Merge pull request technojam#145 from ankur-kayal/kahn-algo

Kahn's Algorithm for Topological Sort of a Directed Graph added

Graphs/KahnAlgorithmTopologicalSort.cpp

@@ -0,0 +1,120 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+/*
+Input Format: number of vertices of the graph, number of edges of the graph, folloewed by the edges of the directed graph
+Output Format: If the graph has cycle then Graph contains cycle else the topological sort of the vertices of the graph
+ALgorithm: Kahn's Algorithm
+Time Complexity: O(V + E), V = number of vertices of the graph, E = number of edges of the graph
+Space Complexity: O(V + E)
+
+Sample Input and Output
+
+**Sample Input 1:**
+
+Enter the number of vertices of the graph: 8
+
+Enter the number of edges of the graph: 9
+
+Enter edges of the graph in the format u v, u has a directed edge to v:
+1 4
+1 2
+4 2
+4 3
+3 2
+5 2
+3 5
+8 2
+8 6
+
+Topological sort of the graph is: 1 4 3 5 7 8 2 6
+
+
+**Sample Input 2:**
+
+Enter the number of vertices of the graph: 2
+
+Enter the number of edges of the graph: 2
+
+Enter edges of the graph in the format u v, u has a directed edge to v:
+1 2
+2 1
+
+Graph contains cycle!
+*/
+
+int main()
+{
+
+  /*
+    n is the number of vertices of the graph
+    m is the number of edges of the graph
+    Note: here graph means a directed graph
+    */
+
+  int n, m;
+  cout << "\nEnter the number of vertices of the graph: ";
+  cin >> n;
+  cout << "\nEnter the number of edges of the graph: ";
+  cin >> m;
+  vector<int> adj[n + 1];      // stores the adjacency list format of the graph
+  vector<int> indeg(n + 1, 0); // stores the indegree of all vertices of the graph
+
+  cout << "\nEnter edges of the graph in the format u v, u has a directed edge to v: \n";
+  for (int i = 0; i < m; i++)
+  {
+    int u, v;
+    cin >> u >> v;
+    adj[u].push_back(v);
+    indeg[v]++;
+  }
+
+  /*
+    open stores the vertices whose indegrees are zero
+    priority queue with min heap will give the lexicographically smallest topological sort of the graph
+    if the order of the topological sort doesn't matter, replace
+    priority_queue <int, vector <int>, greater<int>> open;
+    with queue<int> open;
+    and replace top() function with front()
+    */
+  priority_queue<int, vector<int>, greater<int>> open;
+  for (int i = 1; i <= n; i++)
+  {
+    if (indeg[i] == 0)
+    {
+      open.push(i);
+    }
+  }
+
+  vector<int> toposort; // this stores the topological sort of the graph
+  while (!open.empty())
+  {
+    int node = open.top();
+    toposort.push_back(node);
+    open.pop();
+    for (auto u : adj[node])
+    {
+      indeg[u]--;
+      // if after decreasing the indegree the indegree of the vertex becomes zero include in the open
+      if (indeg[u] == 0)
+      {
+        open.push(u);
+      }
+    }
+  }
+
+  // if toposort vector doesnt contain all the vertices of the graph then it contains a cycle
+  if ((int)toposort.size() != n)
+  {
+    cout << "\nGraph contains cycle!" << '\n';
+  }
+  else
+  {
+    cout << "\nTopological sort of the graph is: ";
+    for (auto u : toposort)
+    {
+      cout << u << " ";
+    }
+    cout << '\n';
+  }
+}