Leetcode

Course Schedule

May 26, 2022 by aAshish

  • Time:O(|V| + |E|), where |V| = \texttt{numCourses} and |E| = |\texttt{prerequisites}|
  • Space:O(|V| + |E|), where |V| = \texttt{numCourses} and |E| = |\texttt{prerequisites}|

C++

 
enum class State { INIT, VISITING, VISITED };

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

    for (const auto& p : prerequisites)
      graph[p[1]].push_back(p[0]);

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

    return true;
  }

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

    state[u] = State::VISITING;
    for (const int v : graph[u])
      if (hasCycle(graph, v, state))
        return true;
    state[u] = State::VISITED;

    return false;
  }
};

JAVA

 
enum State { INIT, VISITING, VISITED }

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

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

    for (int[] p : prerequisites)
      graph[p[1]].add(p[0]);

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

    return true;
  }

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

    state[u] = State.VISITING;
    for (final int v : graph[u])
      if (hasCycle(graph, v, state))
        return true;
    state[u] = State.VISITED;

    return false;
  }
}

Python

 
from enum import Enum


class State(Enum):
  INIT = 0
  VISITING = 1
  VISITED = 2


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

    for a, b in prerequisites:
      graph[b].append(a)

    def hasCycle(u: int) -> bool:
      if state[u] == State.VISITING:
        return True
      if state[u] == State.VISITED:
        return False

      state[u] = State.VISITING
      if any(hasCycle(v) for v in graph[u]):
        return True
      state[u] = State.VISITED

      return False

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