To minimize malware spread, find the infected node whose removal reduces the total infected count the most. By scanning the graph and using hash lookups, determine how the removal impacts the spread. Utilize DFS or BFS to assess how the malware spreads and the outcome of removing each node.
Problem Statement
In this problem, you are given a network represented as an adjacency matrix graph of size n x n. Each node in the graph can be connected to other nodes, and some nodes are initially infected by malware. When a node is infected, it spreads malware to any directly connected node. Your goal is to minimize the spread of malware by removing exactly one node from the initially infected set.
After removing one infected node, the spread of malware continues. You need to find which node, when removed, results in the minimum number of infected nodes. If multiple nodes lead to the same result, return the node with the smallest index. The task involves simulating the malware spread to find the optimal node for removal.
Examples
Example 1
Input: graph = [[1,1,0],[1,1,0],[0,0,1]], initial = [0,1]
Output: 0
Example details omitted.
Example 2
Input: graph = [[1,1,0],[1,1,1],[0,1,1]], initial = [0,1]
Output: 1
Example details omitted.
Example 3
Input: graph = [[1,1,0,0],[1,1,1,0],[0,1,1,1],[0,0,1,1]], initial = [0,1]
Output: 1
Example details omitted.
Constraints
- n == graph.length
- n == graph[i].length
- 2 <= n <= 300
- graph[i][j] is 0 or 1.
- graph[i][j] == graph[j][i]
- graph[i][i] == 1
- 1 <= initial.length < n
- 0 <= initial[i] <= n - 1
- All the integers in initial are unique.
Solution Approach
Graph Traversal and Simulation
Use DFS or BFS to simulate the spread of malware from the initially infected nodes. By traversing the graph, mark all the nodes infected by malware. Then, for each infected node, temporarily remove it from the initial set and simulate the spread again, calculating the number of infected nodes after removal.
Node Impact Assessment
For each infected node, assess how its removal impacts the number of newly infected nodes by considering the connections between nodes. Use hash lookups to track the infection status and calculate how the network's connectivity changes after removing an infected node.
Choose the Optimal Node
After evaluating the impact of each infected node's removal, choose the node that minimizes the total number of infected nodes. In case of a tie, return the node with the smallest index, ensuring that the solution is both optimal and efficient.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
The time complexity depends on the number of nodes (n) and the number of connections. The approach involves simulating the spread of malware multiple times, leading to a time complexity of O(n^2) for graph traversal. The space complexity is also O(n^2) due to the storage of the adjacency matrix and infection states.
What Interviewers Usually Probe
- The candidate demonstrates knowledge of graph traversal algorithms like DFS and BFS.
- The candidate can efficiently evaluate the impact of node removal in a graph with multiple infected nodes.
- The candidate correctly optimizes for the minimum number of infections after node removal.
Common Pitfalls or Variants
Common pitfalls
- Failing to account for the spread of malware from all initially infected nodes and only considering the first infected node.
- Overlooking edge cases where removing a node does not reduce the number of infections.
- Not properly simulating the infection spread after node removal, leading to incorrect calculations of the final result.
Follow-up variants
- Consider variations where the number of initially infected nodes can vary or where different network topologies are used.
- Extend the problem to handle multiple malware types or sources of infection.
- Alter the problem to allow multiple nodes to be removed and find the combination that minimizes malware spread.
How GhostInterview Helps
- GhostInterview helps by guiding you through graph traversal techniques, ensuring you understand how to apply DFS/BFS effectively for the problem.
- It provides insight into optimizing graph-based algorithms by removing unnecessary recalculations during node impact assessment.
- The platform allows you to practice simulating real-world scenarios, helping you refine your approach to solving complex graph problems.
Topic Pages
Related GhostInterview Pages
- LeetCode Interview Copilot - Use GhostInterview as a live solver when you want direct help with LeetCode-style coding questions.
- Coding Interview Assistant - See how GhostInterview supports array, string, linked list, graph, and tree interview workflows.
- How GhostInterview Works - Review the screenshot, reasoning, and answer flow before using the solver in a live interview.
FAQ
How do I minimize malware spread in a network of nodes?
To minimize malware spread, you must determine which infected node to remove. Use graph traversal techniques like DFS or BFS to simulate the spread and assess the impact of removing each infected node.
What graph traversal techniques can I use for this problem?
You can use DFS (Depth-First Search) or BFS (Breadth-First Search) to traverse the graph and simulate the spread of malware, ensuring that all connections are considered when assessing node removal.
What should I do if multiple nodes result in the same infection count?
If multiple nodes lead to the same reduction in infection count, return the node with the smallest index to ensure an optimal solution.
How does removing a node affect the malware spread?
Removing a node reduces the number of nodes it can spread malware to, potentially halting the infection from reaching connected nodes. The impact is evaluated by simulating the spread after node removal.
What is the time complexity of solving this problem?
The time complexity of this problem is O(n^2) due to the graph traversal for each infected node and the simulation of the infection spread. Space complexity is also O(n^2) for storing the graph and infection states.
Need direct help with Minimize Malware Spread II instead of spending more time grinding it?
Download GhostInterview when you want a LeetCode solver, not another long practice loop. Capture Minimize Malware Spread II from a screenshot, get the answer path and complexity, and use supported stealth workflows that stay outside captured layers.
Capture the prompt fast instead of rewriting the problem by hand.
Get the solution path, trade-offs, and complexity summary in one pass.
Stay outside captured layers on supported screen-share workflows.
Stay in the same pattern family
Identify which single infected node to remove to minimize total malware spread in a connected network graph efficiently.
Open problem page#959 Regions Cut By SlashesDetermine the number of regions in a grid divided by slashes using array scanning and union-find techniques efficiently.
Open problem page#839 Similar String GroupsDetermine the number of connected groups of similar strings by swapping at most two letters using array scanning and hash lookup techniques.
Open problem page