Count all possible paths between two vertices

Counting all paths between two nodes in graph

Here given code implementation process.

//C Program to 
//Count all possible paths between two vertices
#include<stdio.h>
#include<stdlib.h>

struct AjlistNode{
  int vId;//Vertices id
  struct AjlistNode*next;
};

struct Graph{
  int data; //node key value
  struct AjlistNode*next;
};



int size; //number of nodes

//set node key value
void setData(struct Graph*node)
{
  if(node!=NULL && size>0)
  {
    int index=0;
    for(index;index<size;index++)
    {
      //set vertic node data
      node[index].data=index;//set node key
      //Initial no AjlistNode
      //set NULL Value
      node[index].next=NULL;
    }
  }else{
    printf("Vertic Node is Empty");
  }
}
//Add Edge from Two given Nodes
void addEdge(struct Graph*node, int V ,int E)
{
    //add edge form V to E
    //V and E is Node location
  if(V<size && E <size)
  {
      //first create Adjacency node
    struct AjlistNode *newEdge=(struct AjlistNode*)malloc(
      sizeof(struct AjlistNode)
      );
    if(newEdge!=NULL)
    {

      newEdge->next=NULL;
      newEdge->vId=E;

      struct AjlistNode *temp=node[V].next;

      if(temp==NULL)
      {
        node[V].next=newEdge;
      }else
      {
                //Add node at last
        while(temp->next!=NULL)
        {
          temp=temp->next;
        }      
        temp->next=newEdge;          
      }
    }else
    {
      printf("\n Memory overflow");
    }
  }else
  {
      //not valid Vertices
    printf("Invalid Node Vertices %d  %d", V,E);
  }
}
//Display Adjacency list of vertex
void printGraph(struct Graph*node)
{
  if(node!=NULL)
  {
    struct AjlistNode *temp=NULL;
    for(int index=0;index<size;index++)
    {
      printf("\n Adjacency list of vertex %d  :",index);
      temp=node[index].next;
      while(temp!=NULL)
      {
        //temp->vId is graph node vertices
        //in this case temp->vId is same as 
        //node[temp->vId].data

        printf("  %d",node[temp->vId].data);
        temp=temp->next;
      }
    }
  }else
  {
    printf("Empty Graph");
  }
}


//This function are capable to count all path between two nodes
void count_path(int start,
  int end,
  int *visit,
  struct Graph*node,
  int*result)
{

  if(start >size 
    || end >size 
    || start<0 
    || end<0 
    || node==NULL)
  {
    //invalid node location
    return ;
  }

  if(visit[start]==1)
  {
    //node is already visited
    return;
  }
  if(start==end)
  {
    //when source and destination are get
    *result=(*result)+1;
  }
  //active the visiting node status
  visit[start]=1;

  struct AjlistNode *temp=node[start].next;

  while(temp!=NULL)
  {
    //check node by edges
    count_path(temp->vId,end,visit,node,result); 

    temp=temp->next;
  }
  //inactive current visiting node status
  visit[start]=0;
}


int main()
{

  size=6; //set number of nodes
  struct Graph*node=NULL;

  int *visit=(int*)calloc(size,sizeof(int));

  //Creating memory of graph nodes
  node=(struct Graph*)malloc(sizeof(struct Graph)*size);
  
  if(node==NULL)
  {
    printf("\n Memory overflow");

  }else
  {
    //First set node keys
    setData(node); 

    //Connected two node with Edges
    addEdge(node,0, 1); 
    addEdge(node,0, 3); 
    addEdge(node,1, 2); 
    addEdge(node,1, 4); 
    addEdge(node,2, 3); 
    addEdge(node,2, 4); 
    addEdge(node,2, 5); 
    addEdge(node,3, 1); 
    addEdge(node,3, 5); 
    addEdge(node,5, 4); 



    printGraph(node);

    //value 0 is source node
    int source = 0;

    //value 4 is destination node
    int destination = 4;

