LeetCode - 207.Course Schedule

link: https://leetcode.com/problems/course-schedule/

题目

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?

Example 1:

Input: 2, [[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: 2, [[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.

Note:

1. The input prerequisites is a graph represented by a list of edges, not adjacency matrices. Read more about how a graph is represented.
2. You may assume that there are no duplicate edges in the input prerequisites.

问题描述

给出一系列的先修课程关系，判断如果按照这个关系，是否能顺利完成所有课程学习

题目分析

此题目实际是判断有向图中是否存在环，而拓扑排序的一个重要应用就是判断有向图中是否存在环，如果图中不存在环，那么是可以根据这个图求出一个拓扑序列

• 根据拓扑排序的求取方式，我们先记录每个节点的入度数，以及以其为起始节点，对应的所有终止节点
• 每次去选取入度数为0的节点，然后访问掉这个节点，如果节点不存在，那就是说这个图中剩余所有节点都有指向其的边，此时即存在环
• 对应的，将其所指向的节点的入度数全部减1
• 接下来接着去寻找入度为0的节点，已经访问过的节点不再检查，重复步骤，直至节点全部被访问，或者存在环

代码实现

# -*- coding: utf-8 -*-


class Solution:
    def canFinish(self, numCourses, prerequisites):
        """
        :type numCourses: int
        :type prerequisites: List[List[int]]
        :rtype: bool
        """
        all_nodes = {i: {'num': 0, 'node': []} for i in range(numCourses)}
        for end, start in prerequisites:
            all_nodes[start]['node'].append(end)
            all_nodes[end]['num'] += 1

        all_nodes_set = set([_ for _ in range(numCourses)])

        while len(all_nodes_set) != 0:
            flag = False
            for start_node in all_nodes_set:
                if all_nodes[start_node]['num'] == 0:
                    flag = True
                    break
            if not flag:
                return False
            all_nodes_set.remove(start_node)
            for end_node in all_nodes[start_node]['node']:
                all_nodes[end_node]['num'] -= 1
        return True


if __name__ == '__main__':
    solution = Solution()
    assert solution.canFinish(2, [[1, 0]]) is True

运行结果

Time Submitted	Status	Runtime	Language
a few seconds ago	Accepted	268 ms	python3

吐槽

LeetCode给出的模板，函数名和变量名没有按照PEP8规范来，正常是不应该驼峰命名的，而应该是小写加下划线形式

赏

谢谢你请我吃糖果