Add topological sort using DFS and Kahn's algorithm

data_structures/sort/topological_sort.py

@@ -0,0 +1,89 @@
+"""
+Topological Sort implementation using:
+1. DFS-based approach
+2. Kahn's Algorithm (BFS-based approach)
+
+Topological sorting is applicable only for Directed Acyclic Graphs (DAGs).
+
+Reference:
+https://en.wikipedia.org/wiki/Topological_sorting
+"""
+
+from collections import deque
+
+
+def _dfs(
+    node: int,
+    graph: list[list[int]],
+    visited: list[int],
+    result: list[int],
+) -> None:
+    """
+    Helper DFS function for topological sorting.
+    """
+    if visited[node] == 1:
+        raise ValueError("Graph contains a cycle")
+    if visited[node] == 2:
+        return
+
+    visited[node] = 1
+    for neighbor in graph[node]:
+        _dfs(neighbor, graph, visited, result)
+    visited[node] = 2
+    result.append(node)
+
+
+def topological_sort_dfs(vertices: int, edges: list[list[int]]) -> list[int]:
+    """
+    Perform topological sort using DFS.
+
+    Example:
+        vertices = 6
+        edges = [[5, 2], [5, 0], [4, 0], [4, 1], [2, 3], [3, 1]]
+        order = topological_sort_dfs(vertices, edges)
+    """
+    graph: list[list[int]] = [[] for _ in range(vertices)]
+    for u, v in edges:
+        graph[u].append(v)
+
+    visited = [0] * vertices
+    result: list[int] = []
+
+    for vertex in range(vertices):
+        if visited[vertex] == 0:
+            _dfs(vertex, graph, visited, result)
+
+    return result[::-1]
+
+
+def topological_sort_kahn(vertices: int, edges: list[list[int]]) -> list[int]:
+    """
+    Perform topological sort using Kahn's Algorithm.
+
+    Example:
+        vertices = 6
+        edges = [[5, 2], [5, 0], [4, 0], [4, 1], [2, 3], [3, 1]]
+        order = topological_sort_kahn(vertices, edges)
+    """
+    graph: list[list[int]] = [[] for _ in range(vertices)]
+    in_degree = [0] * vertices
+
+    for u, v in edges:
+        graph[u].append(v)
+        in_degree[v] += 1
+
+    queue = deque(i for i in range(vertices) if in_degree[i] == 0)
+    topo_order: list[int] = []
+
+    while queue:
+        node = queue.popleft()
+        topo_order.append(node)
+        for neighbor in graph[node]:
+            in_degree[neighbor] -= 1
+            if in_degree[neighbor] == 0:
+                queue.append(neighbor)
+
+    if len(topo_order) != vertices:
+        raise ValueError("Graph contains a cycle")
+
+    return topo_order