3702 - Longest Subsequence With Non-Zero Bitwise XOR (Medium)

Problem Link

https://leetcode.com/problems/longest-subsequence-with-non-zero-bitwise-xor

Problem Statement

You are given an integer array nums.

Return the length of the longest subsequence in nums whose bitwise XOR is non-zero. If no such subsequence exists, return 0.

Example 1:

Input: nums = [1,2,3]

Output: 2

Explanation:

One longest subsequence is [2, 3]. The bitwise XOR is computed as 2 XOR 3 = 1, which is non-zero.

Example 2:

Input: nums = [2,3,4]

Output: 3

Explanation:

The longest subsequence is [2, 3, 4]. The bitwise XOR is computed as 2 XOR 3 XOR 4 = 5, which is non-zero.

Constraints:

• 1 <= nums.length <= 1e5
• 0 <= nums[i] <= 1e9

Approach 1: Bit Manipulation

If the XOR of the entire array is non-zero, use all $n$ elements.

If the total XOR is zero: Removing any one non-zero element makes the remaining XOR equal to that removed element, so the answer is $n - 1$.

If every element is zero, every subsequence has XOR zero, so return $0$.

Time Complexity: $O(n)$

Space Complexity: $O(1)$

class Solution:
    def longestSubsequence(self, nums: List[int]) -> int:
        n = len(nums)
        x = 0
        for v in nums: x ^= v
        if x != 0: return n
        if any(v != 0 for v in nums): return n - 1
        return 0