207. Course Schedule

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, 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.

解题思路：一刷没ac。

一个拓扑排序的思路是将所有课程看成是节点，依赖关系看作是边，先找到度为0的节点，从图中移除，然后继续找堵为0的节点，顺次移除。看是否能够满足全部移除。

public class Solution {
public boolean canFinish(int numCourses, int[][] prerequisites) {
int[][] matrix = new int[numCourses][numCourses];
int[] indegree = new int[numCourses];
int count = 0;
for (int i = 0; i < prerequisites.length; i++) {
int ready = prerequisites[i][0];
int pre = prerequisites[i][1];
if (matrix[pre][ready] == 0)
indegree[ready]++;
matrix[pre][ready] = 1;
}
LinkedList<Integer> queue = new LinkedList<Integer>();
for (int i = 0; i < numCourses; i++) {
if (indegree[i] == 0) queue.offer(i);
}
while (!queue.isEmpty()) {
int course = queue.poll();
count++;
for (int i = 0; i < numCourses; i++) {
if (matrix[course][i] != 0) {
if (--indegree[i] == 0)
queue.offer(i);
}
}
}
return count == numCourses;
}
}