Java Program to Solve TSP using Minimum Spanning Trees

This is a java program to solve TSP using MST.

Here is the source code of the Java Program to Solve TSP Using Minimum Spanning Trees. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.

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package com.sanfoundry.hardgraph;
```
```
 
```
```
import java.io.BufferedReader;
```
```
import java.io.FileReader;
```
```
import java.io.IOException;
```
```
import java.util.StringTokenizer;
```
```
 
```
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public class TSPUsingMST
```
```
{
```

    // Arrays to keep track of info. related to each city

```
    private String[]   cityName;
```
```
    private String[]   cityState;
```
```
    private int[]      cityLat;
```
```
    private int[]      cityLong;
```
```
    private int[]      cityPop;
```

    // 2-D array to keep track of pairwise distances between cities

```
    private int[][]    distances;
```
```
    // number of cities
```
```
    private static int numCities;
```
```
 
```
```
    public TSPUsingMST(int n)
```
```
    {
```
```
        numCities = n;
```

        // Allotting the space for each 1-D array

        cityName = new String[numCities];

        cityState = new String[numCities];

```
        cityLat = new int[numCities];
```
```
        cityLong = new int[numCities];
```
```
        cityPop = new int[numCities];
```

        // Allocate space for each 2-D array. These arrays have 0 elements in

```
        // row 0,
```

        // 1 element in row 1, 2 elements in row 2, etc.

        distances = new int[numCities][];

        for (int i = 0; i < numCities; i++)

```
            distances[i] = new int[i];
```
```
        try
```
```
        {
```

            // Construct a buffered reader object and connect it to the files

```
            // "miles.dat"
```

            BufferedReader in = new BufferedReader(new FileReader("miles.dat"));

            // A counter that keeps track of the index of the current city being

```
            // read
```
```
            int cityNumber = 0;
```

            // While-loop for reading in data from "miles.dat." At the beginning

```
            // of the while-loop
```

            // the expectation is that we'll be reading a line containing the

```
            // city name. Instead,
```

            // if we encounter a line that starts with "*" then we skip to the

```
            // next line
```

            while (cityNumber < numCities)

```
            {
```
```
                // Read in a line
```

                String line = in.readLine();

                // Skip the rest of the loop if line starts with a "*"

                if (line.charAt(0) == '*')

```
                    continue;
```

                // Otherwise tokenize the line

                StringTokenizer tokenizedLine = new StringTokenizer(line, ",[]");

                // Putting actual data into correct position in the array

                cityName[cityNumber] = tokenizedLine.nextToken();

                cityState[cityNumber] = (tokenizedLine.nextToken()).trim(); // trim()

                                                                            // gets

                                                                            // rid

                                                                            // of

                                                                            // leading/trailing

                                                                            // blanks

                cityLat[cityNumber] = Integer.parseInt(tokenizedLine

```
                        .nextToken());
```

                cityLong[cityNumber] = Integer.parseInt(tokenizedLine

```
                        .nextToken());
```

                cityPop[cityNumber] = Integer.parseInt(tokenizedLine

```
                        .nextToken());
```

                // while loop to put distances in the array; this may need to

```
                // read several lines
```
```
                int mileNumber = 0;
```

                while (mileNumber < cityNumber)

```
                {
```

                    // Read a mileage line and tokenize it

                    String mileage = in.readLine();

                    StringTokenizer tokenizedMileage = new StringTokenizer(

                            mileage, " ");

                    // Read all the mileage data in this line into row

                    // cityNumber; increment

                    // mileNumber after each read

                    while (tokenizedMileage.hasMoreTokens())

```
                    {
```

                        distances[cityNumber][cityNumber - mileNumber - 1] = Integer

                                .parseInt(tokenizedMileage.nextToken());

```
                        mileNumber++;
```
```
                    }
```

                } // end of while reading distances

```
                cityNumber++;
```

            } // end of while reading cities

```
            in.close();
```
```
        } // end of try
```
```
        catch (IOException e)
```
```
        {
```

            System.out.println("File not found.");

```
        }
```
```
    } // end of TSPTester() constructor
```
```
 
```

    // A simple getIndex method to help test the constructor

    int getIndex(String city, String state)

```
    {
```
```
        int location;
```

        for (location = 0; location < numCities; location++)

            if ((cityName[location].equals(city))

