LeetCode -- Course Schedule II

题目描述：


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].




输入，需要选择的课程数量n，和课程依赖关系pres，输出选课的数组。对于课程a依赖课程b的依赖关系的表示为[a,b]。


思路：
创建依赖关系列表，存放所有依赖其他课才能选的课，数量表示依赖课程的数量。即初始化dependency[n] ，遍历pres[0...n] 将 dependency[pres[i,1]] += 1;
每次找出课程集合：{不依赖任何课程的课}。 将其添加到选课结果中并更新依赖关系列表dependency[n]，直到{不依赖任何课程的课}为空集为止。 是一个BFS的过程。
查找{不依赖任何课程的课}： 遍历依赖关系表： pres[i] ，其中i∈[0,n-1] ，判断dependency[pres[i,0]] 是否大于0即可。








实现代码：

public class Solution {    public int[] FindOrder(int numCourses, int[,] prerequisites) {var row = prerequisites.GetLength(0);if(row == 0){        int[] c = new int[numCourses];        for(int i=0; i<numCourses; i++){            c[i]=i;        }        return c;    }// save [courseId, refCount]var refCountTable = new int[numCourses];for(var i = 0;i < row; i++){refCountTable[prerequisites[i,0]] ++;}// no ref coursesvar noRefCourses = new Dictionary<int, int>();for(var i = 0;i < row; i++){// find courses does not appear in ref tableif(refCountTable[prerequisites[i,1]] == 0 && !noRefCourses.ContainsKey(prerequisites[i,1])){noRefCourses.Add(prerequisites[i,1],1);}}var size = noRefCourses.Count;var result = new int[numCourses];var count = 0;while(noRefCourses.Count > 0){var c = noRefCourses.Keys.First();result[count++] = c;noRefCourses.Remove(c);for(var i = 0;i < row; i++){if(prerequisites[i,1] == c){refCountTable[prerequisites[i,0]] --;if(refCountTable[prerequisites[i,0]] == 0 && !noRefCourses.ContainsKey(prerequisites[i,1])){noRefCourses.Add(prerequisites[i,0], 1);size++;}}}}if(size == numCourses){return result;}return new int[0];}}