Introduction

In this blog post, we will explore how to solve the LeetCode problem "1938" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

There is a rooted tree consisting of n nodes numbered 0 to n - 1. Each node's number denotes its unique genetic value (i.e. the genetic value of node x is x). The genetic difference between two genetic values is defined as the bitwise-XOR of their values. You are given the integer array parents, where parents[i] is the parent for node i. If node x is the root of the tree, then parents[x] == -1. You are also given the array queries where queries[i] = [nodei, vali]. For each query i, find the maximum genetic difference between vali and pi, where pi is the genetic value of any node that is on the path between nodei and the root (including nodei and the root). More formally, you want to maximize vali XOR pi. Return an array ans where ans[i] is the answer to the ith query. Example 1: Input: parents = [-1,0,1,1], queries = [[0,2],[3,2],[2,5]] Output: [2,3,7] Explanation: The queries are processed as follows: - [0,2]: The node with the maximum genetic difference is 0, with a difference of 2 XOR 0 = 2. - [3,2]: The node with the maximum genetic difference is 1, with a difference of 2 XOR 1 = 3. - [2,5]: The node with the maximum genetic difference is 2, with a difference of 5 XOR 2 = 7. Example 2: Input: parents = [3,7,-1,2,0,7,0,2], queries = [[4,6],[1,15],[0,5]] Output: [6,14,7] Explanation: The queries are processed as follows: - [4,6]: The node with the maximum genetic difference is 0, with a difference of 6 XOR 0 = 6. - [1,15]: The node with the maximum genetic difference is 1, with a difference of 15 XOR 1 = 14. - [0,5]: The node with the maximum genetic difference is 2, with a difference of 5 XOR 2 = 7. Constraints: 2 <= parents.length <= 105 0 <= parents[i] <= parents.length - 1 for every node i that is not the root. parents[root] == -1 1 <= queries.length <= 3 104 0 <= nodei <= parents.length - 1 0 <= vali <= 2 105

Explanation

Here's the solution to the problem, including the high-level approach, complexity analysis, and the complete Python code.

High-Level Approach:

• Path Traversal: For each query (node, val), traverse the path from the given node to the root of the tree.
• XOR Calculation: Calculate the XOR of val with each node's genetic value along the path.
• Maximum Tracking: Maintain and update the maximum XOR value encountered during the path traversal.

Complexity Analysis:

• Runtime Complexity: O(Q H), where Q is the number of queries and H is the maximum height of the tree. In the worst case (skewed tree), H can be equal to N (number of nodes), leading to O(Q N).
• Storage Complexity: O(1), excluding the output array.

Code

    def maxGeneticDifference(parents, queries):
    """
    Calculates the maximum genetic difference for each query.

    Args:
        parents: A list representing the parent of each node.
        queries: A list of queries, where each query is a list [node, val].

    Returns:
        A list of integers representing the maximum genetic difference for each query.
    """

    n = len(parents)
    results = []

    for node, val in queries:
        max_xor = 0
        current_node = node

        while current_node != -1:
            max_xor = max(max_xor, val ^ current_node)
            current_node = parents[current_node]

        results.append(max_xor)

    return results