Is Maximum Subarray XOR with Bounded Range easy or hard?

This problem is considered hard because it combines several advanced techniques: prefix XOR transformation, maximum XOR queries with a trie, and sliding window constraints. Implementing insertion and deletion in the trie correctly is the main challenge.

Maximum Subarray XOR with Bounded Range Python/Java solution

Typical implementations compute prefix XOR values, maintain a binary trie for candidate prefixes, and update the trie as the sliding window moves. The same logic works across Python, Java, C++, and Go with O(n log A) complexity.

How to solve Maximum Subarray XOR with Bounded Range in O(n)?

A true O(n) solution is uncommon because maximizing XOR typically requires bit-level traversal. Using a prefix XOR array with a bitwise trie gives O(n log A), which is effectively linear for fixed integer sizes such as 32-bit values.

What is the best approach for Maximum Subarray XOR with Bounded Range?

The most efficient approach combines prefix XOR with a bitwise trie while maintaining a sliding window of valid prefix indices. Each step inserts and removes prefix values so the subarray length stays within [L, R]. Trie queries maximize XOR in O(log A) time, giving an overall complexity of O(n log A).

Is Maximum Subarray XOR with Bounded Range asked at Google/Amazon/Meta?

Problems involving maximum XOR, prefix XOR arrays, and trie-based bit optimization frequently appear in interviews at companies like Google, Amazon, and Meta. Variants often include constraints such as subarray length limits or sliding window conditions.

What data structure is used in Maximum Subarray XOR with Bounded Range?

The key data structure is a bitwise trie (binary trie) used to compute maximum XOR pairs efficiently. The algorithm also relies on prefix XOR arrays and a sliding window or queue to maintain valid indices for the bounded range.

What is the time complexity of Maximum Subarray XOR with Bounded Range?

The optimal solution runs in O(n log A) time, where n is the array length and A is the maximum integer value range (typically up to 2^31). Each element performs one trie insertion, one removal, and one maximum-XOR query.

Description Hints 3 Solution Video 24:08

3845. Maximum Subarray XOR with Bounded Range

Hard32.3% acceptance

You are given a non-negative integer array nums and an integer k.

You must select a subarray of nums such that the difference between its maximum and minimum elements is at most k. The value of this subarray is the bitwise XOR of all elements in the subarray.

Return an integer denoting the maximum possible value of the selected subarray.

Example 1:

Input: nums = [5,4,5,6], k = 2

Output: 7

Explanation:

Select the subarray [5, 4, 5, 6].
The difference between its maximum and minimum elements is 6 - 4 = 2 <= k.
The value is 4 XOR 5 XOR 6 = 7.

Example 2:

Input: nums = [5,4,5,6], k = 1

Output: 6

Explanation:

Select the subarray [5, 4, 5, 6].
The difference between its maximum and minimum elements is 6 - 6 = 0 <= k.
The value is 6.

Constraints:

1 <= nums.length <= 4 * 10⁴
0 <= nums[i] < 2¹⁵
0 <= k < 2¹⁵

Topics

Hints open one at a time

Hint 1

Maintain an active window such that the difference between its maximum and minimum is at most k

Hint 2

For all valid subarray-start indices i, insert their prefix xors pref[i] into a trie (use pref[0] = 0, pref[i + 1] = pref[i] ^ nums[i]); keep counts per node to support deletions as L moves

Hint 3

For each right index r, query the trie with pref[r + 1] to get the maximum pref[r + 1] ^ pref[l] for l in [L, r]

24:08

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1class Solution:
2    def maxXor(self, nums: list[int], k: int) -> int:
3        

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Examples

Case 1Case 2

Input

[5,4,5,6]
2

Input

[5,4,5,6]
1

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