207. Course Schedule

Medium (Trung bình) Python 🔗 Xem trên LeetCode

📋 Đề Bài

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] = [a_i, b_i] indicates that you must take course b_i first if you want to take course a_i.

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.

Constraints:

1 <= numCourses <= 2000
0 <= prerequisites.length <= 5000
prerequisites[i].length == 2
0 <= a_i, b_i < numCourses
All the pairs prerequisites[i] are unique.

🧠 Thuật Toán & Kỹ Thuật

DFS (Tìm kiếm theo chiều sâu)Hash Table (Bảng băm)Graph (Đồ thị)

⏱️ Thời gian O(V+E)

💾 Không gian O(V)

💻 Lời Giải

Python 0207-course-schedule.py

class Solution:
    def canFinish(self, numCourses: int, prerequisites: List[List[int]]) -> bool:
        adj = defaultdict(list)
        
        for u, v in prerequisites:
            adj[u].append(v)
        
        color = [0] * numCourses
        
        def dfs(u: int) -> bool:
            if color[u] == 1:
                return False
            color[u] = 1
            for v in adj[u]:
                if color[v] == 0:
                    if not dfs(v):
                        return False
                elif color[v] == 1:
                    return False
            color[u] = 2
            return True
        
        for u in range(0, numCourses):
            if color[u] == 0 and not dfs(u):
                return False
        
        return True