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How to Solve Remove Max Number of Edges to Keep Graph Fully Traversable Problem
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LeetCode ProblemRemove Max Number of Edges to Keep Graph Fully Traversable
Alice and Bob have an undirected graph of n nodes and three types of edges: Given an array edges where edges[i] = [typei, ui, vi] represents a bidirectional edge of type typei between nodes ui and vi, find the maximum number of edges you can remove so that after removing the edges, the graph can still be fully traversed by both Alice and Bob. The graph is fully traversed by Alice and Bob if starting from any node, they can reach all other nodes. Return the maximum number of edges you can remove, or return -1 if Alice and Bob cannot fully traverse the graph.
Union FindGraph
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Problem Breakdown
Understanding the Remove Max Number of Edges to Keep Graph Fully Traversable Problem
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Problem Statement
Alice and Bob have an undirected graph of n nodes and three types of edges: Given an array edges where edges[i] = [typei, ui, vi] represents a bidirectional edge of type typei between nodes ui and vi, find the maximum number of edges you can remove so that after removing the edges, the graph can still be fully traversed by both Alice and Bob. The graph is fully traversed by Alice and Bob if starting from any node, they can reach all other nodes. Return the maximum number of edges you can remove, or return -1 if Alice and Bob cannot fully traverse the graph.
HardProblem #1579
LeetCodeRemove Max Number of Edges to Keep Graph Fully Traversable
Related Topics
Union FindGraph
How Phantom Code Helps
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Examples
# Example 1
Input
n = 4, edges = [[3,1,2],[3,2,3],[1,1,3],[1,2,4],[1,1,2],[2,3,4]]
Output
2
# Example 2
Input
n = 4, edges = [[3,1,2],[3,2,3],[1,1,4],[2,1,4]]
Output
0
# Example 3
Input
n = 4, edges = [[3,2,3],[1,1,2],[2,3,4]]
Output
-1
Constraints
1 <= n <= 105
1 <= edges.length <= min(105, 3 * n * (n - 1) / 2)
edges[i].length == 3
1 <= typei <= 3
1 <= ui < vi <= n
All tuples (typei, ui, vi) are distinct.
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Solve Remove Max Number of Edges to Keep Graph Fully Traversable — Alice and Bob have an undirected graph of n nodes and three types of edges: Give...
Here's the optimal approach using Union Find:
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 Remove Max Number of Edges to Keep Graph Fully Traversable and using Phantom Code during coding interviews.
How does Phantom Code help me solve coding problems like Remove Max Number of Edges to Keep Graph Fully Traversable 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 Remove Max Number of Edges to Keep Graph Fully Traversable?
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 Remove Max Number of Edges to Keep Graph Fully Traversable?
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 Remove Max Number of Edges to Keep Graph Fully Traversable 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 Remove Max Number of Edges to Keep Graph Fully Traversable 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 Remove Max Number of Edges to Keep Graph Fully Traversable 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 Remove Max Number of Edges to Keep Graph Fully Traversable 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 Remove Max Number of Edges to Keep Graph Fully Traversable 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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