Binary Trie

1. Introduction

   1. Setting
      Given an array $v$, find the maximum XOR of two numbers from array $v$.

   2. Brute-force Solution
      A trivial brute-force approach is $O(N^2)$: iterate over each pair of numbers and take the maximum XOR among all pairs.

   3. Idea
      A binary trie stores all the numbers in a trie data structure. For each number, we can find the maximum XOR against all other numbers in $v$ in $O(b)$ time, where $b$ is the number of bits. This reduces the overall complexity to $O(N\cdot b)$.