Create main.cpp

Author: JawadSher

23 - Graph Data Structure Problems/10 - Topological Sort using Kahn's Algorithm/main.cpp

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+#include <bits/stdc++.h>
+using namespace std;
+
+// Function to perform Topological Sort using Kahn's Algorithm
+void KahnsAlgorithm(vector<vector<int>>& adj, int V) {
+    // Step 1: Initialize the indegree array with zeros
+    // indegree[i] will store the number of incoming edges to vertex i
+    vector<int> indegree(V, 0);
+
+    // Step 2: Create a queue for processing nodes with indegree 0
+    queue<int> q;
+
+    // Step 3: Create a vector to store the topological order of nodes
+    vector<int> topoOrder;
+
+    // Step 4: Calculate the indegree for all vertices
+    for (int i = 0; i < V; i++) {
+        for (int neighbour : adj[i]) {
+            indegree[neighbour]++; // Increment indegree of each neighbor
+        }
+    }
+
+    // Step 5: Add all vertices with indegree 0 to the queue
+    for (int i = 0; i < V; i++) {
+        if (indegree[i] == 0) {
+            q.push(i); // Push vertices with no dependencies into the queue
+        }
+    }
+
+    // Step 6: Process the vertices in the queue one by one
+    while (!q.empty()) {
+        int node = q.front(); // Get the vertex at the front of the queue
+        q.pop(); // Remove it from the queue
+
+        topoOrder.push_back(node); // Add the vertex to the topological order
+
+        // Step 7: For each neighbor of the current vertex
+        for (auto neighbour : adj[node]) {
+            indegree[neighbour]--; // Decrease the indegree of the neighbor
+
+            // If the indegree of the neighbor becomes 0, add it to the queue
+            if (indegree[neighbour] == 0) {
+                q.push(neighbour);
+            }
+        }
+    }
+
+    // Step 8: If the topological order contains all vertices, print it
+    if (topoOrder.size() != V) {
+        // If the size of the topological order is not equal to the number of vertices
+        // it means there was a cycle in the graph, and topological sort is not possible
+        cout << "The graph is not a DAG. Topological sort not possible.\n";
+        return;
+    }
+
+    // Step 9: Output the topological sort
+    cout << "Topological sorting of the graph: ";
+    for (int node : topoOrder) {
+        cout << node + 1 << " "; // Print node numbers (1-based indexing)
+    }
+    cout << endl;
+}
+
+int main() {
+    // Step 10: Number of vertices (nodes) in the graph
+    int V = 5;
+
+    // Step 11: Define the directed edges of the graph
+    // Format: {from, to}
+    vector<vector<int>> edges = {{1, 2}, {1, 3}, {2, 5}, {3, 5}, {5, 4}};
+
+    // Step 12: Initialize the adjacency list for the graph
+    vector<vector<int>> adj(V);
+
+    // Step 13: Convert the edge list to an adjacency list
+    // Adjusting for 0-based indexing
+    for (auto i : edges) {
+        adj[i[0] - 1].push_back(i[1] - 1);
+    }
+
+    // Step 14: Call the Kahn's Algorithm function to perform topological sort
+    KahnsAlgorithm(adj, V);
+
+    return 0;
+}