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How to Solve Kth Smallest Path XOR Sum Problem
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Hard#3590
LeetCode ProblemKth Smallest Path XOR Sum
You are given an undirected tree rooted at node 0 with n nodes numbered from 0 to n - 1. Each node i has an integer value vals[i], and its parent is given by par[i]. The path XOR sum from the root to a node u is defined as the bitwise XOR of all vals[i] for nodes i on the path from the root node to node u, inclusive. You are given a 2D integer array queries, where queries[j] = [uj, kj]. For each query, find the kjth smallest distinct path XOR sum among all nodes in the subtree rooted at uj. If there are fewer than kj distinct path XOR sums in that subtree, the answer is -1. Return an integer array where the jth element is the answer to the jth query. In a rooted tree, the subtree of a node v includes v and all nodes whose path to the root passes through v, that is, v and its descendants.
ArrayTreeDepth-First SearchOrdered Set
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Problem Breakdown
Understanding the Kth Smallest Path XOR Sum Problem
Let's break down this LeetCode problem and understand what makes it challenging in interview settings.
Problem Statement
You are given an undirected tree rooted at node 0 with n nodes numbered from 0 to n - 1. Each node i has an integer value vals[i], and its parent is given by par[i]. The path XOR sum from the root to a node u is defined as the bitwise XOR of all vals[i] for nodes i on the path from the root node to node u, inclusive. You are given a 2D integer array queries, where queries[j] = [uj, kj]. For each query, find the kjth smallest distinct path XOR sum among all nodes in the subtree rooted at uj. If there are fewer than kj distinct path XOR sums in that subtree, the answer is -1. Return an integer array where the jth element is the answer to the jth query. In a rooted tree, the subtree of a node v includes v and all nodes whose path to the root passes through v, that is, v and its descendants.
HardProblem #3590
LeetCodeKth Smallest Path XOR Sum
Related Topics
ArrayTreeDepth-First SearchOrdered Set
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Examples
# Example 1
Input
par = [-1,0,0], vals = [1,1,1], queries = [[0,1],[0,2],[0,3]]
Output
[0,1,-1]
# Example 2
Input
par = [-1,0,1], vals = [5,2,7], queries = [[0,1],[1,2],[1,3],[2,1]]
Output
[0,7,-1,0]
Constraints
1 <= n == vals.length <= 5 * 104
0 <= vals[i] <= 105
par.length == n
par[0] == -1
0 <= par[i] < n for i in [1, n - 1]
1 <= queries.length <= 5 * 104
queries[j] == [uj, kj]
0 <= uj < n
1 <= kj <= n
The input is generated such that the parent array par represents a valid tree.
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Solve Kth Smallest Path XOR Sum — You are given an undirected tree rooted at node 0 with n nodes numbered from 0 t...
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def solve(input):
# Optimal O(n) solution
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Time: O(n) | Space: O(n)
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Frequently Asked Questions
Common questions about solving Kth Smallest Path XOR Sum and using Phantom Code AI during coding interviews.
How does Phantom Code AI help me solve coding problems like Kth Smallest Path XOR Sum during interviews?
Phantom Code AI generates complete solutions instantly with proper complexity analysis, letting you focus on explaining your approach and demonstrating problem-solving skills rather than getting stuck on implementation details during high-pressure situations.
What if the interviewer asks follow-up questions or modifications to problems like Kth Smallest Path XOR Sum?
Phantom Code AI adapts in real-time. Screenshot the modified problem or use audio mode to capture the interviewer's follow-up, and get an updated solution within seconds — including edge cases and optimizations.
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Yes. Phantom Code AI provides step-by-step approach explanations with 3 progressive thoughts, so you can walk through your solution naturally. It also provides time and space complexity analysis to discuss trade-offs.
How does Phantom Code AI assist with different programming languages for Kth Smallest Path XOR Sum type problems?
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What coding mistakes does Phantom Code AI help me avoid during Kth Smallest Path XOR Sum interviews?
Phantom Code AI catches common mistakes like off-by-one errors, missing edge cases, incorrect base conditions, and suboptimal approaches. It provides clean, well-structured code that handles all edge cases.
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How does Phantom Code AI help when I'm struggling with Kth Smallest Path XOR Sum style questions under pressure?
The AI provides structured guidance: first the approach (what algorithm/data structure to use and why), then the implementation with clean code, and finally complexity analysis. This helps you think clearly even under pressure.
Does Phantom Code AI work for the coding platforms used in Kth Smallest Path XOR Sum interviews?
Yes. Phantom Code AI works with all major coding platforms including LeetCode, HackerRank, CodeSignal, CoderPad, HackerEarth, and any browser-based coding environment.
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