Find Maximum cost from source node to destination

Find Maximum cost from source node to destination

Here given code implementation process.

//C Program
//Find Maximum cost from source node to destination
#include <stdio.h>
#include <stdlib.h>
#include <limits.h> //for INT_MAX
struct AjlistNode
{
  int vId;//Vertices id
  int weight;
  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");
  }
}
void connect_edge(struct Graph*node, int V ,int E,int weight)
{

    // create Adjacency node
  struct AjlistNode *newEdge=(struct AjlistNode*)malloc(
    sizeof(struct AjlistNode)
    );
  if(newEdge!=NULL)
  {

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

    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");

  }
}
  //Add Edge from Two given Nodes
void addEdge(struct Graph*node, int V ,int E,int weight)
{
    //add edge form V to E
    //V and E is Node location
  if(V<size && E <size)
  {

    connect_edge(node,V,E,weight);
    connect_edge(node,E,V,weight);

  }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");
  }
}



void max_cost(int start,int end,int *visit,struct Graph*node,int*result,int sum)
{

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


  if(visit[start]==1)
  {
    return;
  }
  if(start==end)
  {
    if(*result<sum)
    {
      //when get new result
      *result=sum;
    }
  }
  visit[start]=1;
  struct AjlistNode *temp=node[start].next;
  while(temp!=NULL)
  {
    max_cost(temp->vId,end,visit,node,result,sum+temp->weight); 

    temp=temp->next;
  }

  visit[start]=0;
}



int main()

{

  size=6;

  struct Graph*node=NULL;

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

  node=(struct Graph*)malloc(sizeof(struct Graph)*size);

  if(node==NULL)
  {
    printf("\n Memory overflow");
  }else
  {
    //First set node keys
    setData(node); 

    int result=INT_MIN;


    //Connected two node with Edges

    addEdge(node,0, 2, 9); 
    addEdge(node,0, 3, 7); 
    addEdge(node,0, 5, 1); 

    addEdge(node,1, 0, 3); 
    addEdge(node,1, 5, 8); 

    addEdge(node,2, 3, 7); 
    addEdge(node,2, 5, 15);

    addEdge(node,3, 1, -8); 
    addEdge(node,3, 4, 21); 

    addEdge(node,4, 1, 9); 

    addEdge(node,5, 3, 1); 
    addEdge(node,5, 4, 6); 



    printGraph(node);
    //Source node 0 destination 4
    max_cost(0,4,visit,node,&result,0);

    printf("\n Maximum Cost: %d\n",result );
  }  
  return 0;
}

Output

 Adjacency list of vertex 0  :  2  3  5  1
 Adjacency list of vertex 1  :  0  5  3  4
 Adjacency list of vertex 2  :  0  3  5
 Adjacency list of vertex 3  :  0  2  1  4  5
 Adjacency list of vertex 4  :  3  1  5
 Adjacency list of vertex 5  :  0  1  2  3  4
 Minimum Cost: 54
//C++ program
//Find maximum cost from source node to destination
#include <iostream>
#include <limits.h> //for INT_MIN

using namespace std;

struct AjlistNode
{
  int vId;//Vertices id
  int weight;
  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,int);
  void printGraph();
  void connect(int  ,int ,int);
  void find_max_cost(int ,int);
  void max_cost(int,int ,int* ,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,int weight)
{
    //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;
    newEdge->weight =weight;

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

    if(V!=E)
    {
      connect(E,V,weight);
    }
  }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;
  }
}



void Graph:: max_cost(int start,
  int end,
  int visit[],
  int*result,
  int sum)
{

  if (start >size || end >size || start<0 || end<0 || node==NULL)
  {
    //invalid input
    return ;
  }
  if (visit[start]==1)
  {
    return;
  }
  if(start==end)
  {
    if(*result<sum)
    {
      //when get new result
      *result=sum;
    }
  }

  visit[start]=1;
  AjlistNode *temp=node[start].next;
  while(temp!=NULL)
  {
    max_cost(temp->vId,end,visit,result,sum+temp->weight); 
    temp=temp->next;
  }
  visit[start]=0;
}
void Graph :: find_max_cost(int source,int destination)
{

