動機

沒辦法用cache_computing偷懶了

Problem

There are a total of numCourses courses you have to take, labeled from 0 to numCourses - 1. You are given an array prerequisites where prerequisites[i] = [ai, bi] indicates that you must take course bi first if you want to take course ai.

  • For example, the pair [0, 1], indicates that to take course 0 you have to first take course 1.

Return the ordering of courses you should take to finish all courses. If there are many valid answers, return any of them. If it is impossible to finish all courses, return an empty array.

 

Example 1:

Input: numCourses = 2, prerequisites = [[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: numCourses = 4, prerequisites = [[1,0],[2,0],[3,1],[3,2]]Output: [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].

Example 3:

Input: numCourses = 1, prerequisites = []Output: [0]

 

Constraints:

  • 1 <= numCourses <= 2000
  • 0 <= prerequisites.length <= numCourses * (numCourses - 1)
  • prerequisites[i].length == 2
  • 0 <= ai, bi < numCourses
  • ai != bi
  • All the pairs [ai, bi] are distinct.

Sol

因為求時path可以利用共用的狀態，從原本的找修此課之前要修什麼，變成還要修什麼

topo sort還有Kahn’s algorithm

class Solution:
    def findOrder(self, numCourses: int, pres: List[List[int]]) -> List[int]:
        premises = defaultdict(list) # class, [premises]
        [premises[c].append(p) for (c,p) in pres]
        nofrees = set(premises.keys())
        frees = set(range(numCourses)) - nofrees
        seen = {} # True :: done
        
        def dfs(c):
            if c in seen:
                if seen[c]:
                    return []
                else:
                    raise 'loop!!'
            else:
                seen[c] = False
                if c in frees:
                    ret = []
                else:   
                    ret = list(reduce(lambda ret,p: ret+dfs(p), premises[c], []))+[c]
                seen[c] = True
                return ret
        
        try:
            if nofrees:
                return list(frees)+list(reduce(lambda acc,c: acc+dfs(c), nofrees, []))
            else:
                return list(frees)
        except:
            return []