328 lines
14 KiB
Java
328 lines
14 KiB
Java
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import java.io.BufferedReader;
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import java.io.FileReader;
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import java.io.IOException;
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import java.util.StringTokenizer;
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public class TSPUsingMST
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{
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// ArraysC to keep track of info. related to each city
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private String[] cityName;
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private String[] cityState;
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private int[] cityLat;
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private int[] cityLong;
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private int[] cityPop;
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// 2-D array to keep track of pairwise distances between cities
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private int[][] distances;
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// number of cities
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private static int numCities;
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public TSPUsingMST(int n)
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{
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numCities = n;
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// Allotting the space for each 1-D array
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cityName = new String[numCities];
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cityState = new String[numCities];
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cityLat = new int[numCities];
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cityLong = new int[numCities];
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cityPop = new int[numCities];
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// Allocate space for each 2-D array. These arrays have 0 elements in
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// row 0,
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// 1 element in row 1, 2 elements in row 2, etc.
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distances = new int[numCities][];
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for (int i = 0; i < numCities; i++)
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distances[i] = new int[i];
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try
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{
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// Construct a buffered reader object and connect it to the files
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// "miles.dat"
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BufferedReader in = new BufferedReader(new FileReader("miles.dat"));
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// A counter that keeps track of the index of the current city being
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// read
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int cityNumber = 0;
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// While-loop for reading in data from "miles.dat." At the beginning
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// of the while-loop
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// the expectation is that we'll be reading a line containing the
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// city name. Instead,
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// if we encounter a line that starts with "*" then we skip to the
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// next line
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while (cityNumber < numCities)
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{
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// Read in a line
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String line = in.readLine();
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// Skip the rest of the loop if line starts with a "*"
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if (line.charAt(0) == '*')
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continue;
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// Otherwise tokenize the line
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StringTokenizer tokenizedLine = new StringTokenizer(line, ",[]");
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// Putting actual data into correct position in the array
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cityName[cityNumber] = tokenizedLine.nextToken();
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cityState[cityNumber] = (tokenizedLine.nextToken()).trim(); // trim()
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// gets
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// rid
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// of
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// leading/trailing
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// blanks
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cityLat[cityNumber] = Integer.parseInt(tokenizedLine
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.nextToken());
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cityLong[cityNumber] = Integer.parseInt(tokenizedLine
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.nextToken());
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cityPop[cityNumber] = Integer.parseInt(tokenizedLine
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.nextToken());
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// while loop to put distances in the array; this may need to
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// read several lines
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int mileNumber = 0;
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while (mileNumber < cityNumber)
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{
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// Read a mileage line and tokenize it
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String mileage = in.readLine();
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StringTokenizer tokenizedMileage = new StringTokenizer(
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mileage, " ");
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// Read all the mileage data in this line into row
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// cityNumber; increment
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// mileNumber after each read
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while (tokenizedMileage.hasMoreTokens())
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{
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distances[cityNumber][cityNumber - mileNumber - 1] = Integer
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.parseInt(tokenizedMileage.nextToken());
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mileNumber++;
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}
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} // end of while reading distances
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cityNumber++;
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} // end of while reading cities
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in.close();
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} // end of try
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catch (IOException e)
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{
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System.out.println("File not found.");
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}
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} // end of TSPTester() constructor
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// A simple getIndex method to help test the constructor
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int getIndex(String city, String state)
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{
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int location;
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for (location = 0; location < numCities; location++)
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if ((cityName[location].equals(city))
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&& (cityState[location].equals(state)))
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return location;
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return -1;
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}
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// Print information about a city, given a city index
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void printCityInfo(int index)
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{
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System.out
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.println(cityName[index] + " " + cityState[index] + " "
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+ cityLat[index] + " " + cityLong[index] + " "
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+ cityPop[index]);
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}
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// Print distance information between a given pair of cities
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void printDistanceInfo(int i, int j)
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{
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if (i < j)
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System.out.println(distances[j][i]);
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else
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System.out.println(distances[i][j]);
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}
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int getDistance(int i, int j)
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{
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if (i < j)
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return distances[j][i];
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else if (j < i)
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return distances[i][j];
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else
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return 0;
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}
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int[] greedyTSP()
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{
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// Find a cheapest triangle
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// Load triangle 0-1-2 into the the first 3 slots of the greedy array
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int[] greedy = new int[numCities];
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int currentDistance;
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greedy[0] = 0;
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greedy[1] = 1;
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greedy[2] = 2;
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int currentBestDistance = getDistance(0, 1) + getDistance(1, 2)
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+ getDistance(2, 0);
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for (int i = 0; i < numCities; i++)
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for (int j = 0; j < i; j++)
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for (int k = 0; k < j; k++)
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if ((currentDistance = getDistance(i, j)
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+ getDistance(j, k) + getDistance(i, k)) < currentBestDistance)
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{
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greedy[0] = i;
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greedy[1] = j;
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greedy[2] = k;
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currentBestDistance = currentDistance;
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}
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// Try greedily to add a city that yields the smallest increase
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// in the cost of the tour
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int partialTourSize = 3;
