207. Course Schedule (Medium)

https://leetcode.com/problems/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?

Example 1:

Input: 2, [[1,0]] 
Output: true
Explanation: There are a total of 2 courses to take. 
             To take course 1 you should have finished course 0. So it is possible.

Example 2:

Input: 2, [[1,0],[0,1]]
Output: false
Explanation: 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:

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.

Solutions

class Solution {
    public boolean canFinish(int numCourses, int[][] prerequisites) {
        if (numCourses == 0) {
            return true;
        }

        int[] inDegree = new int[numCourses];
        Arrays.fill(inDegree, 0);

        int[][] relation = new int[numCourses][numCourses];
        for (int i = 0; i < numCourses; i++) {
            Arrays.fill(relation[i], 0);
        }

        for (int i = 0; i < prerequisites.length; i++) {
            int[] pair = prerequisites[i];

            // Course pair[1] is the prerequisite for course pair[0]
            relation[pair[0]][pair[1]] = 1;

            inDegree[pair[0]]++;
        }

        Queue<Integer> finished = new ArrayDeque<>();
        for (int i = 0; i < numCourses; i++) {
            if (inDegree[i] == 0) {
                finished.offer(i);
            }
        }

        int count = 0;

        // Courses that can be finished will be added to finished lists. For those
        // correlative dependent courses will never get into this list. So once finished
        // list becomes empty, there are two situations: 1. all completed; 2. There are loops
        // in the prerequisites graph.

        while (!finished.isEmpty()) {
            int course = finished.poll();

            // scan all the courses that depends of current course
            for (int i = 0; i < numCourses; i++) {
                // See if course i depends on current course
                if (relation[i][course] == 0) {
                    continue;
                }

                // already finished, continue
                if (inDegree[i] == 0) {
                    continue;
                }

                // It stands for course i's completion once its in degree becomes 0.
                if ((--inDegree[i]) == 0) {
                    finished.offer(i);
                }
            }

            count++;
        }

        return count == numCourses;
    }
}

Incorrect Solutions

References