210. Course Schedule II

There are a total of n courses you have to take, labeled from 0 to n - 1.

Some courses may have prerequisites, for example to take course 0 you have to first take course 1, which is expressed as a pair: [0,1]

Given the total number of courses and a list of prerequisite pairs, return the ordering of courses you should take to finish all courses.

There may be multiple correct orders, you just need to return one of them. If it is impossible to finish all courses, return an empty array.

For example:

2, [[1,0]]

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]

4, [[1,0],[2,0],[3,1],[3,2]]

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].

Note:

1. The input prerequisites is a graph represented by a list of edges, not adjacency matrices. Read more about how a graph is represented.
2. You may assume that there are no duplicate edges in the input prerequisites.

click to show more hints.

Hints:

1. This problem is equivalent to finding the topological order in a directed graph. If a cycle exists, no topological ordering exists and therefore it will be impossible to take all courses.
2. Topological Sort via DFS - A great video tutorial (21 minutes) on Coursera explaining the basic concepts of Topological Sort.
3. Topological sort could also be done via BFS.

可以用DFS和BFS解题，首先是DFS，代码如下：

public class Solution {    boolean[] visited;    boolean[] isloop;        public int[] findOrder(int numCourses, int[][] prerequisites) {        visited = new boolean[numCourses];        isloop = new boolean[numCourses];        List<List<Integer>> lists = new ArrayList<List<Integer>>();        for (int i = 0; i < numCourses; i ++) {            lists.add(new ArrayList<Integer>());        }        for (int[] pair: prerequisites) {            lists.get(pair[1]).add(pair[0]);        }        Stack<Integer> stack = new Stack<Integer>();        for (int i = 0; i < numCourses; i ++) {            if (!DFS(lists, i, stack)) return new int[0];        }        int[] res = new int[numCourses];        int k = 0;        while (!stack.isEmpty()) {            res[k++] = stack.pop();        }        return res;    }        private boolean DFS(List<List<Integer>> lists, int i, Stack<Integer> stack) {        if(visited[i] == true) return true;        if(isloop[i] == true) return false;        isloop[i] = true;        for (int course: lists.get(i)) {            if (!DFS(lists, course, stack)) return false;        }        visited[i] = true;        stack.push(i);        return true;    }}

接下来是BFS，代码如下：

public int[] findOrder(int numCourses, int[][] prerequisites) {    int[] incLinkCounts = new int[numCourses];    List<List<Integer>> adjs = new ArrayList<>(numCourses);    initialiseGraph(incLinkCounts, adjs, prerequisites);    //return solveByBFS(incLinkCounts, adjs);    return solveByDFS(adjs);}private void initialiseGraph(int[] incLinkCounts, List<List<Integer>> adjs, int[][] prerequisites){    int n = incLinkCounts.length;    while (n-- > 0) adjs.add(new ArrayList<>());    for (int[] edge : prerequisites) {        incLinkCounts[edge[0]]++;        adjs.get(edge[1]).add(edge[0]);    }}private int[] solveByBFS(int[] incLinkCounts, List<List<Integer>> adjs){    int[] order = new int[incLinkCounts.length];    Queue<Integer> toVisit = new ArrayDeque<>();    for (int i = 0; i < incLinkCounts.length; i++) {        if (incLinkCounts[i] == 0) toVisit.offer(i);    }    int visited = 0;    while (!toVisit.isEmpty()) {        int from = toVisit.poll();        order[visited++] = from;        for (int to : adjs.get(from)) {            incLinkCounts[to]--;            if (incLinkCounts[to] == 0) toVisit.offer(to);        }    }    return visited == incLinkCounts.length ? order : new int[0]; }