210. Course Schedule II #

Problem #

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.

Example 1:

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

Example 2:

Input: 4, [[1,0],[2,0],[3,1],[3,2]]
Output: [0,1,2,3] or [0,2,1,3]
Explanation: 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.

Problem Summary #

Now you have a total of n courses to take, labeled from 0 to n-1. Before taking some courses, you need to complete certain prerequisite courses. For example, to take course 0, you need to complete course 1 first; we use a pair to represent this: [0,1]. Given the total number of courses and their prerequisites, return the order in which you should take courses to finish all of them. There may be multiple correct orders; you only need to return one of them. If it is impossible to complete all courses, return an empty array.

Solution Approach #

• Given n tasks, there are dependencies between pairs of tasks; for example, task A must be completed before task B can be completed. Ask whether all tasks can be completed; if they can, output the order to complete the tasks; if not, output an empty array.
• This problem is an enhanced version of Problem 207. The solution approach is topological sorting on an AOV network. Finally, just output the array. The code is basically unchanged from Problem 207. See Problem 207 for the detailed solution approach.

Code #

package leetcode

func findOrder(numCourses int, prerequisites [][]int) []int {
	in := make([]int, numCourses)
	frees := make([][]int, numCourses)
	next := make([]int, 0, numCourses)
	for _, v := range prerequisites {
		in[v[0]]++
		frees[v[1]] = append(frees[v[1]], v[0])
	}
	for i := 0; i < numCourses; i++ {
		if in[i] == 0 {
			next = append(next, i)
		}
	}
	for i := 0; i != len(next); i++ {
		c := next[i]
		v := frees[c]
		for _, vv := range v {
			in[vv]--
			if in[vv] == 0 {
				next = append(next, vv)
			}
		}
	}
	if len(next) == numCourses {
		return next
	}
	return []int{}
}