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Remove Methods From Project

Difficulty: Medium

Problem Description

You are maintaining a project that has n methods numbered from 0 to n - 1. You are given two integers n and k, and a 2D integer array invocations, where invocations[i] = [a_i, b_i] indicates that method a_i invokes method b_i. There is a known bug in method k. Method k, along with any method invoked by it, either directly or indirectly, are considered suspicious and we aim to remove them. A group of methods can only be removed if no method outside the group invokes any methods within it. Return an array containing all the remaining methods after removing all the suspicious methods. You may return the answer in any order. If it is not possible to remove all the suspicious methods, none should be removed.

Key Insights

  • The problem can be represented as a directed graph where methods are nodes and invocations are directed edges.
  • Methods that are directly or indirectly invoked by method k are considered suspicious and should be removed.
  • A method can only be safely removed if it is not invoked by any non-suspicious methods.
  • Depth-First Search (DFS) or Breadth-First Search (BFS) can be used to traverse the graph and identify all suspicious methods.

Space and Time Complexity

Time Complexity: O(n + e), where n is the number of methods and e is the number of invocations.
Space Complexity: O(n + e) for storing the graph and the visited states.

Solution

To solve this problem, we can follow these steps:

  1. Construct a directed graph using an adjacency list representation from the invocations array.
  2. Use DFS or BFS starting from method k to mark all suspicious methods that are directly or indirectly invoked by k.
  3. Create a set to keep track of methods that are invoked by any non-suspicious methods.
  4. Traverse the graph again to identify methods that are not suspicious and are not invoked by any suspicious methods.
  5. Return the list of remaining methods.

Code Solutions

def removeMethods(n, k, invocations):
    from collections import defaultdict, deque

    # Build the graph
    graph = defaultdict(list)
    reverse_graph = defaultdict(list)

    for a, b in invocations:
        graph[a].append(b)
        reverse_graph[b].append(a)

    # Step 1: Find all suspicious methods using DFS
    suspicious = set()
    
    def dfs(method):
        if method in suspicious:
            return
        suspicious.add(method)
        for invoked in graph[method]:
            dfs(invoked)

    dfs(k)

    # Step 2: Find methods invoked by suspicious methods
    invoked_by_suspicious = set()
    
    for method in suspicious:
        for invoker in reverse_graph[method]:
            invoked_by_suspicious.add(invoker)

    # Step 3: Collect remaining methods
    remaining_methods = []
    for method in range(n):
        if method not in suspicious and method not in invoked_by_suspicious:
            remaining_methods.append(method)

    return remaining_methods if len(remaining_methods) == n - len(suspicious) else []
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