feat(work): implement Course Schedule II solution

apps/docs/content/topological-sort/210-course-schedule-ii.mdx

@@ -36,4 +36,36 @@ sidebar:
 ```py
 class Solution:
     def findOrder(self, numCourses: int, prerequisites: list[list[int]]) -> list[int]:
+        prereq = {c: [] for c in range(numCourses)}
+        for crs, pre in prerequisites:
+            prereq[crs].append(pre)
+
+        # course has 3 possible states:
+        # visited -> crs has been added to output
+        # visiting -> crs not added to output, but added to cycle
+        # unvisited -> crs not added to output nor cycle
+        output = []
+        visit, cycle = set(), set()
+
+        def dfs(crs):
+            if crs in cycle:
+                return False
+            if crs in visit:
+                return True
+
+            cycle.add(crs)
+            for pre in prereq[crs]:
+                if dfs(pre) == False:
+                    return False
+
+            cycle.remove(crs)
+            visit.add(crs)
+            output.append(crs)
+            return True
+
+        for c in range(numCourses):
+            if dfs(c) == False:
+                return []
+
+        return output
 ```

work/1/Medium/Depth-First Search/210.course-schedule-ii.py

@@ -46,19 +46,51 @@ Output: [0]
 
 Constraints:
 
-	• 1 <= numCourses <= 2000
+        • 1 <= numCourses <= 2000
 
-	• 0 <= prerequisites.length <= numCourses * (numCourses - 1)
+        • 0 <= prerequisites.length <= numCourses * (numCourses - 1)
 
-	• prerequisites[i].length == 2
+        • prerequisites[i].length == 2
 
-	• 0 <= ai, bi < numCourses
+        • 0 <= ai, bi < numCourses
 
-	• ai != bi
+        • ai != bi
 
-	• All the pairs [ai, bi] are distinct.
+        • All the pairs [ai, bi] are distinct.
 """
 
+
 class Solution:
     def findOrder(self, numCourses: int, prerequisites: list[list[int]]) -> list[int]:
+        prereq = {c: [] for c in range(numCourses)}
+        for crs, pre in prerequisites:
+            prereq[crs].append(pre)
 
+        # course has 3 possible states:
+        # visited -> crs has been added to output
+        # visiting -> crs not added to output, but added to cycle
+        # unvisited -> crs not added to output nor cycle
+        output = []
+        visit, cycle = set(), set()
+
+        def dfs(crs):
+            if crs in cycle:
+                return False
+            if crs in visit:
+                return True
+
+            cycle.add(crs)
+            for pre in prereq[crs]:
+                if dfs(pre) == False:
+                    return False
+
+            cycle.remove(crs)
+            visit.add(crs)
+            output.append(crs)
+            return True
+
+        for c in range(numCourses):
+            if dfs(c) == False:
+                return []
+
+        return output