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Eventual Safe States - Step-by-Step Explanation for Multiple Languages

This repository provides solutions to the "Eventual Safe States" problem implemented in C++, Java, JavaScript, Python, and Go. Below is a step-by-step explanation for each language, with a friendly and approachable tone. Let's dive into how we solved the problem and broke it into understandable steps!

C++ Code Explanation

  1. Graph Representation:
    Represent the input graph as an adjacency list where each node points to the nodes it can visit.

  2. Tracking Node States:
    Use an array to track the states of each node:

    • 0: Node is unvisited.
    • 1: Node is being visited (part of the current path).
    • 2: Node is already determined to be safe.

  3. DFS Traversal:
    Perform a depth-first search to determine if a node leads to a cycle:

    • Mark the node as being visited.
    • For each connected node, recursively check if it leads to a cycle.
    • If any neighbor leads to a cycle, the current node is unsafe.

  4. Marking Safe Nodes:
    If all neighbors are safe, mark the current node as safe and continue.

  5. Result Compilation:
    After processing all nodes, return the list of nodes marked as safe.

Java Code Explanation

  1. Graph Representation:
    Convert the input into an adjacency list to represent the graph efficiently.

  2. State Tracking:
    Use an array to keep track of whether a node is safe:

    • 0: Node is not yet processed.
    • 1: Node is safe.
    • 2: Node is unsafe or part of a cycle.

  3. DFS Logic:
    Recursively check each node:

    • If a node is already marked, return its state.
    • If not, explore its neighbors.
    • If any neighbor leads to a cycle, the current node is unsafe.

  4. Storing Safe Nodes:
    Collect all nodes that are eventually determined to be safe.

  5. Return Result:
    Sort the list of safe nodes and return as the result.

JavaScript Code Explanation

  1. Graph Conversion:
    Parse the input graph into a usable format, typically an adjacency list.

  2. State Management:
    Create a state array to track each node's status:

    • 0: Not visited.
    • 1: Safe.
    • 2: Unsafe or cyclic.

  3. Recursive DFS Function:
    Write a helper function to explore each node recursively:

    • If a node is already marked, return its state.
    • Otherwise, check all its neighbors.
    • If any neighbor is part of a cycle, mark the current node as unsafe.

  4. Identifying Safe Nodes:
    Add nodes identified as safe to the result array.

  5. Final Output:
    Return the sorted list of safe nodes.

Python Code Explanation

  1. Graph Input:
    Read and transform the input graph into an adjacency list for easier traversal.

  2. State Array:
    Use an array to track whether a node is:

    • 0: Not yet processed.
    • 1: Safe.
    • 2: Unsafe.

  3. DFS Implementation:
    Define a recursive function to explore nodes:

    • Check if a node has been visited before.
    • Explore its neighbors recursively.
    • If all neighbors are safe, mark the node as safe.

  4. Collecting Results:
    Iterate through all nodes and call the DFS function to determine their safety.

  5. Output:
    Return a sorted list of nodes that are safe.

Go Code Explanation

  1. Graph Structure:
    Represent the input graph as an adjacency list using slices for efficient traversal.

  2. State Management:
    Use a slice to track node states:

    • 0: Not processed.
    • 1: Safe.
    • 2: Unsafe or cyclic.

  3. Recursive DFS Function:
    Implement a helper function to determine if a node leads to a cycle:

    • Mark nodes during traversal.
    • Check neighbors recursively.
    • If any neighbor is unsafe, mark the current node as unsafe.

  4. Identifying Safe Nodes:
    Iterate through the graph, marking nodes as safe if they meet the conditions.

  5. Result Compilation:
    Collect all safe nodes, sort them, and return the final list.

Conclusion

By following the above steps, you can confidently understand how the solutions work across different programming languages. Each implementation uses depth-first search (DFS) and state tracking to determine whether nodes are eventually safe. Feel free to explore the respective code files for a more detailed view of the implementation!