Find Maximum Balanced XOR Subarray Length - Video Solutions
Find Maximum Balanced XOR Subarray Length | LeetCode 3755 | Weekly Contest 477
Find Maximum Balanced XOR Subarray Length - Video Solution
Watch 9 video solutions for Find Maximum Balanced XOR Subarray Length, a medium level problem involving Array, Hash Table, Bit Manipulation. This walkthrough by Sanyam IIT Guwahati has 905 views views. Want to try solving it yourself? Practice on FleetCode or read the detailed text solution.
Problem Statement
Given an integer array nums, return the length of the longest subarray that has a bitwise XOR of zero and contains an equal number of even and odd numbers. If no such subarray exists, return 0.
Example 1:
Input: nums = [3,1,3,2,0]
Output: 4
Explanation:
The subarray [1, 3, 2, 0] has bitwise XOR 1 XOR 3 XOR 2 XOR 0 = 0 and contains 2 even and 2 odd numbers.
Example 2:
Input: nums = [3,2,8,5,4,14,9,15]
Output: 8
Explanation:
The whole array has bitwise XOR 0 and contains 4 even and 4 odd numbers.
Example 3:
Input: nums = [0]
Output: 0
Explanation:
No non-empty subarray satisfies both conditions.
Constraints:
1 <= nums.length <= 1050 <= nums[i] <= 109
Approach Overview
Problem Overview: You are given an array of integers and need to find the maximum length subarray whose XOR result is balanced (effectively zero). The task is to identify the longest contiguous segment where the cumulative XOR cancels out.
Approach 1: Brute Force Enumeration (O(n2) time, O(1) space)
The simplest approach checks every possible subarray. Start from each index i, keep a running XOR while expanding the end index j, and update the maximum length whenever the XOR becomes 0. This works because the XOR of a subarray can be computed incrementally as you extend the window. The downside is quadratic time since every starting index explores all remaining elements. This method is useful for verifying correctness or understanding how XOR behaves over ranges in an array, but it does not scale for large inputs.
Approach 2: Prefix XOR + Hash Table (O(n) time, O(n) space)
The optimal solution uses the prefix XOR concept. Maintain a running value prefixXor where prefixXor[i] represents the XOR of elements from index 0 to i. If two indices have the same prefix XOR, the XOR of the subarray between them is zero because the values cancel out. Store the first occurrence of each prefix XOR in a hash table. When the same XOR appears again at index i, the subarray between the stored index and i has XOR equal to zero. Update the maximum length accordingly.
This method relies on the associative property of XOR and the ability to compare prefix states efficiently. Each element is processed once, and hash lookups are constant time on average. The algorithm combines ideas from prefix sum techniques with bit manipulation, making it both efficient and interview-friendly.
Recommended for interviews: Start by describing the brute force method to show you understand how XOR behaves across subarrays. Then move to the prefix XOR + hash table optimization. Interviewers expect the O(n) solution because it demonstrates familiarity with prefix techniques and hash-based indexing patterns commonly used for subarray problems.
Complexity Analysis
| Approach | Time | Space | When to Use |
|---|---|---|---|
| Brute Force Subarray XOR | O(n^2) | O(1) | Small arrays or validating logic while learning XOR properties |
| Prefix XOR + Hash Table | O(n) | O(n) | General case and expected interview solution for large inputs |