course-schedule.py

# Time:  O(|V| + |E|)
# Space: O(|E|)
#
# 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.
# 
# click to show more hints.
# 
# Hints:
# This problem is equivalent to finding if a cycle exists in a directed graph. 
# If a cycle exists, no topological ordering exists and therefore it will be impossible to take all courses.
# There are several ways to represent a graph. For example, the input prerequisites is a graph represented by
#  a list of edges. Is this graph representation appropriate?
# Topological Sort via DFS - A great video tutorial (21 minutes) on Coursera explaining the basic concepts
#  of Topological Sort.
# Topological sort could also be done via BFS.
#
class Solution(object):
    def canFinish(self, numCourses, prerequisites):
        """
        :type numCourses: int
        :type prerequisites: List[List[int]]
        :rtype: bool
        """
        zero_in_degree_queue, in_degree, out_degree = collections.deque(), {}, {}
        
        for i, j in prerequisites:
            if i not in in_degree:
                in_degree[i] = set()
            if j not in out_degree:
                out_degree[j] = set()
            in_degree[i].add(j)
            out_degree[j].add(i)
        
        for i in xrange(numCourses):
            if i not in in_degree:
                zero_in_degree_queue.append(i)
        
        while zero_in_degree_queue:
            prerequisite = zero_in_degree_queue.popleft()
            
            if prerequisite in out_degree:
                for course in out_degree[prerequisite]:
                    in_degree[course].discard(prerequisite)
                    if not in_degree[course]:
                        zero_in_degree_queue.append(course)
            
                del out_degree[prerequisite]
        
        if out_degree:
            return False
        
        return True


if __name__ == "__main__":
    print Solution().canFinish(1, [])