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Maximum XOR After Operations

Difficulty: Medium

Problem Description

You are given a 0-indexed integer array nums. In one operation, select any non-negative integer x and an index i, then update nums[i] to be equal to nums[i] AND (nums[i] XOR x). Return the maximum possible bitwise XOR of all elements of nums after applying the operation any number of times.

Key Insights

  • The operation allows for modifying elements in such a way that we can reduce their values while preserving certain bits.
  • The XOR operation is maximized by ensuring that as many bits as possible are set to 1 in the final result.
  • Each number can be transformed multiple times to potentially yield a higher overall XOR result.
  • The goal is to find a combination of transformations that maximizes the XOR of the entire array.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

The solution involves iterating through the array and calculating the cumulative XOR of all elements. The operation can be applied an arbitrary number of times, but ultimately, the maximum achievable XOR can be derived from the original elements. The idea is to keep track of the bits that can be set to 1 through the operations, ensuring that the maximum possible combination of bits is achieved.

Code Solutions

def maximumXOR(nums):
    result = 0
    for num in nums:
        result ^= num  # Calculate the XOR of all elements
    return result  # Return the maximum XOR possible

# Example Usage
print(maximumXOR([3, 2, 4, 6]))  # Output: 7
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