add course schedule article

Author: neetcode-gh

articles/course-schedule.md

@@ -0,0 +1,75 @@
+## 1. Cycle Detection (DFS)
+
+```python
+class Solution:
+    def canFinish(self, numCourses: int, prerequisites: List[List[int]]) -> bool:
+        # Map each course to its prerequisites
+        preMap = {i: [] for i in range(numCourses)}
+        for crs, pre in prerequisites:
+            preMap[crs].append(pre)
+
+        # Store all courses along the current DFS path
+        visiting = set()
+
+        def dfs(crs):
+            if crs in visiting:
+                # Cycle detected
+                return False
+            if preMap[crs] == []:
+                return True
+
+            visiting.add(crs)
+            for pre in preMap[crs]:
+                if not dfs(pre):
+                    return False
+            visiting.remove(crs)
+            preMap[crs] = []
+            return True
+
+        for c in range(numCourses):
+            if not dfs(c):
+                return False
+        return True
+```
+
+### Time & Space Complexity
+
+* Time complexity: $O(V + E)$
+* Space complexity: $O(V + E)$
+
+---
+
+## 2. Topological Sort (Kahn's Algorithm)
+
+```python
+class Solution:
+    def canFinish(self, numCourses: int, prerequisites: List[List[int]]) -> bool:
+        # Build adjacency list
+        indegree = [0] * numCourses
+        adj = [[] for i in range(numCourses)]
+        for src, dst in prerequisites:
+            indegree[dst] += 1
+            adj[src].append(dst)
+
+        # Initialize Queue
+        q = deque()
+        for n in range(numCourses):
+            if indegree[n] == 0:
+                q.append(n)
+
+        # BFS
+        while q:
+            node = q.popleft()
+            for nei in adj[node]:
+                indegree[nei] -= 1
+                if indegree[nei] == 0:
+                    q.append(nei)
+                
+        return sum(indegree) == 0
+```
+
+### Time & Space Complexity
+
+* Time complexity: $O(V + E)$
+* Space complexity: $O(V + E)$
+