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How to Solve Number of Operations to Make Network Connected Problem
Master the Number of Operations to Make Network Connected LeetCode problem with undetectable real-time assistance. Get instant solutions and explanations during your coding interviews.
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Start Free for WindowsMedium#1319
LeetCode ProblemNumber of Operations to Make Network Connected
There are n computers numbered from 0 to n - 1 connected by ethernet cables connections forming a network where connections[i] = [ai, bi] represents a connection between computers ai and bi. Any computer can reach any other computer directly or indirectly through the network. You are given an initial computer network connections. You can extract certain cables between two directly connected computers, and place them between any pair of disconnected computers to make them directly connected. Return the minimum number of times you need to do this in order to make all the computers connected. If it is not possible, return -1.
Depth-First SearchBreadth-First SearchUnion FindGraph
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Problem Breakdown
Understanding the Number of Operations to Make Network Connected Problem
Let's break down this LeetCode problem and understand what makes it challenging in interview settings.
Problem Statement
There are n computers numbered from 0 to n - 1 connected by ethernet cables connections forming a network where connections[i] = [ai, bi] represents a connection between computers ai and bi. Any computer can reach any other computer directly or indirectly through the network. You are given an initial computer network connections. You can extract certain cables between two directly connected computers, and place them between any pair of disconnected computers to make them directly connected. Return the minimum number of times you need to do this in order to make all the computers connected. If it is not possible, return -1.
MediumProblem #1319
LeetCodeNumber of Operations to Make Network Connected
Related Topics
Depth-First SearchBreadth-First SearchUnion FindGraph
How Phantom Code Helps
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Examples
# Example 1
Input
n = 4, connections = [[0,1],[0,2],[1,2]]
Output
1
# Example 2
Input
n = 6, connections = [[0,1],[0,2],[0,3],[1,2],[1,3]]
Output
2
# Example 3
Input
n = 6, connections = [[0,1],[0,2],[0,3],[1,2]]
Output
-1
Constraints
1 <= n <= 105
1 <= connections.length <= min(n * (n - 1) / 2, 105)
connections[i].length == 2
0 <= ai, bi < n
ai != bi
There are no repeated connections.
No two computers are connected by more than one cable.
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Solve Number of Operations to Make Network Connected — There are n computers numbered from 0 to n - 1 connected by ethernet cables conn...
Here's the optimal approach using Depth-First Search:
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 Number of Operations to Make Network Connected and using Phantom Code during coding interviews.
How does Phantom Code help me solve coding problems like Number of Operations to Make Network Connected 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 Number of Operations to Make Network Connected?
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 Number of Operations to Make Network Connected?
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 Number of Operations to Make Network Connected 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 Number of Operations to Make Network Connected 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 Number of Operations to Make Network Connected 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 Number of Operations to Make Network Connected 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 Number of Operations to Make Network Connected 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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