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boolean[] visited = new boolean[numCities];
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for (int i = 0; i < numCities; i++)
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visited[i] = false;
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visited[greedy[0]] = true;
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visited[greedy[1]] = true;
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visited[greedy[2]] = true;
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// Main loop: keep repeating until partial tour covers all cities
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while (partialTourSize < numCities)
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{
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int smallestIncrease = Integer.MAX_VALUE;
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int increase = 0;
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int bestInsertionPoint = 0;
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int bestCity = 0;
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// Scan through all cities, stopping at unvisited cities
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for (int i = 0; i < numCities; i++)
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{
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if (!visited[i])
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{
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// Consider all possible positions of inserting city i into
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// the tour
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// and record the smallest increase
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for (int j = 0; j < partialTourSize; j++)
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{
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increase = getDistance(greedy[j], i)
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+ getDistance(i, greedy[(j + 1) % numCities])
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- getDistance(greedy[j], greedy[(j + 1)
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% numCities]);
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if (increase < smallestIncrease)
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{
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smallestIncrease = increase;
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bestCity = i;
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bestInsertionPoint = j;
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} // end of if we have found a smaller increase
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} // end of for-j
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} // end of if not visited
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} // end of for-i
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// Now we are ready to insert the bestCity at the bestInsertionPoint
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for (int j = partialTourSize - 1; j > bestInsertionPoint; j--)
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greedy[j + 1] = greedy[j];
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greedy[bestInsertionPoint + 1] = bestCity;
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visited[bestCity] = true;
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partialTourSize++;
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} // end-while
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return greedy;
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}
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void copy(int[] source, int[] dest)
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{
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for (int i = 0; i < dest.length; i++)
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dest[i] = source[i];
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}
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void TSP(int[] R, int partialTourSize, boolean[] visited, int[] T)
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{
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// Base case: we have discovered a tour better than T
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if ((partialTourSize == numCities) && (cost(R) < cost(T)))
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{
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System.out.println("Base case. Tour cost is " + cost(R));
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copy(R, T);
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return;
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}
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// Another base case: our partial tour is not worth completing
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if (cost(R, partialTourSize) >= cost(T))
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return;
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// Recursive case: R is not complete and is currently better than T
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// and is therefore worth completing
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for (int i = 0; i < numCities; i++)
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{
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if (!visited[i])
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{
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// System.out.println("Appending " + i);
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visited[i] = true;
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R[partialTourSize++] = i;
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TSP(R, partialTourSize, visited, T);
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partialTourSize--;
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visited[i] = false;
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// System.out.println("Deleting " + i);
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}
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} // end of for-loop
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} // end of TSP
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double cost(int[] tour)
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{
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return cost(tour, tour.length);
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}
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double cost(int[] tour, int tourSize)
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{
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double c = 0;
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for (int i = 0; i < tourSize - 1; i++)
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c = c + getDistance(tour[i], tour[i + 1]);
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c = c + getDistance(tour[tourSize - 1], tour[0]);
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return c;
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}
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// Main method
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public static void main(String[] args)
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{
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int n = 15;
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TSPUsingMST T = new TSPUsingMST(n);
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// Initialize the list of vertices in the tree
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// Initially, no one except vertex 0 is in the tree
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boolean[] visited = new boolean[n];
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for (int i = 0; i < n; i++)
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visited[i] = false;
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visited[0] = true;
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// Initialize the int[] that maintains the tree to default values
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// No vertices have parents set, except vertex 0 whose parent is itself
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int[] tree = new int[n];
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for (int i = 0; i < n; i++)
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tree[i] = -1;
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tree[0] = 0;
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for (int i = 1; i <= n - 1; i++)
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{
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long minWeight = Long.MAX_VALUE;
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int bestVertex = -1;
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int bestParent = -1;
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for (int j = 0; j < n; j++)
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{
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for (int k = 0; k < n; k++)
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{
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if ((visited[j]) && (!visited[k]))
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{
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if (T.getDistance(j, k) < minWeight)
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{
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minWeight = T.getDistance(j, k);
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bestVertex = k;
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bestParent = j;
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} // end if better distance is found
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} // end if an edge between a visited and an unvisited is
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// found
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} // end for-k
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} // end for-j
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// Update visited and tree
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visited[bestVertex] = true;
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tree[bestVertex] = bestParent;
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} // end for-i
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// Printing the MST
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for (int i = 1; i < n; i++)
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System.out.println(T.cityName[i] + " " + T.cityState[i] + ", "
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+ T.cityName[tree[i]] + " " + T.cityState[tree[i]]);
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// Compting the MST cost
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long cost = 0;
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for (int i = 0; i < n; i++)
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cost += T.getDistance(i, tree[i]);
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System.out.println("The cost of the minimum spanning tree is " + cost);
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} // end main method
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} // end class
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/*
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Yankton SD, Wisconsin Dells WI
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Yakima WA, Williston ND
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Worcester MA, Wilmington DE
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Wisconsin Dells WI, Youngstown OH
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Winston-Salem NC, Winchester VA
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Winnipeg MB, Yankton SD
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Winchester VA, Wilmington DE
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Wilmington NC, Winston-Salem NC
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Wilmington DE, Williamsport PA
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Williston ND, Winnipeg MB
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Williamsport PA, Youngstown OH
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Williamson WV, Winston-Salem NC
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Wichita Falls TX, Wichita KS
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Wichita KS, Yankton SD
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The cost of the minimum spanning tree is 5461
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