    //for resultant paths
    int result=0;

    count_path(source,destination,visit,node,&result);

    printf("\n Possible Path : %d\n",result );
  }  
  return 0;
}

Output

 Adjacency list of vertex 0  :  1  3
 Adjacency list of vertex 1  :  2  4
 Adjacency list of vertex 2  :  3  4  5
 Adjacency list of vertex 3  :  1  5
 Adjacency list of vertex 4  :
 Adjacency list of vertex 5  :  4
 Possible Path : 8
//C++ program
//Count all possible paths between two vertices
#include <iostream>
using namespace std;

struct AjlistNode
{
    int vId;//Vertices id
    struct AjlistNode*next;
  };

  struct Vertices
  {
    int data; //node key value
    struct AjlistNode*next;
  };


  class Graph
  {
    Vertices *node;
  int size;//number of 
public:
  Graph(int);
  void setData();
  void addEdge(int,int);
  void printGraph();
  void connect(int  ,int );
  void count_path(int,int ,int* ,int*);
  void total_path(int,int);
};
Graph::Graph(int size)
{
  this->size = size;
    //set number of nodes
  node = new Vertices[size];
}
//set node key value
void Graph:: setData()
{
  if(node!=NULL)
  {
    int index=0;

    for(index;index<size;index++)
    {
      //set vertic node data
      node[index].data=index;//set node key
      //Initial no AjlistNode
      //set NULL Value
      node[index].next=NULL;
    }
  }
  else
  {
    cout<<"Vertic Node is Empty"<<endl;
  }
}
//Add Edge from Two given Nodes
void Graph ::connect(int start ,int end)
{
    //add edge form start to end
    //start and end is Node location
    //first create Adjacency node
  AjlistNode *newEdge=new AjlistNode;

  if(newEdge!=NULL)
  {

    newEdge->next = NULL;
    newEdge->vId = end;

    AjlistNode *temp=node[start].next;

    if(temp==NULL)
    {
      node[start].next=newEdge;
    }else
    {
            //Add node at last
      while(temp->next!=NULL)
      {
        temp=temp->next;
      }      
      temp->next=newEdge;          
    }
  }

}


void Graph ::  addEdge(int V ,int E)
{
  //add edge form V to E
  //V and E is Node location
  if(V<size && E <size)
  {
    connect(V,E);

  }else
  {
        //not valid Vertices
    cout<<"Invalid Node Vertices "<< V<<" "<<E;
  }
}

//Display Adjacency list of vertex
void Graph:: printGraph()
{
  if(node!=NULL)
  {
    AjlistNode *temp=NULL;
    for(int index=0; index < size; index++)
    {
      cout<<"\n Adjacency list of vertex "<<index<<" :";
      temp=node[index].next;
      while(temp!=NULL)
      {
        //temp->vId is graph node vertices
        //in this case temp->vId is same as 
        //node[temp->vId].data

        cout<<" "<<node[temp->vId].data;
        temp=temp->next;
      }
    }
  }else
  {
    cout<<"Empty Graph"<<endl;
  }
}


//This function are capable to count all path between two nodes
void Graph:: count_path(int start,
 int end,
 int *visit,
 int*result)
{
  if(start >size 
   || end >size 
   || start<0 
   || end<0 
   || node==NULL)
  {
    //invalid node location
    return ;
  }
  if(visit[start]==1)
  {
    //node is already visited
    return;
  }
  if(start==end)
  {
    //when source and destination are get
    *result=(*result)+1;
  }
  //active the visiting node status
  visit[start]=1;
  AjlistNode *temp=node[start].next;
  while(temp!=NULL)
  {
    //check node by edges
    count_path(temp->vId,end,visit,result); 
    temp=temp->next;
  }
  //inactive current visiting node status
  visit[start]=0;
}

void Graph :: total_path(int source,int destination)
{
   //for resultant paths
  int result=0;
  int visit[size];
  for(int i=0;i<size;i++)
  {
    visit[i]=0;
  }
  count_path(source,destination,visit,&result);
  cout<<"\n Possible Path : "<<result<<"\n";
}

int main()
{
  //Create Object
  Graph g=Graph(6); //6 nodes
  //First set node keys
  g.setData();

