Course Schedule(拓扑)
There are a total ofncourses you have to take, labeled from0
ton - 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 prerequisitepairs, is it possible for you to finish all courses?
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 it is possible.
2, [[1,0],[0,1]]
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.
Note:
The input prerequisites is a graph represented by a list of edges ,not adjacency matrices. Read more about
You may assume that there are no duplicate edges in the input prerequisites.
Hints:
This problem is equivalent to finding if a cycle exists in a directed graph. If a cycle exists, no topological ordering exists and therefore it will be impossible to take all courses.
A great video tutorial (21 minutes) on Coursera explaining the basic concepts of Topological Sort.
Topological sort could also be done via
分析
有序图用拓扑排序检查是否有环,无序图用并查集。注意这里课程是反序input。
用一个map存node和它的neighbors们List,一个数组存入度。然后BFS,用一个Queue.最后若是所有数组都遍历到,则无环。
有环的话入度不为0不会被加入queue,所以不可达。
class Solution {
public boolean canFinish(int numCourses, int[][] prerequisites) {
Map<Integer, List<Integer>> neighbors = new HashMap<Integer, List<Integer>>();//node and its neighbors
Queue<Integer> q = new LinkedList<Integer>();//bfs
int[] indegree = new int[numCourses];//indegree出度
int cnt = numCourses;
for(int[] p : prerequisites){
indegree[p[0]] ++;
if(neighbors.containsKey(p[1])){
neighbors.get(p[1]).add(p[0]);
}else{
List<Integer> ns = new ArrayList<Integer>();
ns.add(p[0]);
neighbors.put(p[1], ns);
}
}
for(int i = 0; i < indegree.length; i ++){
if(indegree[i] == 0){
q.offer(i);
}
}
while(!q.isEmpty()){
int cur = q.poll();
cnt --;
if(neighbors.containsKey(cur)){
for(int i : neighbors.get(cur)){
indegree[i] --;
if(indegree[i] == 0){
q.offer(i);
}
}
}
}
return cnt == 0;
}
}
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