# Posts published in “Trie”

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

The answer to the ith query is the maximum bitwise XOR value of xi and any element of nums that does not exceed mi. In other words, the answer is max(nums[j] XOR xi) for all j such that nums[j] <= mi. If all elements in nums are larger than mi, then the answer is -1.

Return an integer array answer where answer.length == queries.length and answer[i] is the answer to the ith query.

Example 1:

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.
2) 1 XOR 2 = 3.
3) 5 XOR 2 = 7.


Example 2:

Input: nums = [5,2,4,6,6,3], queries = [[12,4],[8,1],[6,3]]
Output: [15,-1,5]


Constraints:

• 1 <= nums.length, queries.length <= 105
• queries[i].length == 2
• 0 <= nums[j], xi, mi <= 109

## Solution: Trie on the fly

We can build the trie on the fly by sorting nums in ascending order and queries by its limit, insert nums into the trie up the limit.

Time complexity: O(nlogn + QlogQ)
Space complexity: O(n)

## C++

Given an integer array nums, return the maximum result of nums[i] XOR nums[j], where 0 ≤ i ≤ j < n.

Follow up: Could you do this in O(n) runtime?

Example 1:

Input: nums = [3,10,5,25,2,8]
Output: 28
Explanation: The maximum result is 5 XOR 25 = 28.

Example 2:

Input: nums = 
Output: 0


Example 3:

Input: nums = [2,4]
Output: 6


Example 4:

Input: nums = [8,10,2]
Output: 10


Example 5:

Input: nums = [14,70,53,83,49,91,36,80,92,51,66,70]
Output: 127


Constraints:

• 1 <= nums.length <= 2 * 104
• 0 <= nums[i] <= 231 - 1

## Solution: Trie

Time complexity: O(31*2*n)
Space complexity: O(31*2*n)