  //Connected two node with Edges
  g.addEdge(0, 1); 
  g.addEdge(0, 3); 
  g.addEdge(1, 2); 
  g.addEdge(1, 4); 
  g.addEdge(2, 3); 
  g.addEdge(2, 4); 
  g.addEdge(2, 5); 
  g.addEdge(3, 1); 
  g.addEdge(3, 5); 
  g.addEdge(5, 4); 

  g.printGraph();

  //value 0 is source node
  int source = 0;
  //value 4 is destination node
  int destination = 4;

  g.total_path(source,destination);
 
  return 0;
}

Output

 Adjacency list of vertex 0 : 1 3
 Adjacency list of vertex 1 : 2 4
 Adjacency list of vertex 2 : 3 4 5
 Adjacency list of vertex 3 : 1 5
 Adjacency list of vertex 4 :
 Adjacency list of vertex 5 : 4
 Possible Path : 8
//Java program
//Count all possible paths between two vertices
public class MyGraph
{

    static class AjlistNode
    {
        int id;//Vertices node key
        AjlistNode next;
    }
    static class Vertices
    {
        int data;
        AjlistNode next;
    }

    //number of Vertices
    public int size,result;
    Vertices node[];

    MyGraph(int size)
    {
        //set value
        this.size = size;
        result = 1;
        node = new Vertices[size];
        
    }

    //set initial node value
    public void setData()
    {
        if(node == null)
        {
            System.out.println("\nEmpty Graph");
        }else
        {
            for(int index = 0; index < size; index++)
            {
                // avoid java.lang.nullPointerException
                node[index]=new Vertices(); 
                node[index].data=index;//set your data
                node[index].next=null;
            }
        }
    }
    //connect two nodes
    public void connect(int start,int end)
    {
        AjlistNode newEdge=new AjlistNode();
        newEdge.id=end;//end node
        newEdge.next=null;
        if(node[start].next==null)
        {
            node[start].next=newEdge;
        }else
        {
            AjlistNode temp=node[start].next;

            while(temp.next!=null)
            {
                temp=temp.next;
            }
            temp.next=newEdge;
        }
    }
    //Add edge at the end
    public void addEdge(int start,int end)
    {
        if(start < size && end < size && node != null)
        {
           connect(start,end);
           
        }else{
            System.out.println("\nEmpty Graph");
        }
    }

    public void printGraph()
    {

        if(size>0 && node!=null)
        {
            for(int index=0;index < size;index++)
            {
                System.out.print("\nAdjacency list of vertex "+index+" :");
                
                AjlistNode temp=node[index].next;

                while(temp!=null)
                {
                    System.out.print("  "+node[temp.id].data);

                    temp=temp.next;
                }
            }
        }
    }
    //This function are capable to count all path between two nodes
    public void  count_path(int start,int end,boolean []visit)
    {
      if(start >size 
       || end >size 
       || start<0 
       || end<0 
       || node==null)
      {
        //invalid node location
        return ;
      }
      if(visit[start]==true)
      {
        //node is already visited
        return;
      }
      if(start==end)
      {
        //when source and destination are get
         result=result+1;
      }
      //active the visiting node status
      visit[start]=true;
      AjlistNode  temp=node[start].next;
      while(temp!=null)
      {
        //check node by edges
        count_path(temp.id,end,visit); 
        temp=temp.next;
      }
      //inactive current visiting node status
      visit[start]=false;
    }

    public void  total_path(int source,int destination)
    {
      //for resultant paths
      result=0;
      boolean []visit=new boolean[size];
      for(int i=0;i<size;i++)
      {
        visit[i]=false;
      }
      count_path(source,destination,visit);
      System.out.println("\n Possible Path : "+result);
    }
    
    public static void main(String[] args) 
    {
        int totalNode=6;

