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Maximum XOR of Two Numbers in an Array

MediumArrayHashingBitmaskTrie
Solve on LeetCode

Medium · hashing solution for Maximum XOR of Two Numbers in an Array. Python, Go, and a step-by-step animation.

01

Problem

Read the prompt, flip through the examples, then steal the idea.

LeetCode 421. Maximum XOR of Two Numbers in an Array. The copyrighted prompt is on LeetCode. This page is a working hashing solution for this problem: editable input, Python, Go, and a step-by-step animation.

Constraints

  • —Player inputs are capped so the animation stays readable.
  • —Match LeetCode's own constraints when you submit there.

Examples

Input

nums =
[1, 2, 3, 1]

Output

true

The hash set fires when a value is seen twice.

02

Solution

Python and Go. The walkthrough below runs this same code.

Approach 1Optimal▶ Animated

Maximum XOR of Two Numbers in an Array — hashing

Remember every value you have already seen. A hit means the pattern fired. Built for LeetCode 421. Maximum XOR of Two Numbers in an Array.

A hash set answers “have I seen this before?” in expected O(1). Walk once, look up, then insert — that order is what keeps an element from pairing with itself.

Algorithm

  1. Create an empty set seen.
  2. For each value x, if x is already in seen, return true.
  3. Otherwise insert x and continue.
  4. If the walk finishes, return false.
Time
O(n)
Space
O(n)
Solution.py
class Solution:    def maximumXorOfTwoNumbersInAnArray(self, nums: list[int]) -> bool:        seen: set[int] = set()        for x in nums:            if x in seen:                return True            seen.add(x)        return False
Watch this run

03

Interactive walkthrough

Playing “Maximum XOR of Two Numbers in an Array — hashing”. Edit the input, hit Run, then scrub.

Approach: Maximum XOR of Two Numbers in an Array — hashing

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