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HomeLeetCode ProblemsMaximum Path Quality of a Graph
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How to Solve Maximum Path Quality of a Graph Problem

Master the Maximum Path Quality of a Graph LeetCode problem with undetectable real-time assistance. Get instant solutions and explanations during your coding interviews.

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Hard#2065
LeetCode Problem

Maximum Path Quality of a Graph

There is an undirected graph with n nodes numbered from 0 to n - 1 (inclusive). You are given a 0-indexed integer array values where values[i] is the value of the ith node. You are also given a 0-indexed 2D integer array edges, where each edges[j] = [uj, vj, timej] indicates that there is an undirected edge between the nodes uj and vj, and it takes timej seconds to travel between the two nodes. Finally, you are given an integer maxTime. A valid path in the graph is any path that starts at node 0, ends at node 0, and takes at most maxTime seconds to complete. You may visit the same node multiple times. The quality of a valid path is the sum of the values of the unique nodes visited in the path (each node's value is added at most once to the sum). Return the maximum quality of a valid path. Note: There are at most four edges connected to each node.

ArrayBacktrackingGraph

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Problem Breakdown

Understanding the Maximum Path Quality of a Graph Problem

Let's break down this LeetCode problem and understand what makes it challenging in interview settings.

Problem Statement

There is an undirected graph with n nodes numbered from 0 to n - 1 (inclusive). You are given a 0-indexed integer array values where values[i] is the value of the ith node. You are also given a 0-indexed 2D integer array edges, where each edges[j] = [uj, vj, timej] indicates that there is an undirected edge between the nodes uj and vj, and it takes timej seconds to travel between the two nodes. Finally, you are given an integer maxTime. A valid path in the graph is any path that starts at node 0, ends at node 0, and takes at most maxTime seconds to complete. You may visit the same node multiple times. The quality of a valid path is the sum of the values of the unique nodes visited in the path (each node's value is added at most once to the sum). Return the maximum quality of a valid path. Note: There are at most four edges connected to each node.

HardProblem #2065
LeetCode

Maximum Path Quality of a Graph

Related Topics

ArrayBacktrackingGraph

How Phantom Code Helps

Get real-time assistance for Maximum Path Quality of a Graph problems during coding interviews. Phantom Code provides instant solutions and explanations.

Examples

# Example 1

Input
values = [0,32,10,43], edges = [[0,1,10],[1,2,15],[0,3,10]], maxTime = 49
Output
75

# Example 2

Input
values = [5,10,15,20], edges = [[0,1,10],[1,2,10],[0,3,10]], maxTime = 30
Output
25

# Example 3

Input
values = [1,2,3,4], edges = [[0,1,10],[1,2,11],[2,3,12],[1,3,13]], maxTime = 50
Output
7

Constraints

n == values.length
1 <= n <= 1000
0 <= values[i] <= 108
0 <= edges.length <= 2000
edges[j].length == 3
0 <= uj < vj <= n - 1
10 <= timej, maxTime <= 100
All the pairs [uj, vj] are unique.
There are at most four edges connected to each node.
The graph may not be connected.

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Solve Maximum Path Quality of a Graph — There is an undirected graph with n nodes numbered from 0 to n - 1 (inclusive). ...

Here's the optimal approach using Array:

def solve(input):
# Optimal O(n) solution
return result

Time: O(n)  |  Space: O(n)

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Frequently Asked Questions

Common questions about solving Maximum Path Quality of a Graph and using Phantom Code during coding interviews.

How does Phantom Code help me solve coding problems like Maximum Path Quality of a Graph during interviews?
Phantom Code 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 Maximum Path Quality of a Graph?
Phantom Code 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.
Can Phantom Code help me communicate my solution for problems like Maximum Path Quality of a Graph?
Yes. Phantom Code 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 assist with different programming languages for Maximum Path Quality of a Graph type problems?
Phantom Code supports 11 programming languages including Python, Java, C++, JavaScript, TypeScript, Go, Rust, Ruby, Swift, Kotlin, and C#. Set your preferred language and get idiomatic solutions.
What coding mistakes does Phantom Code help me avoid during Maximum Path Quality of a Graph interviews?
Phantom Code 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.
Is Phantom Code detectable when solving problems like Maximum Path Quality of a Graph during live interviews?
No. Phantom Code runs as an invisible desktop overlay that doesn't appear in screen shares, recordings, or proctoring software. It works with Zoom, HackerRank, CodeSignal, CoderPad, and all major platforms.
How does Phantom Code help when I'm struggling with Maximum Path Quality of a Graph 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 work for the coding platforms used in Maximum Path Quality of a Graph interviews?
Yes. Phantom Code works with all major coding platforms including LeetCode, HackerRank, CodeSignal, CoderPad, HackerEarth, and any browser-based coding environment.
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