LeetCode-in-All

207. Course Schedule

Medium

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.

Example 1:

Input: numCourses = 2, prerequisites = [[1,0]]

Output: true

Explanation: There are a total of 2 courses to take. To take course 1 you should have finished course 0. So it is possible.

Example 2:

Input: numCourses = 2, prerequisites = [[1,0],[0,1]]

Output: false

Explanation: There are a total of 2 courses to take. To take course 1 you should have finished course 0, and to take course 0 you should also have finished course 1. So it is impossible.

Constraints:

• 1 <= numCourses <= 105
• 0 <= prerequisites.length <= 5000
• prerequisites[i].length == 2
• 0 <= ai, bi < numCourses
• All the pairs prerequisites[i] are unique.

Solution

#include <vector>

class Solution {
private:
    const int WHITE = 0;
    const int GRAY = 1;
    const int BLACK = 2;

public:
    bool canFinish(int numCourses, std::vector<std::vector<int>>& prerequisites) {
        std::vector<std::vector<int>> adj(numCourses);
        for (const auto& pre : prerequisites) {
            adj[pre[1]].push_back(pre[0]);
        }
        std::vector<int> colors(numCourses, WHITE);
        for (int i = 0; i < numCourses; i++) {
            if (colors[i] == WHITE && !adj[i].empty() && hasCycle(adj, i, colors)) {
                return false;
            }
        }
        return true;
    }

private:
    bool hasCycle(const std::vector<std::vector<int>>& adj, int node, std::vector<int>& colors) {
        colors[node] = GRAY;
        for (int nei : adj[node]) {
            if (colors[nei] == GRAY) {
                return true;
            }
            if (colors[nei] == WHITE && hasCycle(adj, nei, colors)) {
                return true;
            }
        }
        colors[node] = BLACK;
        return false;
    }
};

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