CSES Solutions – Course Schedule

Last Updated : 19 May, 2024

You have to complete n courses. There are m requirements of form "course a has to be completed before course b". Your task is to find an order in which you can complete the courses.

Examples:

Input: n = 5, m = 3, requirements[][] = {{1, 2}, {3, 1}, {4, 5}}
Output: 3 4 1 5 2
Explanation:

Since course 3 and 4 have no requirements, we can complete course 3 and 4.
After completing course 3, we can complete course 1.
After completing course 4, we can complete course 5.
After completing course 1, we can complete course 2.
Input: n = 4, m = 2, requirements[][] = {{4, 2}, {3, 1}}
Output: 3 4 1 2
Explanation:

Since course 3 and 4 have on requirements, we can complete course 3 and 4.
After completing course 3, we can complete course 1.
After completing course 4, we can complete course 2.

Approach: To solve the problem, follow the below idea:

The problem can be solved using Topological Sort. Each course can be considered as a node and each requirement (a, b) can be considered as a directed edge from node a to node b. Now, we can find the topological sort of the graph to find the order in which courses can be completed.

Step-by-step approach:

Construct a graph of N nodes for N courses.
For every requirement, draw directed edges between the nodes and keep track of the indegree of each node.
Maintain a queue to keep track of nodes which we can visit next.
Push all the nodes with indegree 0 into the queue.
Till queue is not empty,
- Pop the node at the front of the queue and push it into the ans vector.
- Decrease the indegree of all the neighboring nodes by 1.
- If the indegree of neighboring node becomes 0, push the neighboring node to the queue.
After the queue becomes empty, print the ans vector as the final answer.

Below is the implementation of the algorithm:

C++

#include <bits/stdc++.h>
using namespace std;

// Function to perform topological sort and find the order
// in which courses can be completed
vector<int> solve(int n, vector<vector<int> >& adj,
                  vector<int>& indeg)
{
    queue<int> q;
    vector<int> ans;
    // Initialize queue with nodes having in-degree 0
    for (int i = 1; i <= n; ++i) {
        if (indeg[i] == 0)
            q.push(i);
    }
    // Iterate till q is not empty
    while (!q.empty()) {
        // Pop the front node of the queue
        int node = q.front();
        q.pop();
        // Push the front node to the answer
        ans.push_back(node);
        // Update in degree of adjacent nodes
        for (int child : adj[node]) {
            indeg[child] -= 1;
            if (indeg[child] == 0) {
                q.push(child);
            }
        }
    }
    return ans;
}
int main()
{
    int n, m;
    // Sample input
    n = 5;
    m = 3;
    vector<pair<int, int> > requirements
        = { { 1, 2 }, { 3, 1 }, { 4, 5 } };
    vector<vector<int> > graph(n + 1);
    vector<int> indeg(n + 1, 0);
    // Build directed graph and calculate in-degrees
    for (int i = 0; i < m; ++i) {
        int u = requirements[i].first;
        int v = requirements[i].second;
        graph[u].push_back(v);
        indeg[v] += 1;
    }

    // Get the topological sort
    vector<int> ans = solve(n, graph, indeg);

    // Print the result
    if (ans.size() != n) {
        cout << "IMPOSSIBLE";
    }
    else {
        for (int i = 0; i < n; i++)
            cout << ans[i] << " ";
    }
    return 0;
}

Java

import java.util.*;

public class CourseSchedule {

    // Function to perform topological sort and find the
    // order in which courses can be completed
    public static List<Integer>
    solve(int n, List<List<Integer> > adj, int[] indeg)
    {
        Queue<Integer> q = new LinkedList<>();
        List<Integer> ans = new ArrayList<>();

        // Initialize queue with nodes having in-degree 0
        for (int i = 1; i <= n; ++i) {
            if (indeg[i] == 0) {
                q.add(i);
            }
        }

