Merge pull request #127 from pankajsingh92533/main

Implemented Tarjan's Algorithm.

Author: himanshu-03

Graphs/Tarjan's_Algorithm.py

@@ -0,0 +1,82 @@
+"""  "defaultdict" in Python
+ is a dictionary-like container from the collections
+module that provides a default value for keys that do not exist."""
+
+from collections import defaultdict
+
+# Function to run Tarjan's algorithm
+def tarjan(graph):
+
+    index = 0
+    stack = []
+    components = []
+
+    # Track visited and index for each node
+    indexes = {}
+    lowlinks = {}
+
+    def strongconnect(node):
+
+        # Set the depth index for this node to the smallest unused index
+        nonlocal index
+        indexes[node] = index
+        lowlinks[node] = index
+        index += 1
+        stack.append(node)
+
+        # Consider successors of `node`
+        try:
+            successors = graph[node]
+        except:
+
+            successors = []
+        for successor in successors:
+            if successor not in indexes:
+                # Successor has not yet been visited; recurse on it
+                strongconnect(successor)
+                lowlinks[node] = min(lowlinks[node], lowlinks[successor])
+            elif successor in stack:
+                # Successor is in the stack, hence in the current SCC
+                lowlinks[node] = min(lowlinks[node], indexes[successor])
+
+        # If `node` is a root node, pop the stack and generate an SCC
+        if lowlinks[node] == indexes[node]:
+            connected_component = []
+
+            while True:
+                successor = stack.pop()
+                connected_component.append(successor)
+                if successor == node:
+                    break
+            components.append(connected_component)
+
+    for node in graph:
+        if node not in indexes:
+            strongconnect(node)
+
+    return components
+
+# Accept dynamic input for the graph
+graph = defaultdict(list)
+num_nodes = int(input("Enter the number of nodes: "))
+for i in range(num_nodes):
+    node = int(input(f"Enter the successors of node {i}: "))
+    successors = list(map(int, input().split()))
+    graph[node] = successors
+
+print("Strongly Connected Components:")
+print(tarjan(graph))
+
+
+
+""" Explanation:->
+
+1)  Tarjan's algorithm performs a DFS on the graph to find strongly connected components. 
+
+2) It maintains an index (incremented for each visited node), a stack of visited nodes, and a lowlink value for each node (lowest index reachable from that node).
+
+3) When visiting a node, if any successor is in the stack, the lowlink is updated to be the minimum of its current value and the successor's index. 
+
+4) If the lowlink of a node equals its own index, it is a root node and the current stack represents an SCC. This SCC is popped from the stack and added to the final components list.
+
+5) After Tarjan's finishes, the components list contains all the SCCs in the graph."""