  int result = INT_MIN;

  int visit[size];

  for(int i=0;i<size;i++)
  {
    visit[i]=0;
  }
  max_cost(source,destination,visit,&result,0);
  cout<<"\n Maximum Cost in between nodes \
  [ "<< source <<","<< destination <<"] is "<< result<<"\n";
}
int main()
{
  //Create Object
  Graph g=Graph(6); //6 nodes
  //First set node keys
  g.setData();


  g.addEdge(0, 2, 9); 
  g.addEdge(0, 3, 7); 
  g.addEdge(0, 5, 1); 

  g.addEdge(1, 0, 3); 
  g.addEdge(1, 5, 8); 

  g.addEdge(2, 3, 7); 
  g.addEdge(2, 5, 15);

  g.addEdge(3, 1, -8); 
  g.addEdge(3, 4, 21); 

  g.addEdge(4, 1, 9); 

  g.addEdge(5, 3, 1); 
  g.addEdge(5, 4, 6); 
  g.printGraph();

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

  g.find_max_cost(source,destination);

  return 0;
}

Output

 Adjacency list of vertex 0 : 2 3 5 1
 Adjacency list of vertex 1 : 0 5 3 4
 Adjacency list of vertex 2 : 0 3 5
 Adjacency list of vertex 3 : 0 2 1 4 5
 Adjacency list of vertex 4 : 3 1 5
 Adjacency list of vertex 5 : 0 1 2 3 4
 Maximum Cost in between nodes   [ 0,4] is 54
//Java program
//Find Maximum cost from source node to destination
public class MyGraph
{

  static class AjlistNode
  {
    int id;//Vertices node key
    int weight;
    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 ,int weight)
  {
    AjlistNode newEdge=new AjlistNode();
    newEdge.id=end;//end node
    newEdge.next=null;
    newEdge.weight=weight;
    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 of two nodes
  public void addEdge(int start,int end,int weight)
  {
    if(start < size && end < size && node != null)
    {
      connect(start,end,weight);
      if(start!=end)
      {
        connect(end,start,weight);  
      }

    }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;
        }
      }
    }
  }
  public void max_cost(int start,
    int end,
    boolean []visit,
    int sum)
  {

    if (start >size || end >size || start<0 || end<0 || node==null)
    {
      //invalid input
      return ;
    }
    if (visit[start]==true)
    {
      return;
    }
    if (start==end)
    {
      if ( sum >  result)
      {
        result=sum;
      }
    }
    visit[start]=true;
    AjlistNode temp=node[start].next;
    while(temp!=null)
    {
      max_cost(temp.id,end,visit,sum+temp.weight); 
      temp=temp.next;
    }
    visit[start]=false;
  }
  public void  find_max_cost(int source,int destination)
  {
    //For resultant 
    result=Integer.MIN_VALUE;
    boolean []visit=new boolean[size];
    for(int i=0; i < size; i++)
    {
      visit[i]=false;
    }
    max_cost(source,destination,visit,0);
    System.out.println("\n Maximum Cost in between nodes ["+ source +","+ destination +"] is "+ result+"\n");
  }

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

    MyGraph g=new MyGraph(totalNode);

    g.setData();

    g.addEdge(0, 2, 9); 
    g.addEdge(0, 3, 7); 
    g.addEdge(0, 5, 1); 

    g.addEdge(1, 0, 3); 
    g.addEdge(1, 5, 8); 

    g.addEdge(2, 3, 7); 
    g.addEdge(2, 5, 15);

    g.addEdge(3, 1, -8); 
    g.addEdge(3, 4, 21); 

    g.addEdge(4, 1, 9); 

    g.addEdge(5, 3, 1); 
    g.addEdge(5, 4, 6); 
    g.printGraph();

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

    g.find_max_cost(source,destination);

