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  • Travelling Salesman Problem

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    Hello!!!

    Travelling Salesman Problem is for finding the shortest possible root that visit every node in the graph and return to the origin point. It is used to find the shortest path.

    For example:-

    In this graph, Their is many way to reach the starting point but here is a shortest way to return the starting point travelling all the node once.

    The shortest way is known as TSP.

    Shotest way:-1-2-4-3-1=80 .

     

     

     

    Here is the code for this problem.

    Code:- 

    import java.util.*;
    import java.text.*;
    class TSP
    {
    int weight[][],n,tour[],finalCost;
    final int INF=1000;
    public TSP()
    {
    Scanner s=new Scanner(System.in);
    System.out.println("Enter no. of nodes:=>");
    n=s.nextInt();
    weight=new int[n][n];
    tour=new int[n-1];
    for(int i=0;i<n;i++)
    
    {
    for(int j=0;j<n;j++)
    {
    if(i!=j)
    {
    System.out.print("Enter weight of "+(i+1)+" to "+(j+1)+":=>");
    weight[i][j]=s.nextInt();
    }
    }
    }
    System.out.println();
    System.out.println("Starting node assumed to be node 1.");
    eval();
    }
    public int COST(int currentNode,int inputSet[],int setSize)
    {
    if(setSize==0)
    return weight[currentNode][0];
    int min=INF,minindex=0;
    int setToBePassedOnToNextCallOfCOST[]=new int[n-1];
    for(int i=0;i<setSize;i++)
    {
    int k=0;//initialise new set
    for(int j=0;j<setSize;j++)
    {
    if(inputSet[i]!=inputSet[j])
    setToBePassedOnToNextCallOfCOST[k++]=inputSet[j];
    }
    int temp=COST(inputSet[i],setToBePassedOnToNextCallOfCOST,setSize-1);
    if((weight[currentNode][inputSet[i]]+temp) < min)
    {
    min=weight[currentNode][inputSet[i]]+temp;
    minindex=inputSet[i];
    }
    }
    return min;
    }
    public int MIN(int currentNode,int inputSet[],int setSize)
    {
    if(setSize==0)
    return weight[currentNode][0];
    int min=INF,minindex=0;
    int setToBePassedOnToNextCallOfCOST[]=new int[n-1];
    for(int i=0;i<setSize;i++)//considers each node of inputSet
    {
    int k=0;
    for(int j=0;j<setSize;j++)
    {
    if(inputSet[i]!=inputSet[j])
    setToBePassedOnToNextCallOfCOST[k++]=inputSet[j];
    }
    int temp=COST(inputSet[i],setToBePassedOnToNextCallOfCOST,setSize-1);
    if((weight[currentNode][inputSet[i]]+temp) < min)
    {
    min=weight[currentNode][inputSet[i]]+temp;
    minindex=inputSet[i];
    }
    }
    return minindex;
    }
    public void eval()
    {
    int dummySet[]=new int[n-1];
    for(int i=1;i<n;i++)
    dummySet[i-1]=i;
    finalCost=COST(0,dummySet,n-1);
    constructTour();
    }
    public void constructTour()
    {
    int previousSet[]=new int[n-1];
    int nextSet[]=new int[n-2]; for(int i=1;i<n;i++)
    previousSet[i-1]=i;
    int setSize=n-1;
    tour[0]=MIN(0,previousSet,setSize);
    for(int i=1;i<n-1;i++)
    {
    int k=0;
    for(int j=0;j<setSize;j++)
    {
    if(tour[i-1]!=previousSet[j])
    nextSet[k++]=previousSet[j];
    }
    --setSize;
    tour[i]=MIN(tour[i-1],nextSet,setSize);
    for(int j=0;j<setSize;j++)
    previousSet[j]=nextSet[j];
    }
    display();
    }
    public void display()
    {
    System.out.println();
    System.out.print("The tour is 1-");
    for(int i=0;i<n-1;i++)
    System.out.print((tour[i]+1)+"-");
    System.out.print("1");
    System.out.println();
    System.out.println("The final cost is "+finalCost);
    }
    }
    class TSPExp
    {
    public static void main(String args[])
    {
    TSP obj=new TSP();
    }
    }

     

     Travelling Salesman Problem

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