How hard is LeetCode 1707. Maximum XOR With an Element From Array?

LeetCode 1707. Maximum XOR With an Element From Array is rated Hard on LeetCode.

What is the time complexity of LeetCode 1707. Maximum XOR With an Element From Array?

The Python solution on this page runs in O(m \times \log m + n \times (\log n + \log M)).

What is the space complexity of LeetCode 1707. Maximum XOR With an Element From Array?

The Python solution on this page uses O(n \times \log M) auxiliary space.

What topics does LeetCode 1707. Maximum XOR With an Element From Array cover?

LeetCode 1707. Maximum XOR With an Element From Array is tagged Bit Manipulation, Trie and Array on LeetCode.

Maximum XOR With an Element From Array — LeetCode 1707 Python Solution

HardBit ManipulationTrieArray

Problem: #1707
Pattern: Trie
Reading time: 7 min
Source: leetcode.com

The problem

You are given an array nums consisting of non-negative integers. You are also given a queries array, where queries[i] = [xi, mi].

Example

Input: nums = [0,1,2,3,4], queries = [[3,1],[1,3],[5,6]]
Output: [3,3,7]
Explanation: 1) 0 and 1 are the only two integers not greater than 1. 0 XOR 3 = 3 and 1 XOR 3 = 2. The larger of the two is 3.

Python solution

Python

class Trie:
    __slots__ = ["children"]

    def __init__(self):
        self.children = [None] * 2

    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]
            elif node.children[v]:
                node = node.children[v]
            else:
                return -1
        return ans


class Solution:
    def maximizeXor(self, nums: List[int], queries: List[List[int]]) -> List[int]:
        trie = Trie()
        nums.sort()
        j, n = 0, len(queries)
        ans = [-1] * n
        for i, (x, m) in sorted(zip(range(n), queries), key=lambda x: x[1][1]):
            while j < len(nums) and nums[j] <= m:
                trie.insert(nums[j])
                j += 1
            ans[i] = trie.search(x)
        return ans

Complexity

Measure	Complexity
Time	O(m \times \log m + n \times (\log n + \log M))
Space	O(n \times \log M) auxiliary

Pattern: Trie

Store a set of words by their shared prefixes so lookups cost the length of the word. LeetCode 1707. Maximum XOR With an Element From Array is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Trie.

The trie guide has the Python template for the pattern and the 49 LeetCode problems that use it.

Frequently asked questions

How hard is LeetCode 1707. Maximum XOR With an Element From Array?: LeetCode 1707. Maximum XOR With an Element From Array is rated Hard on LeetCode.
What is the time complexity of LeetCode 1707. Maximum XOR With an Element From Array?: The Python solution on this page runs in O(m \times \log m + n \times (\log n + \log M)).
What is the space complexity of LeetCode 1707. Maximum XOR With an Element From Array?: The Python solution on this page uses O(n \times \log M) auxiliary space.
What topics does LeetCode 1707. Maximum XOR With an Element From Array cover?: LeetCode 1707. Maximum XOR With an Element From Array is tagged Bit Manipulation, Trie and Array on LeetCode.