the condition |x - y| <= min(x, y) into a predictable range (if x < y, then y <= 2x). You then use a sliding window to maintain a set of numbers that are currently "strong" relative to your current element. A Trie is used to store the binary bits of these numbers, allowing you to find the maximum XOR partner in logarithmic time by greedily traversing the Trie for opposite bits.

4. Example explanation

Consider a sorted array: [5, 6, 10, 12].

• For x = 5, the strong condition is y <= 2 * 5 = 10. Valid partners are {6, 10}.
• For x = 6, the strong condition is y <= 2 * 6 = 12. Valid partners are {10, 12}. As we move from x=5 to x=6, we might add 12 to our Trie and potentially remove 5 if it was being used as a partner for something else. When looking at x=10 (binary 1010), we would search the Trie for a partner that has a '0' in the first position, a '1' in the second, and so on, to maximize the XOR result, while only considering numbers currently in the [10, 20] range.

5. Common mistakes candidates make

The most frequent mistake in this "Maximum Strong Pair XOR II coding problem" is failing to efficiently remove elements from the Trie as they fall out of the sliding window. Simply adding elements is easy, but maintaining a frequency count in Trie nodes is necessary to "delete" numbers that are no longer "strong." Another mistake is not handling the bit-length correctly—since we are maximizing XOR, we must consider a consistent number of bits (like 20 or 30) for all entries in the Trie.

6. Interview preparation tip

Focus on mastering the "XOR Trie" pattern. This is a specific application of a Trie where you store numbers bit by bit. Practice implementing a Trie with insert and remove methods that update node counts. Also, get comfortable with the sliding window technique on sorted arrays. Being able to explain why sorting helps simplify the absolute value inequality will show the interviewer you have a strong grasp of both mathematics and algorithm design.