#3310

Medium

auto_awesomeGraph traversal with depth-first search

LeetCode Problem Workspace

Remove Methods From Project

Remove suspicious methods in a project that are invoked directly or indirectly from a buggy method using graph traversal.

depth first search breadth first search graph

Problem Statement

You are maintaining a project with n methods, numbered from 0 to n - 1. You are given a 2D array invocations, where each element invocations[i] = [ai, bi] represents that method ai invokes method bi. There is a known bug in method k. You need to remove method k and any methods it invokes, either directly or indirectly, as they are considered suspicious.

The task is to identify and remove all suspicious methods from the project. These are the methods that are either method k or any methods invoked by method k through any chain of invocations. You are given an array of invocations, and the goal is to efficiently remove all suspicious methods using graph traversal techniques.

Examples

Example 1

Input: n = 4, k = 1, invocations = [[1,2],[0,1],[3,2]]

Output: [0,1,2,3]

Method 2 and method 1 are suspicious, but they are directly invoked by methods 3 and 0, which are not suspicious. We return all elements without removing anything.

Example 2

Input: n = 5, k = 0, invocations = [[1,2],[0,2],[0,1],[3,4]]

Output: [3,4]

Methods 0, 1, and 2 are suspicious and they are not directly invoked by any other method. We can remove them.

Example 3

Input: n = 3, k = 2, invocations = [[1,2],[0,1],[2,0]]

Output: []

All methods are suspicious. We can remove them.

Constraints

1 <= n <= 105
0 <= k <= n - 1
0 <= invocations.length <= 2 * 105
invocations[i] == [ai, bi]
0 <= ai, bi <= n - 1
ai != bi
invocations[i] != invocations[j]

Solution Approach

Graph Representation

Represent the methods and their invocations as a directed graph where each method is a node and each invocation is a directed edge. This allows us to efficiently track the methods that are invoked by others.

Depth-First Search (DFS)

Use DFS starting from method k to explore all methods that are either directly or indirectly invoked by k. Each visited method will be marked as suspicious, and all such methods should be removed from the project.

Handling Edge Cases

Handle edge cases such as when no methods are invoked or when all methods are invoked indirectly by method k. Ensure the algorithm handles large inputs efficiently, especially with the constraints provided.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time complexity depends on the number of methods and invocations. A DFS approach will have a time complexity of O(n + m), where n is the number of methods and m is the number of invocations. The space complexity is O(n + m) due to the storage of the graph and visited nodes.

What Interviewers Usually Probe

Tests the candidate's ability to apply graph traversal techniques, especially DFS.
Evaluates the candidate's understanding of handling large inputs efficiently.
Assesses problem-solving abilities with edge cases and graph traversal patterns.

Common Pitfalls or Variants

Common pitfalls

Failing to properly traverse all indirect invocations, potentially missing some methods.
Not handling the case where no invocations exist, leading to unnecessary processing.
Inadequate space management when handling large graphs with many methods and invocations.

Follow-up variants

Implementing a BFS approach instead of DFS to explore the graph.
Handling a dynamic set of invocations that may change over time during execution.
Optimizing the algorithm to minimize space complexity in large projects with many methods.

FAQ

How can I apply graph traversal to remove methods from a project?

You can represent methods and invocations as a graph, and use DFS or BFS to explore and remove all methods invoked by the buggy method.

What is the main technique for solving this problem?

The main technique is graph traversal, particularly Depth-First Search (DFS), to explore methods invoked by the buggy method and remove them.

What if there are no invocations in the project?

If there are no invocations, the algorithm should simply return the methods that are not directly or indirectly invoked by method k.

How does DFS help in solving the 'Remove Methods From Project' problem?

DFS helps by efficiently traversing all methods invoked by the buggy method, marking them as suspicious, and ensuring they are removed from the project.

What is the time complexity of the DFS approach for this problem?

The time complexity of the DFS approach is O(n + m), where n is the number of methods and m is the number of invocations in the project.

terminal

Solution

Solution 1: Two DFS

We can start from $k$ and find all suspicious methods, recording them in the array $\textit{suspicious}$. Then, we traverse from $0$ to $n-1$, starting from all non-suspicious methods, and mark all reachable methods as non-suspicious. Finally, we return all non-suspicious methods.

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class Solution:
    def remainingMethods(
        self, n: int, k: int, invocations: List[List[int]]
    ) -> List[int]:
        def dfs(i: int):
            suspicious[i] = True
            for j in g[i]:
                if not suspicious[j]:
                    dfs(j)

        def dfs2(i: int):
            vis[i] = True
            for j in f[i]:
                if not vis[j]:
                    suspicious[j] = False
                    dfs2(j)

        f = [[] for _ in range(n)]
        g = [[] for _ in range(n)]
        for a, b in invocations:
            f[a].append(b)
            f[b].append(a)
            g[a].append(b)
        suspicious = [False] * n
        dfs(k)

        vis = [False] * n
        ans = []
        for i in range(n):
            if not suspicious[i] and not vis[i]:
                dfs2(i)
        return [i for i in range(n) if not suspicious[i]]

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