                    && (cityState[location].equals(state)))

```
                return location;
```
```
        return -1;
```
```
    }
```
```
 
```

    // Print information about a city, given a city index

```
    void printCityInfo(int index)
```
```
    {
```
```
        System.out
```

                .println(cityName[index] + " " + cityState[index] + " "

                        + cityLat[index] + " " + cityLong[index] + " "

                        + cityPop[index]);

```
    }
```
```
 
```

    // Print distance information between a given pair of cities

    void printDistanceInfo(int i, int j)

```
    {
```
```
        if (i < j)
```

            System.out.println(distances[j][i]);

```
        else
```

            System.out.println(distances[i][j]);

```
    }
```
```
 
```
```
    int getDistance(int i, int j)
```
```
    {
```
```
        if (i < j)
```
```
            return distances[j][i];
```
```
        else if (j < i)
```
```
            return distances[i][j];
```
```
        else
```
```
            return 0;
```
```
    }
```
```
 
```
```
    int[] greedyTSP()
```
```
    {
```
```
        // Find a cheapest triangle
```

        // Load triangle 0-1-2 into the the first 3 slots of the greedy array

        int[] greedy = new int[numCities];

```
        int currentDistance;
```
```
        greedy[0] = 0;
```
```
        greedy[1] = 1;
```
```
        greedy[2] = 2;
```

        int currentBestDistance = getDistance(0, 1) + getDistance(1, 2)

```
                + getDistance(2, 0);
```

        for (int i = 0; i < numCities; i++)

```
            for (int j = 0; j < i; j++)
```

                for (int k = 0; k < j; k++)

                    if ((currentDistance = getDistance(i, j)

                            + getDistance(j, k) + getDistance(i, k)) < currentBestDistance)

```
                    {
```
```
                        greedy[0] = i;
```
```
                        greedy[1] = j;
```
```
                        greedy[2] = k;
```

                        currentBestDistance = currentDistance;

```
                    }
```

        // Try greedily to add a city that yields the smallest increase

```
        // in the cost of the tour
```
```
        int partialTourSize = 3;
```

        boolean[] visited = new boolean[numCities];

        for (int i = 0; i < numCities; i++)

```
            visited[i] = false;
```
```
        visited[greedy[0]] = true;
```
```
        visited[greedy[1]] = true;
```
```
        visited[greedy[2]] = true;
```

        // Main loop: keep repeating until partial tour covers all cities

        while (partialTourSize < numCities)

```
        {
```

            int smallestIncrease = Integer.MAX_VALUE;

```
            int increase = 0;
```
```
            int bestInsertionPoint = 0;
```
```
            int bestCity = 0;
```

            // Scan through all cities, stopping at unvisited cities

            for (int i = 0; i < numCities; i++)

```
            {
```
```
                if (!visited[i])
```
```
                {
```

                    // Consider all possible positions of inserting city i into

```
                    // the tour
```

                    // and record the smallest increase

                    for (int j = 0; j < partialTourSize; j++)

```
                    {
```

                        increase = getDistance(greedy[j], i)

                                + getDistance(i, greedy[(j + 1) % numCities])

                                - getDistance(greedy[j], greedy[(j + 1)

                                        % numCities]);

                        if (increase < smallestIncrease)

```
                        {
```

                            smallestIncrease = increase;

                            bestCity = i;

                            bestInsertionPoint = j;

                        } // end of if we have found a smaller increase

```
                    } // end of for-j
```

                } // end of if not visited

```
            } // end of for-i
```

              // Now we are ready to insert the bestCity at the bestInsertionPoint

            for (int j = partialTourSize - 1; j > bestInsertionPoint; j--)

                greedy[j + 1] = greedy[j];

            greedy[bestInsertionPoint + 1] = bestCity;

```
            visited[bestCity] = true;
```
```
            partialTourSize++;
```
```
        } // end-while
```
```
        return greedy;
```
```
    }
```
```
 
```
```
    void copy(int[] source, int[] dest)
```
```
    {
```

        for (int i = 0; i < dest.length; i++)

```
            dest[i] = source[i];
```
```
    }
```
```
 
```

    void TSP(int[] R, int partialTourSize, boolean[] visited, int[] T)

```
    {
```

