Maximum XOR of Two Numbers in an Array — LeetCode 421 Python Solution
MediumBit ManipulationTrieArrayHash Table
- Problem
- #421
- Pattern
- Trie
- Reading time
- 6 min
- Source
- leetcode.com
The problem
Given an integer array nums, return the maximum result of nums[i] XOR nums[j], where 0 <= i <= j < n.
Example
- Input
- nums = [3,10,5,25,2,8]
- Output
- 28
- Explanation
- The maximum result is 5 XOR 25 = 28.
Python solution
Python
class Trie:
__slots__ = ("children",)
def __init__(self):
self.children: List[Trie | None] = [None, None]
def insert(self, x: int):
node = self
for i in range(30, -1, -1):
v = x >> i & 1
if node.children[v] is None:
node.children[v] = Trie()
node = node.children[v]
def search(self, x: int) -> int:
node = self
ans = 0
for i in range(30, -1, -1):
v = x >> i & 1
if node.children[v ^ 1]:
ans |= 1 << i
node = node.children[v ^ 1]
else:
node = node.children[v]
return ans
class Solution:
def findMaximumXOR(self, nums: List[int]) -> int:
trie = Trie()
for x in nums:
trie.insert(x)
return max(trie.search(x) for x in nums)Complexity
| Measure | Complexity |
|---|---|
| Time | O(n) |
| Space | O(n) auxiliary |
Pattern: Trie
Store a set of words by their shared prefixes so lookups cost the length of the word. LeetCode 421. Maximum XOR of Two Numbers in an Array is filed here because LeetCode tags it Trie, which is the vocabulary this hub collects.
The trie guide has the Python template for the pattern and the 49 LeetCode problems that use it.
Related problems
Frequently asked questions
- How hard is LeetCode 421. Maximum XOR of Two Numbers in an Array?
- LeetCode 421. Maximum XOR of Two Numbers in an Array is rated Medium on LeetCode.
- What is the time complexity of LeetCode 421. Maximum XOR of Two Numbers in an Array?
- The Python solution on this page runs in O(n).
- What is the space complexity of LeetCode 421. Maximum XOR of Two Numbers in an Array?
- The Python solution on this page uses O(n) auxiliary space.
- What topics does LeetCode 421. Maximum XOR of Two Numbers in an Array cover?
- LeetCode 421. Maximum XOR of Two Numbers in an Array is tagged Bit Manipulation, Trie, Array and Hash Table on LeetCode.