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] = [a_i, b_i] indicates that you must take course b_i first if you want to take course a_i.

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 <= 2000
0 <= prerequisites.length <= 5000
prerequisites[i].length == 2
0 <= a_i, b_i < numCourses
All the pairs prerequisites[i] are unique.

Solution

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

  bool canFinish(int numCourses, List<List<int>> prerequisites) {
    List<List<int>> adj = List.generate(numCourses, (_) => []);

    for (var pre in prerequisites) {
      adj[pre[1]].add(pre[0]);
    }

    List<int> colors = List.filled(numCourses, WHITE);

    for (int i = 0; i < numCourses; i++) {
      if (colors[i] == WHITE && adj[i].isNotEmpty && _hasCycle(adj, i, colors)) {
        return false;
      }
    }
    return true;
  }

  bool _hasCycle(List<List<int>> adj, int node, List<int> colors) {
    colors[node] = GRAY;

    for (int nei in 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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