Course Schedule

Problem

There are a total of numCourses courses you have to take, labeled from 0 to numCourses - 1. You are given an array prerequisites where prerequisites[i] = [ai, bi] indicates that you must take course bi first if you want to take course ai.

• For example, the pair [0, 1], indicates that to take course 0 you have to first take course 1.

Return true if you can finish all courses. Otherwise, return false.

Solution Approach

Expected Time complexity: $O(n)$

Click - to see solution code

C++

class Solution {
   public:
    int check = 1;
    vector<int> vis, st;
    unordered_map<int, vector<int>> edges;

    void dfs(int cur) {
        if (vis[cur] || check == 0) {
            check = 0;
            return;
        }
        vis[cur] = 1;
        st[cur] = 1;
        for (auto nbr : edges[cur]) {
            if (!vis[nbr])
                dfs(nbr);
            else if (st[nbr])
                check = 0;
        }
        st[cur] = 0;
    }

    bool canFinish(int numCourses, vector<vector<int>>& pre) {
        vis.resize(numCourses);
        st.resize(numCourses);
        for (int i = 0; i < pre.size(); i++) {
            int x = pre[i][0];
            int y = pre[i][1];
            edges[x].push_back(y);
            // edges[y].push_back(x);
        }

        for (int i = 0; i < numCourses; i++) {
            if (!vis[i]) {
                dfs(i);
            }
        }
        return check;
    }
};