        MyGraph g=new MyGraph(totalNode);
        
        g.setData();

        //Connected two node with Edges
        g.addEdge(0, 1); 
        g.addEdge(0, 3); 
        g.addEdge(1, 2); 
        g.addEdge(1, 4); 
        g.addEdge(2, 3); 
        g.addEdge(2, 4); 
        g.addEdge(2, 5); 
        g.addEdge(3, 1); 
        g.addEdge(3, 5); 
        g.addEdge(5, 4); 

        g.printGraph();

        //value 0 is source node
        int source = 0;
        //value 4 is destination node
        int destination = 4;

        g.total_path(source,destination);

    }
}

Output

Adjacency list of vertex 0 :  1  3
Adjacency list of vertex 1 :  2  4
Adjacency list of vertex 2 :  3  4  5
Adjacency list of vertex 3 :  1  5
Adjacency list of vertex 4 :
Adjacency list of vertex 5 :  4
 Possible Path : 8
#Python program
#Count all possible paths between two vertices
#Using DFS
class AjLinkeNode:
  def __init__(self,data):
    self.id=data
    self.next=None

class Vertices:
  def __init__(self,data):
    self.data=data
    self.next=None

class Graph:
  """Constructor for Graph"""
  def __init__(self, size):
    self.size=size
    self.node=[]
    self.result=0
    

  def setData(self):
    if(self.size>0 and self.node!=None):

      index=0
      while(index<self.size):

        self.node.append(Vertices(index))

        index+=1


  #connect two node with  edge
  def connect(self,start,end):

    new_edge=AjLinkeNode(end)

    if(self.node[start].next==None):

      self.node[start].next=new_edge
    else:

      temp=self.node[start].next

      while(temp.next!=None):

        temp=temp.next

      temp.next=new_edge  

  #add edge
  def addEdge(self,start,end):
     
    #start,end is two nodes
    if(self.size > start and self.size > start):
      
      self.connect(start,end)

    else:
      print("Invalid nodes")


  def printGraph(self):

    if(self.size>0 and self.node!=None):

      index=0

      while(index < self.size):

        print("\nAdjacency list of vertex {0} : ".format(index),end=" ")
        
        temp=self.node[index].next
        
        while temp!=None:

          print(" {0}".format(temp.id),end=" ")

          temp=temp.next

        index+=1

  
  #This function are capable to count all path between two nodes
  def count_path(self,start,end,visit) :

    if(start >self.size  or  end >self.size or start<0 or end<0 or self.node==None) :

      #invalid node location
      return 
    if(visit[start]==True) :

      #node is already visited
      return
    if(start==end) :

      #when source and destination are get
      self.result+=1

    #active the visiting node status
    visit[start]=True
    temp=self.node[start].next
    while(temp!=None) :

      #check node by edges
      self.count_path(temp.id,end,visit) 
      temp=temp.next

    #inactive current visiting node status
    visit[start]=False

  def  total_path(self,source,destination) :

    #for resultant paths
    self.result=0
    visit=[False]*self.size

    self.count_path(source,destination,visit)
    print("\n Possible Path : ",self.result)
    


    
def main():
  g=Graph(6)
  g.setData() 
  #Connected two node with Edges
  g.addEdge(0, 1) 
  g.addEdge(0, 3) 
  g.addEdge(1, 2) 
  g.addEdge(1, 4) 
  g.addEdge(2, 3) 
  g.addEdge(2, 4) 
  g.addEdge(2, 5) 
  g.addEdge(3, 1) 
  g.addEdge(3, 5) 
  g.addEdge(5, 4) 
  g.printGraph()
  #value 0 is source node
  source = 0
  #value 4 is destination node
  destination = 4
  g.total_path(source,destination)

if __name__=="__main__":
    main()

