Merge pull request #635 from Anirban166/patch-3

feat: add Kosaraju's algorithm to find all the strongly connected components in a graph.

Graph/kosaraju.cpp

@@ -0,0 +1,134 @@
+/* Implementation of Kosaraju's Algorithm to find out the strongly connected components (SCCs) in a graph. 
+   Author:Anirban166
+*/   
+
+#include<iostream>
+#include<vector>
+
+using namespace std;
+
+/**
+* Iterative function/method to print graph:
+* @param a[] : array of vectors (2D)
+* @param V : vertices
+* @return void 
+**/
+void print(vector<int> a[],int V)
+{
+    for(int i=0;i<V;i++)
+    {
+        if(!a[i].empty())
+            cout<<"i="<<i<<"-->";
+        for(int j=0;j<a[i].size();j++)
+            cout<<a[i][j]<<" ";
+        if(!a[i].empty())
+            cout<<endl;
+    }
+}
+
+/**
+* //Recursive function/method to push vertices into stack passed as parameter:
+* @param v : vertices
+* @param &st : stack passed by reference
+* @param vis[] : array to keep track of visited nodes (boolean type)
+* @param adj[] : array of vectors to represent graph
+* @return void 
+**/
+void push_vertex(int v,stack<int> &st,bool vis[],vector<int> adj[])
+{
+    vis[v]=true;
+    for(auto i=adj[v].begin();i!=adj[v].end();i++)
+    {
+        if(vis[*i]==false)
+            push_vertex(*i,st,vis,adj);
+    }
+    st.push(v);
+}
+
+
+/**
+* //Recursive function/method to implement depth first traversal(dfs):
+* @param v : vertices
+* @param vis[] : array to keep track of visited nodes (boolean type)
+* @param grev[] : graph with reversed edges
+* @return void 
+**/
+void dfs(int v,bool vis[],vector<int> grev[])
+{
+    vis[v]=true;
+    // cout<<v<<" ";
+    for(auto i=grev[v].begin();i!=grev[v].end();i++)
+    {
+        if(vis[*i]==false)
+            dfs(*i,vis,grev);
+    }
+}
+
+//function/method to implement Kosaraju's Algorithm:
+/**
+* Info about the method
+* @param V : vertices in graph
+* @param adj[] : array of vectors that represent a graph (adjacency list/array)
+* @return int ( 0, 1, 2..and so on, only unsigned values as either there can be no SCCs i.e. none(0) or there will be x no. of SCCs (x>0))
+   i.e. it returns the count of (number of) strongly connected components (SCCs) in the graph. (variable 'count_scc' within function)
+**/
+int kosaraju(int V, vector<int> adj[])
+{
+    bool vis[V]={};
+    stack<int> st;
+    for(int v=0;v<V;v++)
+    {
+        if(vis[v]==false)
+            push_vertex(v,st,vis,adj);
+    }
+    //making new graph (grev) with reverse edges as in adj[]:
+    vector<int> grev[V];
+    for(int i=0;i<V+1;i++)
+    {
+        for(auto j=adj[i].begin();j!=adj[i].end();j++)
+        {
+            grev[*j].push_back(i);
+        }
+    }
+    // cout<<"grev="<<endl; ->debug statement
+    // print(grev,V);       ->debug statement
+    //reinitialise visited to 0
+    for(int i=0;i<V;i++)
+        vis[i]=false;
+    int count_scc=0;
+    while(!st.empty())
+    {
+        int t=st.top();
+        st.pop();
+        if(vis[t]==false)
+        {
+            dfs(t,vis,grev);
+            count_scc++;
+        }
+    }
+    // cout<<"count_scc="<<count_scc<<endl; //in case you want to print here itself, uncomment & change return type of function to void.
+    return count_scc;
+}
+
+//All critical/corner cases have been taken care of.
+//Input your required values: (not hardcoded)
+int main()
+{
+    int t;
+    cin>>t; 
+    while(t--)
+    {
+        int a,b ; //a->number of nodes, b->directed edges.
+   	  cin>>a>>b;
+   	  int m,n;
+   	  vector<int> adj[a+1];
+        for(int i=0;i<b;i++) //take total b inputs of 2 vertices each required to form an edge.
+        {
+            cin>>m>>n; //take input m,n denoting edge from m->n.
+            adj[m].push_back(n);
+        }
+        //pass number of nodes and adjacency array as parameters to function:
+        cout<<kosaraju(a, adj)<<endl;
+    }
+    return 0;
+}