  }
}

Output

Adjacency list of vertex 0 :  2  3  5  1
Adjacency list of vertex 1 :  0  5  3  4
Adjacency list of vertex 2 :  0  3  5
Adjacency list of vertex 3 :  0  2  1  4  5
Adjacency list of vertex 4 :  3  1  5
Adjacency list of vertex 5 :  0  1  2  3  4
 Maximum Cost in between nodes [0,4] is 54
#Python Program 
#Find maximum cost from source node to destination
import sys
class AjLinkeNode:
  def __init__(self,data,weight):
    self.id = data
    self.weight = weight
    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,weight):

    new_edge=AjLinkeNode(end,weight)

    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,weight):
     
    #start,end is two nodes
    if(self.size > start and self.size > start):
      
      self.connect(start,end,weight)
      if(start!=end):
      
        self.connect(end,start,weight)
      

    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

  

  def max_cost(self,start,end,visit,node_sum) :

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

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

      return
    if (start==end) :

      if (node_sum > self.result) :

        self.result=node_sum

    visit[start]=True

    temp=self.node[start].next

    while(temp!=None) :

      self.max_cost(temp.id,end,visit,node_sum +temp.weight) 
      temp=temp.next
    visit[start]=False

  def  find_max_cost(self,source,destination) :

    #for resultant paths
    self.result=-sys.maxsize-1

    visit=[False]*self.size

    self.max_cost(source,destination,visit,0)
    print("\n  Maximum Cost in between nodes [",source,",",destination,"] : ",self.result)
    


    
def main():
  g=Graph(6)
  g.setData() 

  #Connected two node with Edges
  g.addEdge(0, 2, 9); 
  g.addEdge(0, 3, 7); 
  g.addEdge(0, 5, 1); 

  g.addEdge(1, 0, 3); 
  g.addEdge(1, 5, 8); 

  g.addEdge(2, 3, 7); 
  g.addEdge(2, 5, 15);

  g.addEdge(3, 1, -8); 
  g.addEdge(3, 4, 21); 

  g.addEdge(4, 1, 9); 

  g.addEdge(5, 3, 1); 
  g.addEdge(5, 4, 6); 
  g.printGraph()
  #value 0 is source node
  source = 0
  #value 4 is destination node
  destination = 4
  g.find_max_cost(source,destination)

if __name__=="__main__":
    main()

Output

Adjacency list of vertex 0 :   2  3  5  1 
Adjacency list of vertex 1 :   0  5  3  4 
Adjacency list of vertex 2 :   0  3  5 
Adjacency list of vertex 3 :   0  2  1  4  5 
Adjacency list of vertex 4 :   3  1  5 
Adjacency list of vertex 5 :   0  1  2  3  4 
  Maximum Cost in between nodes [ 0 , 4 ] :  54
//C# program
//Find maximum cost from source node to destination
using System;
public class AjlistNode
{
  public int id;//Vertices node key
  public int weight;
  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 ,int weight)
  {
    AjlistNode newEdge=new AjlistNode();
    newEdge.id=end;//end node
    newEdge.next=null;
    newEdge.weight=weight;
    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 of two nodes
  public void addEdge(int start,int end,int weight)
  {
    if(start < size && end < size && node != null)
    {
      connect(start,end,weight);
      if(start!=end)
      {
        connect(end,start,weight);  
      }

    }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;
        }
      }
    }
  }
  public void min_cost(int start,
    int end,
    Boolean []visit,
    int sum)
  {

    if (start >size || end >size || start<0 || end<0 || node==null)
    {
      //invalid input
      return ;
    }
    if (visit[start]==true)
    {
      return;
    }
    if (start==end)
    {
      if ( sum >  result)
      {
        result=sum;
      }
    }
    visit[start]=true;
    AjlistNode temp=node[start].next;
    while(temp!=null)
    {
      min_cost(temp.id,end,visit,sum+temp.weight); 
      temp=temp.next;
    }
    visit[start]=false;
  }
  public void  find_min_cost(int source,int destination)
  {
    //For resultant 
    result=int.MinValue;
    Boolean []visit=new Boolean[size];
    for(int i=0; i < size; i++)
    {
      visit[i]=false;
    }
    min_cost(source,destination,visit,0);
    Console.WriteLine("\n Maximum Cost in between nodes ["+ source +","+ destination +"] is "+ result+"\n");
  }