Output

Adjacency list of vertex 0 :   1  3 
Adjacency list of vertex 1 :   2  4 
Adjacency list of vertex 2 :   3  4  5 
Adjacency list of vertex 3 :   1  5 
Adjacency list of vertex 4 :  
Adjacency list of vertex 5 :   4 
 Possible Path :  8
//C# program
//Count all possible paths between two vertices
//Using DFS
using System;
public class AjlistNode
{
  public int id;//Vertices node key
  public AjlistNode next;
}
public class Vertices
{
  public int data;
  public AjlistNode next;
}

public class MyGraph
{

  //number of Vertices
  public int size,result;
  public Vertices []node;

  MyGraph(int size)
  {
    //set value
    this.size = size;
    result = 1;
    node = new Vertices[size];

  }

  //set initial node value
  public void setData()
  {
    if(node == null)
    {
      Console.WriteLine("\nEmpty Graph");
    }else
    {
      for(int index = 0; index < size; index++)
      {
        // avoid java.lang.nullPointerException
        node[index]=new Vertices(); 
        node[index].data=index;//set your data
        node[index].next=null;
      }
    }
  }
  //connect two nodes
  public void connect(int start,int end)
  {
    AjlistNode newEdge=new AjlistNode();
    newEdge.id=end;//end node
    newEdge.next=null;
    if(node[start].next==null)
    {
      node[start].next=newEdge;
    }else
    {
      AjlistNode temp=node[start].next;

      while(temp.next!=null)
      {
        temp=temp.next;
      }
      temp.next=newEdge;
    }
  }
  //Add edge at the end
  public void addEdge(int start,int end)
  {
    if(start < size && end < size && node != null)
    {
      connect(start,end);

    }else{
      Console.WriteLine("\nEmpty Graph");
    }
  }

  public void printGraph()
  {

    if(size>0 && node!=null)
    {
      for(int index=0;index < size;index++)
      {
        Console.Write("\nAdjacency list of vertex "+index+" :");

        AjlistNode temp=node[index].next;

        while(temp!=null)
        {
          Console.Write("  "+node[temp.id].data);

          temp=temp.next;
        }
      }
    }
  }
  //This function are capable to count all path between two nodes
  public void  count_path(int start,int end,Boolean []visit)
  {
    if(start >size 
      || end >size 
      || start<0 
      || end<0 
      || node==null)
    {
      //invalid node location
      return ;
    }
    if(visit[start]==true)
    {
      //node is already visited
      return;
    }
    if(start==end)
    {
      //when source and destination are get
      result=result+1;
    }
    //active the visiting node status
    visit[start]=true;
    AjlistNode  temp=node[start].next;
    while(temp!=null)
    {
      //check node by edges
      count_path(temp.id,end,visit); 
      temp=temp.next;
    }
    //inactive current visiting node status
    visit[start]=false;
  }

  public void  total_path(int source,int destination)
  {
    //for resultant paths
    result=0;
    Boolean []visit=new Boolean[size];
    for(int i=0;i<size;i++)
    {
      visit[i]=false;
    }
    count_path(source,destination,visit);
    Console.WriteLine("\n Possible Path : "+result);
  }

  public static void Main(String[] args) 
  {
    int totalNode=6;

    MyGraph g=new MyGraph(totalNode);

    g.setData();

    //Connected two node with Edges
    g.addEdge(0, 1); 
    g.addEdge(0, 3); 
    g.addEdge(1, 2); 
    g.addEdge(1, 4); 
    g.addEdge(2, 3); 
    g.addEdge(2, 4); 
    g.addEdge(2, 5); 
    g.addEdge(3, 1); 
    g.addEdge(3, 5); 
    g.addEdge(5, 4); 

    g.printGraph();

    //value 0 is source node
    int source = 0;
    //value 4 is destination node
    int destination = 4;

    g.total_path(source,destination);