        // Base case: we have discovered a tour better than T

        if ((partialTourSize == numCities) && (cost(R) < cost(T)))

```
        {
```

            System.out.println("Base case. Tour cost is " + cost(R));

```
            copy(R, T);
```
```
            return;
```
```
        }
```

        // Another base case: our partial tour is not worth completing

        if (cost(R, partialTourSize) >= cost(T))

```
            return;
```

        // Recursive case: R is not complete and is currently better than T

        // and is therefore worth completing

        for (int i = 0; i < numCities; i++)

```
        {
```
```
            if (!visited[i])
```
```
            {
```

                // System.out.println("Appending " + i);

```
                visited[i] = true;
```

                R[partialTourSize++] = i;

                TSP(R, partialTourSize, visited, T);

```
                partialTourSize--;
```
```
                visited[i] = false;
```

                // System.out.println("Deleting " + i);

```
            }
```
```
        } // end of for-loop
```
```
    } // end of TSP
```
```
 
```
```
    double cost(int[] tour)
```
```
    {
```
```
        return cost(tour, tour.length);
```
```
    }
```
```
 
```

    double cost(int[] tour, int tourSize)

```
    {
```
```
        double c = 0;
```

        for (int i = 0; i < tourSize - 1; i++)

            c = c + getDistance(tour[i], tour[i + 1]);

        c = c + getDistance(tour[tourSize - 1], tour[0]);

```
        return c;
```
```
    }
```
```
 
```
```
    // Main method
```

    public static void main(String[] args)

```
    {
```
```
        int n = 15;
```

        TSPUsingMST T = new TSPUsingMST(n);

        // Initialize the list of vertices in the tree

        // Initially, no one except vertex 0 is in the tree

        boolean[] visited = new boolean[n];

```
        for (int i = 0; i < n; i++)
```
```
            visited[i] = false;
```
```
        visited[0] = true;
```

        // Initialize the int[] that maintains the tree to default values

        // No vertices have parents set, except vertex 0 whose parent is itself

```
        int[] tree = new int[n];
```
```
        for (int i = 0; i < n; i++)
```
```
            tree[i] = -1;
```
```
        tree[0] = 0;
```

        for (int i = 1; i <= n - 1; i++)

```
        {
```

            long minWeight = Long.MAX_VALUE;

```
            int bestVertex = -1;
```
```
            int bestParent = -1;
```
```
            for (int j = 0; j < n; j++)
```
```
            {
```

                for (int k = 0; k < n; k++)

```
                {
```

                    if ((visited[j]) && (!visited[k]))

```
                    {
```

                        if (T.getDistance(j, k) < minWeight)

```
                        {
```

                            minWeight = T.getDistance(j, k);

                            bestVertex = k;

                            bestParent = j;

                        } // end if better distance is found

                    } // end if an edge between a visited and an unvisited is

```
                      // found
```
```
                } // end for-k
```
```
            } // end for-j
```

              // Update visited and tree

```
            visited[bestVertex] = true;
```

            tree[bestVertex] = bestParent;

```
        } // end for-i
```
```
          // Printing the MST
```
```
        for (int i = 1; i < n; i++)
```

            System.out.println(T.cityName[i] + " " + T.cityState[i] + ", "

                    + T.cityName[tree[i]] + " " + T.cityState[tree[i]]);

```
        // Compting the MST cost
```
```
        long cost = 0;
```
```
        for (int i = 0; i < n; i++)
```

            cost += T.getDistance(i, tree[i]);

        System.out.println("The cost of the minimum spanning tree is " + cost);

```
    } // end main method
```
```
} // end class
```

Output:

$ javac TSPUsingMST.java
$ java TSPUsingMST
 
Yankton SD, Wisconsin Dells WI
Yakima WA, Williston ND
Worcester MA, Wilmington DE
Wisconsin Dells WI, Youngstown OH
Winston-Salem NC, Winchester VA
Winnipeg MB, Yankton SD
Winchester VA, Wilmington DE
Wilmington NC, Winston-Salem NC
Wilmington DE, Williamsport PA
Williston ND, Winnipeg MB
Williamsport PA, Youngstown OH
Williamson WV, Winston-Salem NC
Wichita Falls TX, Wichita KS
Wichita KS, Yankton SD
The cost of the minimum spanning tree is 5461

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