        // Iterate till q is not empty
        while (!q.isEmpty()) {
            // Pop the front node of the queue
            int node = q.poll();
            // Push the front node to the answer
            ans.add(node);
            // Update in-degree of adjacent nodes
            for (int child : adj.get(node)) {
                indeg[child] -= 1;
                if (indeg[child] == 0) {
                    q.add(child);
                }
            }
        }

        return ans;
    }

    public static void main(String[] args)
    {
        int n, m;
        // Sample input
        n = 5;
        m = 3;
        List<int[]> requirements = Arrays.asList(
            new int[] { 1, 2 }, new int[] { 3, 1 },
            new int[] { 4, 5 });

        List<List<Integer> > graph = new ArrayList<>(n + 1);
        for (int i = 0; i <= n; ++i) {
            graph.add(new ArrayList<>());
        }
        int[] indeg = new int[n + 1];

        // Build directed graph and calculate in-degrees
        for (int[] req : requirements) {
            int u = req[0];
            int v = req[1];
            graph.get(u).add(v);
            indeg[v] += 1;
        }

        // Get the topological sort
        List<Integer> ans = solve(n, graph, indeg);

        // Print the result
        if (ans.size() != n) {
            System.out.println("IMPOSSIBLE");
        }
        else {
            for (int i = 0; i < n; ++i) {
                System.out.print(ans.get(i) + " ");
            }
        }
    }
}

// This code is contributed by shivamgupta0987654321

Python

from collections import deque, defaultdict

# Function to perform topological sort and find the order
# in which courses can be completed


def solve(n, adj, indeg):
    q = deque()
    ans = []

    # Initialize queue with nodes having in-degree 0
    for i in range(1, n + 1):
        if indeg[i] == 0:
            q.append(i)

    # Iterate till q is not empty
    while q:
        # Pop the front node of the queue
        node = q.popleft()
        # Push the front node to the answer
        ans.append(node)
        # Update in degree of adjacent nodes
        for child in adj[node]:
            indeg[child] -= 1
            if indeg[child] == 0:
                q.append(child)

    return ans


def main():
    # Sample input
    n = 5
    m = 3
    requirements = [(1, 2), (3, 1), (4, 5)]
    graph = defaultdict(list)
    indeg = [0] * (n + 1)

    # Build directed graph and calculate in-degrees
    for u, v in requirements:
        graph[u].append(v)
        indeg[v] += 1

    # Get the topological sort
    ans = solve(n, graph, indeg)

    # Print the result
    if len(ans) != n:
        print("IMPOSSIBLE")
    else:
        print(" ".join(map(str, ans)))


if __name__ == "__main__":
    main()
# This code is contributed by Ayush Mishra

JavaScript

class CourseSchedule {
    // Function to perform topological sort and find the
    // order in which courses can be completed
    static solve(n, adj, indeg) {
        let q = [];
        let ans = [];

        // Initialize queue with nodes having in-degree 0
        for (let i = 1; i <= n; ++i) {
            if (indeg[i] === 0) {
                q.push(i);
            }
        }

        // Iterate till q is not empty
        while (q.length !== 0) {
            // Pop the front node of the queue
            let node = q.shift();
            // Push the front node to the answer
            ans.push(node);
            // Update in-degree of adjacent nodes
            for (let child of adj[node]) {
                indeg[child] -= 1;
                if (indeg[child] === 0) {
                    q.push(child);
                }
            }
        }

        return ans;
    }

    static main() {
        let n, m;
        // Sample input
        n = 5;
        m = 3;
        let requirements = [
            [ 1, 2 ], [ 3, 1 ], [ 4, 5 ]
        ];

        let graph = new Array(n + 1).fill(null).map(() => []);
        let indeg = new Array(n + 1).fill(0);

        // Build directed graph and calculate in-degrees
        for (let req of requirements) {
            let u = req[0];
            let v = req[1];
            graph[u].push(v);
            indeg[v] += 1;
        }

        // Get the topological sort
        let ans = CourseSchedule.solve(n, graph, indeg);

        // Print the result
        if (ans.length !== n) {
            console.log("IMPOSSIBLE");
        } else {
            console.log(ans.join(" "));
        }
    }
}

// Call the main function
CourseSchedule.main();

Output

3 4 1 5 2

Time Complexity: O(N)
Auxiliary Space: O(N)

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