Question

210. Course Schedule II

中文文档

Description

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 _the ordering of courses you should take to finish all courses_. If there are many valid answers, return any of them. If it is impossible to finish all courses, return an empty array.

 

Example 1:

Input: numCourses = 2, prerequisites = [[1,0]]
Output: [0,1]
Explanation: There are a total of 2 courses to take. To take course 1 you should have finished course 0. So the correct course order is [0,1].

Example 2:

Input: numCourses = 4, prerequisites = [[1,0],[2,0],[3,1],[3,2]]
Output: [0,2,1,3]
Explanation: There are a total of 4 courses to take. To take course 3 you should have finished both courses 1 and 2. Both courses 1 and 2 should be taken after you finished course 0.
So one correct course order is [0,1,2,3]. Another correct ordering is [0,2,1,3].

Example 3:

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

 

Constraints:

• 1 <= numCourses <= 2000
• 0 <= prerequisites.length <= numCourses * (numCourses - 1)
• prerequisites[i].length == 2
• 0 <= ai, bi < numCourses
• ai != bi
• All the pairs [ai, bi] are distinct.

Solutions

Solution 1

class Solution:
  def findOrder(self, numCourses: int, prerequisites: List[List[int]]) -> List[int]:
    g = defaultdict(list)
    indeg = [0] * numCourses
    for a, b in prerequisites:
      g[b].append(a)
      indeg[a] += 1
    ans = []
    q = deque(i for i, x in enumerate(indeg) if x == 0)
    while q:
      i = q.popleft()
      ans.append(i)
      for j in g[i]:
        indeg[j] -= 1
        if indeg[j] == 0:
          q.append(j)
    return ans if len(ans) == numCourses else []

class Solution {
  public int[] findOrder(int numCourses, int[][] prerequisites) {
    List<Integer>[] g = new List[numCourses];
    Arrays.setAll(g, k -> new ArrayList<>());
    int[] indeg = new int[numCourses];
    for (var p : prerequisites) {
      int a = p[0], b = p[1];
      g[b].add(a);
      ++indeg[a];
    }
    Deque<Integer> q = new ArrayDeque<>();
    for (int i = 0; i < numCourses; ++i) {
      if (indeg[i] == 0) {
        q.offer(i);
      }
    }
    int[] ans = new int[numCourses];
    int cnt = 0;
    while (!q.isEmpty()) {
      int i = q.poll();
      ans[cnt++] = i;
      for (int j : g[i]) {
        if (--indeg[j] == 0) {
          q.offer(j);
        }
      }
    }
    return cnt == numCourses ? ans : new int[0];
  }
}

class Solution {
public:
  vector<int> findOrder(int numCourses, vector<vector<int>>& prerequisites) {
    vector<vector<int>> g(numCourses);
    vector<int> indeg(numCourses);
    for (auto& p : prerequisites) {
      int a = p[0], b = p[1];
      g[b].push_back(a);
      ++indeg[a];
    }
    queue<int> q;
    for (int i = 0; i < numCourses; ++i) {
      if (indeg[i] == 0) {
        q.push(i);
      }
    }
    vector<int> ans;
    while (!q.empty()) {
      int i = q.front();
      q.pop();
      ans.push_back(i);
      for (int j : g[i]) {
        if (--indeg[j] == 0) {
          q.push(j);
        }
      }
    }
    return ans.size() == numCourses ? ans : vector<int>();
  }
};

func findOrder(numCourses int, prerequisites [][]int) []int {
  g := make([][]int, numCourses)
  indeg := make([]int, numCourses)
  for _, p := range prerequisites {
    a, b := p[0], p[1]
    g[b] = append(g[b], a)
    indeg[a]++
  }
  q := []int{}
  for i, x := range indeg {
    if x == 0 {
      q = append(q, i)
    }
  }
  ans := []int{}
  for len(q) > 0 {
    i := q[0]
    q = q[1:]
    ans = append(ans, i)
    for _, j := range g[i] {
      indeg[j]--
      if indeg[j] == 0 {
        q = append(q, j)
      }
    }
  }
  if len(ans) == numCourses {
    return ans
  }
  return []int{}
}

function findOrder(numCourses: number, prerequisites: number[][]): number[] {
  const g: number[][] = Array.from({ length: numCourses }, () => []);
  const indeg: number[] = new Array(numCourses).fill(0);
  for (const [a, b] of prerequisites) {
    g[b].push(a);
    indeg[a]++;
  }
  const q: number[] = [];
  for (let i = 0; i < numCourses; ++i) {
    if (indeg[i] === 0) {
      q.push(i);
    }
  }
  const ans: number[] = [];
  while (q.length) {
    const i = q.shift()!;
    ans.push(i);
    for (const j of g[i]) {
      if (--indeg[j] === 0) {
        q.push(j);
      }
    }
  }
  return ans.length === numCourses ? ans : [];
}

impl Solution {
  pub fn find_order(num_courses: i32, prerequisites: Vec<Vec<i32>>) -> Vec<i32> {
    let n = num_courses as usize;
    let mut adjacency = vec![vec![]; n];
    let mut entry = vec![0; n];
    // init
    for iter in prerequisites.iter() {
      let (a, b) = (iter[0], iter[1]);
      adjacency[b as usize].push(a);
      entry[a as usize] += 1;
    }
    // construct deque & reslut
    let mut deque = std::collections::VecDeque::new();
    for index in 0..n {
      if entry[index] == 0 {
        deque.push_back(index);
      }
    }
    let mut result = vec![];
    // bfs
    while !deque.is_empty() {
      let head = deque.pop_front().unwrap();
      result.push(head as i32);
      // update degree of entry
      for &out_entry in adjacency[head].iter() {
        entry[out_entry as usize] -= 1;
        if entry[out_entry as usize] == 0 {
          deque.push_back(out_entry as usize);
        }
      }
    }
    if result.len() == n {
      result
    } else {
      vec![]
    }
  }
}

public class Solution {
  public int[] FindOrder(int numCourses, int[][] prerequisites) {
    var g = new List<int>[numCourses];
    for (int i = 0; i < numCourses; ++i) {
      g[i] = new List<int>();
    }
    var indeg = new int[numCourses];
    foreach (var p in prerequisites) {
      int a = p[0], b = p[1];
      g[b].Add(a);
      ++indeg[a];
    }
    var q = new Queue<int>();
    for (int i = 0; i < numCourses; ++i) {
      if (indeg[i] == 0) {
        q.Enqueue(i);
      }
    }
    var ans = new int[numCourses];
    var cnt = 0;
    while (q.Count > 0) {
      int i = q.Dequeue();
      ans[cnt++] = i;
      foreach (int j in g[i]) {
        if (--indeg[j] == 0) {
          q.Enqueue(j);
        }
      }
    }
    return cnt == numCourses ? ans : new int[0];
  }
}