Merge pull request #129 from Sugyanee/add-graph-algorithm-cpp

Add Topological sorting algorithm cpp

Author: admirerr

CPP/graph/topological_sorting.cpp

@@ -0,0 +1,85 @@
+/****************************************
+Problem: Topological Sorting of a Directed Acyclic Graph (DAG)
+
+Description:
+Given a Directed Acyclic Graph (DAG) with V vertices and E edges, 
+find any valid topological ordering of the graph. In a topological 
+ordering, for every directed edge u -> v, node u will always appear 
+before node v in the ordering. 
+
+This ordering is useful in scenarios such as task scheduling, 
+course prerequisite resolution, and resolving symbol dependencies 
+in compilers.
+
+Time Complexity: O(V + E) - each vertex and edge is processed once
+Space Complexity: O(V + E) - adjacency list, in-degree array/stack/queue, and output list
+****************************************/
+
+#include <bits/stdc++.h>
+using namespace std;
+
+class Solution {
+private:
+// Helper function to perform DFS and push nodes into stack
+	void dfs(int node, int vis[], stack<int> &st,
+	         vector<int> adj[]) {
+		vis[node] = 1; // Mark node as visited
+
+		for (auto it : adj[node]) {  // Visit all unvisited neighbors
+			if (!vis[it]) dfs(it, vis, st, adj);
+		}
+
+        // Once all neighbors are processed, push current node
+		st.push(node);
+	}
+public:
+	//Function to return list containing vertices in Topological order.
+	vector<int> topoSort(int V, vector<int> adj[])
+	{
+		int vis[V] = {0};
+		stack<int> st;
+
+        // Run DFS from every unvisited node
+		for (int i = 0; i < V; i++) {
+			if (!vis[i]) {
+				dfs(i, vis, st, adj);
+			}
+		}
+
+        // Extract nodes from stack to get topological order
+		vector<int> ans;
+		while (!st.empty()) {
+			ans.push_back(st.top());
+			st.pop();
+		}
+		return ans;
+	}
+};
+
+
+int main() {
+
+    // Example graph:
+    // V = 6
+    // Edges: 2 -> 3, 3 -> 1, 4 -> 0, 4 -> 1, 5 -> 0, 5 -> 2
+	vector<int> adj[6] = {{}, {}, {3}, {1}, {0, 1}, {0, 2}};
+	int V = 6;
+	Solution obj;
+	vector<int> ans = obj.topoSort(V, adj);
+    cout<<"Topological sorting: ";
+	for (auto node : ans) {
+		cout << node << " ";
+	}
+	cout << endl;
+
+	return 0;
+}
+
+/****************************************
+Expected Output for the test case:
+
+Topological Sorting: 5 4 2 3 1 0 
+
+(Note: For topological sort, multiple valid outputs are possible.
+For example, "4 5 2 3 1 0" is also valid.)
+****************************************/