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207. Course Schedule 👍

  • Time: $O(|V| + |E|)$, where $|V| = \texttt{numCourses}$ and $|E| = |\texttt{prerequisites}|$
  • Space: $O(|V| + |E|)$, where $|V| = \texttt{numCourses}$ and $|E| = |\texttt{prerequisites}|$
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enum class State { kInit, kVisiting, kVisited };

class Solution {
 public:
  bool canFinish(int numCourses, vector<vector<int>>& prerequisites) {
    vector<vector<int>> graph(numCourses);
    vector<State> states(numCourses);

    for (const vector<int>& prerequisite : prerequisites) {
      const int u = prerequisite[1];
      const int v = prerequisite[0];
      graph[u].push_back(v);
    }

    for (int i = 0; i < numCourses; ++i)
      if (hasCycle(graph, i, states))
        return false;

    return true;
  }

 private:
  bool hasCycle(const vector<vector<int>>& graph, int u,
                vector<State>& states) {
    if (states[u] == State::kVisiting)
      return true;
    if (states[u] == State::kVisited)
      return false;

    states[u] = State::kVisiting;
    for (const int v : graph[u])
      if (hasCycle(graph, v, states))
        return true;
    states[u] = State::kVisited;

    return false;
  }
};

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enum State { kInit, kVisiting, kVisited }

class Solution {
  public boolean canFinish(int numCourses, int[][] prerequisites) {
    List<Integer>[] graph = new List[numCourses];
    State[] states = new State[numCourses];

    for (int i = 0; i < numCourses; ++i)
      graph[i] = new ArrayList<>();

    for (int[] prerequisite : prerequisites) {
      final int u = prerequisite[1];
      final int v = prerequisite[0];
      graph[u].add(v);
    }

    for (int i = 0; i < numCourses; ++i)
      if (hasCycle(graph, i, states))
        return false;

    return true;
  }

  private boolean hasCycle(List<Integer>[] graph, int u, State[] states) {
    if (states[u] == State.kVisiting)
      return true;
    if (states[u] == State.kVisited)
      return false;

    states[u] = State.kVisiting;
    for (final int v : graph[u])
      if (hasCycle(graph, v, states))
        return true;
    states[u] = State.kVisited;

    return false;
  }
}

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from enum import Enum


class State(Enum):
  kInit = 0
  kVisiting = 1
  kVisited = 2


class Solution:
  def canFinish(self, numCourses: int, prerequisites: list[list[int]]) -> bool:
    graph = [[] for _ in range(numCourses)]
    states = [State.kInit] * numCourses

    for v, u in prerequisites:
      graph[u].append(v)

    def hasCycle(u: int) -> bool:
      if states[u] == State.kVisiting:
        return True
      if states[u] == State.kVisited:
        return False

      states[u] = State.kVisiting
      if any(hasCycle(v) for v in graph[u]):
        return True
      states[u] = State.kVisited

      return False

    return not any(hasCycle(i) for i in range(numCourses))