problem210.py

'''

210. Course Schedule II
Medium

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] .

Solution:
Compute the zero indegrees iteratively.
If the node's indgree is 0, means that the course do not have any prerequest or all its prerequisites has been
fullfiled.
Minus them iteratively.
'''

		
class Solution(object):
	def findOrder(self, numCourses, prerequisites):
		from collections import defaultdict
		inDegrees = {i:0 for i in range(numCourses)}
		preReq = defaultdict(list)
		for toTake, prereq in prerequisites:
			inDegrees[toTake] += 1
			preReq[prereq].append(toTake)

		zeroIndegrees = []
		for key in inDegrees:
			if inDegrees[key] == 0:
				zeroIndegrees.append(key)

		rst = []
		while zeroIndegrees:
			node = zeroIndegrees.pop()
			rst.append(node)
			if node in preReq:
				for i in preReq[node]:
					inDegrees[i] -= 1
					if inDegrees[i] == 0:
						zeroIndegrees.append(i)
			else:
				continue
		return rst if len(rst) == numCourses else []

		

if __name__ == '__main__':
	s = Solution()
	numCourses = 4
	prerequisites = [[1,0],[2,0],[3,1],[3,2]]
	print s.findOrder(numCourses,prerequisites)