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Problem: Check If a Prerequisite Exists

This repository provides solutions to the problem "Check If a Prerequisite Exists" implemented in C++, Java, JavaScript, Python, and Go. Below, you'll find step-by-step explanations for each language.

C++ Code Implementation: Step-by-Step

  1. Initialize the Adjacency Matrix
    Start by initializing a 2D matrix to store whether a course is a prerequisite of another course.

  2. Set up the Prerequisite Relationships
    Using the prerequisites list, update the adjacency matrix with direct relationships between courses.

  3. Floyd-Warshall Algorithm
    Apply the Floyd-Warshall algorithm to compute all pairs' reachability. This updates the matrix to reflect indirect prerequisites.

  4. Process the Queries
    For each query, check the adjacency matrix to see if one course is a prerequisite of another.

Java Code Implementation: Step-by-Step

  1. Prepare the Adjacency Matrix
    Create a 2D array to store whether a course is a prerequisite for another.

  2. Update Relationships from Prerequisites
    Populate the matrix with the prerequisites directly given in the input.

  3. Use Floyd-Warshall Algorithm
    Implement Floyd-Warshall to ensure all transitive prerequisites are captured in the matrix.

  4. Answer the Queries
    For each query, use the matrix to determine if the prerequisite relationship exists.

JavaScript Code Implementation: Step-by-Step

  1. Build the Graph
    Create a graph representation using a 2D array to represent the prerequisite relationships.

  2. Populate Direct Relationships
    Populate the graph with direct prerequisites using the input data.

  3. Compute Transitive Closure
    Utilize the Floyd-Warshall algorithm to compute transitive relationships between courses.

  4. Evaluate Queries
    Loop through each query and return whether the course relationship exists.

Python Code Implementation: Step-by-Step

  1. Initialize a 2D Matrix
    Create a matrix where matrix[i][j] indicates whether course i is a prerequisite for course j.

  2. Update the Matrix for Direct Prerequisites
    Populate the matrix with the relationships provided in the prerequisites list.

  3. Apply Floyd-Warshall Algorithm
    Implement the Floyd-Warshall algorithm to find all indirect relationships between courses.

  4. Answer the Queries
    For each query, check the value in the matrix to determine if the prerequisite exists.

Go Code Implementation: Step-by-Step

  1. Set up the Graph as a 2D Slice
    Initialize a 2D slice to represent the adjacency matrix of course relationships.

  2. Add Direct Relationships
    Update the graph with the direct prerequisites based on the input data.

  3. Floyd-Warshall Algorithm for Transitive Closure
    Implement Floyd-Warshall to propagate indirect prerequisites across the matrix.

  4. Handle Queries
    For each query, determine whether a course is a prerequisite by checking the matrix.

Each implementation shares a common approach:

  1. Build a representation of prerequisites.
  2. Compute all transitive relationships using the Floyd-Warshall algorithm.
  3. Check the matrix to answer queries.

For the complete implementation, refer to the respective files:

  • solution.cpp
  • solution.java
  • solution.js
  • solution.py
  • solution.go

Complexity Analysis

  • Time Complexity:
    The Floyd-Warshall algorithm takes $$O(n^3)$$ time, where (n) is the number of courses. Processing the queries takes $$O(q)$$, where (q) is the number of queries.

  • Space Complexity:
    The space complexity is $$O(n^2)$$ for the adjacency matrix.