// TSP.java

class Graph<Type> {
    // the matrix stores the edge information
    private int[][] matrix;

    // this stores the values being stored by this graph
    private Type[] values;

    // the size of the graph
    private int size;

    // set the graph as empty
    public Graph(int size) {
        matrix = new int[size][size];
        this.size = size;

        for(int i = 0; i < size; i++) {
            for(int j = 0; j < size; j++) {
                matrix[i][j] = 1000000;
            }
        }

        // make space for the values (and ignore the cast warning)
        @SuppressWarnings("unchecked")
        Type[] values = (Type[]) new Object[size];
        this.values = values;
    }

    // lookup a node number by value
    public int lookup(Type value) {
        for (int i = 0; i < size; i++) {
            if (values[i].equals(value)) {
                return i;
            }
        }
        return -1;
    }

    // insert an edge by index
    public void insertEdge(int from, int to, int cost) {
        matrix[from][to] = cost;
        matrix[to][from] = cost;
    }

    // insert an edge by value
    public void insertEdge(Type from, Type to, int cost) {
        int fromIndex = lookup(from);
        int toIndex = lookup(to);
        insertEdge(fromIndex, toIndex, cost);
    }

    // remove an edge
    public void removeEdge(int from, int to) {
        matrix[from][to] = 0;
    }

    // return the cost of an edge or 0 for none
    public int getCost(int from, int to) {
        return matrix[from][to];
    }

    // add a node's data to the graph
    public void setValue(int node, Type value) {
        values[node] = value;
    }

    // return the size of the graph
    public int getSize() {
        return size;
    }

    // get the value of a node
    public Type getValue(int index) {
        return values[index];
    }
}

public class TSP {
    // varaibles for best path so far
    private static int best_cost = Integer.MAX_VALUE;
    private static int[] best_path;

    // run through all permutations
    public static void permute(Graph<String> graph, int[] array, int start, int end) {
        int N = graph.getSize();

        // if this is the end, consider this path
        if (start == end) {
            int total_cost = 0;
            // add up this route
            for (int i = 0; i < (N - 1); i++) {
                total_cost = total_cost + graph.getCost(array[i], array[i + 1]);
            }
            // add end city back to start
            total_cost = total_cost + graph.getCost(array[N - 1], array[0]);

            // check if this is the best so far
            if (total_cost < best_cost) {
                best_cost = total_cost;
                for (int i = 0; i < N; i++) {
                    best_path[i] = array[i];
                }
            }
        }

        else {
            // for each node in the array
            for (int i = start; i <= end; i++) {
                // swap this with the start
                int temp = array[start];
                array[start] = array[i];
                array[i] = temp;

                // permute all after the start
                permute(graph, array, start + 1, end);

                // swap it back
                temp = array[start];
                array[start] = array[i];
                array[i] = temp;
            }
        }
    }

    public static void shortestTour(Graph<String> graph) {
        int N = graph.getSize();

        // make an array of the nodes
        int[] nodes = new int[graph.getSize()];
        for (int i = 0; i < N; i++) {
            nodes[i] = i;
        }

        // run through all permutations
        // we start at 1 since first location can be arbitrarily fixed
        permute(graph, nodes, 1, N - 1);

        // print the results
        System.out.println("The tour should go through: ");
        for (int i = 0; i < N; i++) {
            System.out.println(graph.getValue(best_path[i]) + ", ");
        }
        System.out.println("and back to " + graph.getValue(best_path[0]) + ".");
        System.out.println("For a total cost of " + best_cost);
    }

    public static void main(String args[]) {
        // create a graph with 6 connected nodes
        Graph<String> graph = new Graph<String>(6);
        graph.setValue(0, "A");
        graph.setValue(1, "B");
        graph.setValue(2, "C");
        graph.setValue(3, "D");
        graph.setValue(4, "E");
        graph.setValue(5, "F");

        graph.insertEdge("A", "B", 13);
        graph.insertEdge("A", "C", 29);
        graph.insertEdge("A", "D", 31);
        graph.insertEdge("A", "F", 48);
        graph.insertEdge("B", "C", 13);
        graph.insertEdge("B", "D", 23);
        graph.insertEdge("B", "E", 26);
        graph.insertEdge("B", "F", 15);
        graph.insertEdge("C", "E", 24);
        graph.insertEdge("C", "F", 18);
        graph.insertEdge("D", "E", 14);

        best_path = new int[6];

        // compute the shortest tour
        shortestTour(graph);
    }
}