207. Course Schedule

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 true if you can finish all courses. Otherwise, return false.

Example 1:

Input: numCourses = 2, prerequisites = [[1,0]]
Output: true
Explanation: There are a total of 2 courses to take. 
To take course 1 you should have finished course 0. So it is possible.

Example 2:

Input: numCourses = 2, prerequisites = [[1,0],[0,1]]
Output: false
Explanation: 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.

有向無環圖，ex2修課順序互相依賴，所以不可能，每次把依賴移除。

# T:O(nˆ2), S:O:(n)
class Solution:
    def canFinish(self, numCourses: int, prerequisites: List[List[int]]) -> bool:
        n = numCourses
        graph = [[] for _ in range(n)]
        g = [0] * n
        
        for v, u in prerequisites:
            print(v,u)
            graph[u].append(v)
            g[v] += 1
        S = [ v for v in range(n) if g[v] == 0]
        
        while S:
            u = S.pop()
            for v in graph[u]:
                g[v] -= 1
                if g[v] == 0:
                    S.append(v)
        return not any(g)

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