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

    MyGraph g=new MyGraph(totalNode);

    g.setData();

    g.addEdge(0, 2, 9); 
    g.addEdge(0, 3, 7); 
    g.addEdge(0, 5, 1); 

    g.addEdge(1, 0, 3); 
    g.addEdge(1, 5, 8); 

    g.addEdge(2, 3, 7); 
    g.addEdge(2, 5, 15);

    g.addEdge(3, 1, -8); 
    g.addEdge(3, 4, 21); 

    g.addEdge(4, 1, 9); 

    g.addEdge(5, 3, 1); 
    g.addEdge(5, 4, 6); 
    g.printGraph();

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

    g.find_min_cost(source,destination);

  }
}

Output

Adjacency list of vertex 0 :  2  3  5  1
Adjacency list of vertex 1 :  0  5  3  4
Adjacency list of vertex 2 :  0  3  5
Adjacency list of vertex 3 :  0  2  1  4  5
Adjacency list of vertex 4 :  3  1  5
Adjacency list of vertex 5 :  0  1  2  3  4
 Maximum Cost in between nodes [0,4] is 54

<?php 
/*
* PHP Program 
  Find maximum cost from source node to destination
*/

  class AjlistNode
  {
    public $vId;
    public $weight;
    public $next;
    function __construct($vId,$weight)
    {
      $this->weight=$weight;
      $this->vId=$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,$weight)
  {
    $newEdge=new AjlistNode($end,$weight);
    if($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,$end,$weight)
  {
    if($this->size > $start && $this->size>$end)
    {
      $this->connect($start,$end,$weight);
      if($start!=$end)
      {
        $this->connect($end,$start,$weight);
      }
    }
    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;
        }
      }
    }
  }
  public function  max_cost($start,$end,$visit,&$result,$sum)
  {

    if ($start > $this->size|| $end>$this->size|| $start<0|| $end<0|| $this->node==NULL)
    {
      //invalid input
      return ;
    }
    if ($visit[$start]==true)
    {
      return;
    }
    if ($start== $end)
    {
      if ($sum>$result)
      {
        $result= $sum;
      }
    }
    $visit[$start]=true;
    $temp =  $this->node[$start]->next;
    while($temp!=NULL)
    {
      $this->max_cost($temp->vId,$end,$visit,$result,$sum+$temp->weight); 
      $temp=$temp->next;
    }
    $visit[$start]=false;
  }

  public function find_max_cost($source,$destination)
  {
    //for resultant paths
    $result= PHP_INT_MIN;
    $visit= array_fill(0, $this->size, false);
    $this->max_cost($source,$destination,$visit,$result,0);
    echo "\n Maximum Cost in between nodes[". $source.",". $destination."] is ". $result."\n";
  }

}


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

  //Connected two node with Edges
  $g->addEdge(0, 2, 9); 
  $g->addEdge(0, 3, 7); 
  $g->addEdge(0, 5, 1); 

  $g->addEdge(1, 0, 3); 
  $g->addEdge(1, 5, 8); 

  $g->addEdge(2, 3, 7); 
  $g->addEdge(2, 5, 15);

  $g->addEdge(3, 1, -8); 
  $g->addEdge(3, 4, 21); 

  $g->addEdge(4, 1, 9); 

  $g->addEdge(5, 3, 1); 
  $g->addEdge(5, 4, 6); 
  
  $g->printGraph();
  
  //value 0 is source node
  $source=0;
  //value 4 is destination node
  $destination=4;
  
  $g->find_max_cost($source,$destination);

}
main();
?>

Output

Adjacency list of vertex 0 :   2  3  5  1
Adjacency list of vertex 1 :   0  5  3  4
Adjacency list of vertex 2 :   0  3  5
Adjacency list of vertex 3 :   0  2  1  4  5
Adjacency list of vertex 4 :   3  1  5
Adjacency list of vertex 5 :   0  1  2  3  4
 Maximum Cost in between nodes[0,4] is 54


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