Create 207_course_schedule.md

Author: Joseph Luce

leetcode/medium/207_course_schedule.md

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+# 207. Course Schedule
+
+## DFS Recursive Solution
+- Runtime: O(N)
+- Space: O(N)
+- N = Number of courses
+
+When the problem has relationships, such as a course needing more than one prerequisite, you can think of a graph.
+In this case, its a directed graph.
+The core of the problem is to find a cycle in the graph, as example 2 of the problem shows that.
+
+We will need to create a graph, as it is not provided to us, it can be an adjacent list or a matrix, doesn't matter.
+For any dfs, you will need a global visited and a local visited.
+The global visited will tell us if we need to dfs starting at this node, this is to reduce run-time, else it will be O(N^N).
+The local visited is for when we are traversing the graph via. dfs and looking for cycles.
+I decided to use a dictionary to simplify the code, -1 will be used during the dfs, then after the dfs, changed into a 1, showing that its already visited and has no cycles.
+
+```
+from collections import defaultdict
+
+class Solution:
+    def canFinish(self, numCourses: int, prerequisites: List[List[int]]) -> bool:
+        adj_list = self.create_adj_list(prerequisites)
+        visited = defaultdict(int)
+        for node in adj_list:
+            if not self.dfs(node, adj_list, visited):
+                return False
+        return True
+        
+    def dfs(self, node, adj_list, visited):
+        if visited[node] == -1: # currently visiting, cycle
+            return False
+        if visited[node] == 1: # already visited, no cycle
+            return True
+        visited[node] = -1
+        for neighbor in adj_list[node]:
+            if not self.dfs(neighbor, adj_list, visited):
+                return False
+        visited[node] = 1
+        return True
+        
+    def create_adj_list(self, prereqs):
+        adj_list = defaultdict(list)
+        for course, prereq in prereqs:
+            adj_list[course].append(prereq)
+            adj_list[prereq]
+        return adj_list
+```