  }
}

Output

Adjacency list of vertex 0 :  1  3
Adjacency list of vertex 1 :  2  4
Adjacency list of vertex 2 :  3  4  5
Adjacency list of vertex 3 :  1  5
Adjacency list of vertex 4 :
Adjacency list of vertex 5 :  4
 Possible Path : 8
<?php 
/*
* PHP Program 
//Count all possible paths between two vertices
*/

class AjlistNode
{
  public $vId;
  public $next;
  function __construct($vId)
  {
    $this->vId=$vId;
    $this->next=NULL;
  }
}
class Node
{
  public $data;
  public $next;
  function __construct($data)
  {
    $this->data=$data;
    $this->next=NULL;

  }
}
class MyGraph
{

  public $node;
  public $size;
  function __construct($size)
  {
    $this->size=$size;
    $this->node=[];  //empty array
  }
  public function setData()
  {
    if($this->size>0)
    {
      for($index=0;$index<$this->size;$index++)
      {
        $this->node[$index]=new Node($index);
      }

    }
  }
  public function connect($start,$end)
  {
    $newEdge=new AjlistNode($end);
    if($this->node[$start]->next==NULL)
    {
      $this->node[$start]->next=$newEdge;
    }
    else
    {

      $temp=$this->node[$start]->next;
      while($temp->next!=NULL)
      {
        $temp=$temp->next;
      }
      $temp->next= $newEdge;
    }
  }
  public function addEdge($start,$end)
  {
    if($this->size > $start && $this->size>$end)
    {
      $this->connect($start,$end);
    }
    else
    {
      echo "\n Invalid node";
    }
  }
  public function printGraph()
  {
    if($this->size>0 && count($this->node)>0 && $this->node!=NULL)
    {
      for($index=0;$index<$this->size;$index++)
      {
        echo ("\nAdjacency list of vertex ".$index." : ");
        $temp=$this->node[$index]->next;
        while($temp!=NULL)
        {
          echo ("  ".$this->node[$temp->vId]->data);
          $temp=$temp->next;
        }
      }
    }
  }




  
//This function are capable to count all path between two nodes
  public function count_path($start,
    $end,
    &$visit,
    &$result)
  {
    if($start>$this->size 
      || $end>$this->size 
      || $start<0 
      || $end<0 
    )
    {
      //invalid node location
      return ;
    }
    if($visit[$start]==true)
    {
      //node is already visited
      return;
    }
    if($start==$end)
    {
      //when source and destination are get
      $result=($result)+1;
    }
    //active the visiting node status
    $visit[$start]=true;
    $temp= $this->node[$start]->next;
    while($temp!=NULL)
    {
      //check node by edges
      $this->count_path($temp->vId,$end,$visit,$result); 
      $temp=$temp->next;
    }
    //inactive current visiting node status
    $visit[$start]=false;
  }
  
  public function total_path($source,$destination)
  {
   //for resultant paths
   $result=0;
   $visit= array_fill(0, $this->size, false);
   $this->count_path($source,$destination,$visit,$result);
   echo "\n Possible Path : ".$result."\n";
 }

}


function main()
{
    //create object
  $g=new MyGraph(6);
  $g->setData();

  //Connected two node with Edges
  $g->addEdge(0,1); 
  $g->addEdge(0,3); 
  $g->addEdge(1,2); 
  $g->addEdge(1,4); 
  $g->addEdge(2,3); 
  $g->addEdge(2,4); 
  $g->addEdge(2,5); 
  $g->addEdge(3,1); 
  $g->addEdge(3,5); 
  $g->addEdge(5,4); 

  $g->printGraph();
  
  //value 0 is source node
  $source=0;
  //value 4 is destination node
  $destination=4;
  
  $g->total_path($source,$destination);

}
main();
?>

Output

Adjacency list of vertex 0 :   1  3
Adjacency list of vertex 1 :   2  4
Adjacency list of vertex 2 :   3  4  5
Adjacency list of vertex 3 :   1  5
Adjacency list of vertex 4 : 
Adjacency list of vertex 5 :   4
 Possible Path : 8


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