course-schedule dfs py3

0207_course-schedule/README.md

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+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.
+    
+
+**Constraints:**
+
+*   `1 <= numCourses <= 2000`
+*   `0 <= prerequisites.length <= 5000`
+*   `prerequisites[i].length == 2`
+*   `0 <= ai, bi < numCourses`
+*   All the pairs prerequisites\[i\] are **unique**.
+
+https://leetcode.com/problems/course-schedule

0207_course-schedule/python3/dfs.py

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+from collections import defaultdict
+
+class Solution:
+    def canFinish(self, numCourses: int, prerequisites: List[List[int]]) -> bool:
+        graph = defaultdict(list)
+        
+        for course, pre in prerequisites:
+            graph[course].append(pre)
+        
+        cycles = set()
+        visited = set()
+        
+        def dfs(course):
+            if course in cycles:
+                return False
+            
+            if course in visited:
+                return True
+            
+            visited.add(course)
+            cycles.add(course)
+            
+            for dep in graph[course]:
+                if not dfs(dep):
+                    return False
+                
+            cycles.remove(course)
+            
+            return True
+        
+        for course in range(numCourses):
+            cycles = set()
+            
+            if not dfs(course):
+                return False
+        
+        return True
+