Add topological sorting using Khan's algorithm

algorithms/sort/topo_sort_khan.py

@@ -0,0 +1,57 @@
+from collections import defaultdict, deque
+
+def topological_sort(num_vertices, edges):
+    """
+    Perform Topological Sorting using Kahn's Algorithm.
+
+    Parameters:
+    -----------
+    num_vertices : int
+        Number of vertices in the graph (vertices labeled 0 to num_vertices - 1)
+    edges : list of tuple
+        List of directed edges represented as (u, v) meaning u → v
+
+    Returns:
+    --------
+    list
+        A list representing the topological order of vertices.
+        If the graph has a cycle, returns an empty list.
+    """
+
+    # Step 1: Build adjacency list and compute in-degree
+    graph = defaultdict(list)
+    in_degree = [0] * num_vertices
+
+    for u, v in edges:
+        graph[u].append(v)
+        in_degree[v] += 1
+
+    # Step 2: Initialize queue with vertices having in-degree 0
+    queue = deque([i for i in range(num_vertices) if in_degree[i] == 0])
+    topo_order = []
+
+    # Step 3: Process the queue
+    while queue:
+        u = queue.popleft()
+        topo_order.append(u)
+
+        # Decrease in-degree of neighbors
+        for neighbor in graph[u]:
+            in_degree[neighbor] -= 1
+            if in_degree[neighbor] == 0:
+                queue.append(neighbor)
+
+    # Step 4: Check for cycle
+    if len(topo_order) != num_vertices:
+        print("Cycle detected: Topological sort not possible.")
+        return []
+
+    return topo_order
+
+
+# Example Usage
+if __name__ == "__main__":
+    vertices = 6
+    edges = [(5, 2), (5, 0), (4, 0), (4, 1), (2, 3), (3, 1)]
+    order = topological_sort(vertices, edges)
+    print("Topological Sort:", order)