/*
This is a java program find a path between two nodes in a graph if it exists.
Path exists between two nodes if there is a connectivity between them through other nodes.
A simple run of Breadth First Search will decide whether there is path between two given nodes or not.
*/

//This is a sample program to find the minimum wire length between two component in a electrical circuits
import java.util.*;
class Node
{
    public int label; // this node's label (parent node in path tree)
    public int weight; // weight of edge to this node (distance to start)

    public Node(int v, int w)
    {
        label = v;
        weight = w;
    }
}

public class ShortestPath
{
    public static Scanner in; // for standard input
    public static int n, m; // n = #vertices, m = #edges
    public static LinkedList[] graph; // adjacency list representation
    public static int start, end; // start and end points for shortest path

    public static void main(String[] args)
    {
        in = new Scanner(System.in);
        // Input the graph:
        System.out
        .println("Enter the number of components and wires in a circuit:");
        n = in.nextInt();
        m = in.nextInt();
        // Initialize adjacency list structure to empty lists:
        graph = new LinkedList[n];
        for (int i = 0; i < n; i++)
            graph[i] = new LinkedList();
        // Add each edge twice, once for each endpoint:
        System.out
        .println("Mention the wire between components and its length:");
        for (int i = 0; i < m; i++)
            {
                int v1 = in.nextInt();
                int v2 = in.nextInt();
                int w = in.nextInt();
                graph[v1].add(new Node(v2, w));
                graph[v2].add(new Node(v1, w));
            }
        // Input starting and ending vertices:
        System.out
        .println("Enter the start and end for which length is to be minimized: ");
        start = in.nextInt();
        end = in.nextInt();
        // FOR DEBUGGING ONLY:
        displayGraph();
        // Print shortest path from start to end:
        shortest();
    }

    public static void shortest()
    {
        boolean[] done = new boolean[n];
        Node[] table = new Node[n];
        for (int i = 0; i < n; i++)
            table[i] = new Node(-1, Integer.MAX_VALUE);
        table[start].weight = 0;
        for (int count = 0; count < n; count++)
            {
                int min = Integer.MAX_VALUE;
                int minNode = -1;
                for (int i = 0; i < n; i++)
                    if (!done[i] && table[i].weight < min)
                        {
                            min = table[i].weight;
                            minNode = i;
                        }
                done[minNode] = true;
                ListIterator iter = graph[minNode].listIterator();
                while (iter.hasNext())
                    {
                        Node nd = (Node) iter.next();
                        int v = nd.label;
                        int w = nd.weight;
                        if (!done[v] && table[minNode].weight + w < table[v].weight)
                            {
                                table[v].weight = table[minNode].weight + w;
                                table[v].label = minNode;
                            }
                    }
            }
        for (int i = 0; i < n; i++)
            {
                if (table[i].weight < Integer.MAX_VALUE)
                    {
                        System.out.print("Wire from " + i + " to " + start
                                         + " with length " + table[i].weight + ": ");
                        int next = table[i].label;
                        while (next >= 0)
                            {
                                System.out.print(next + " ");
                                next = table[next].label;
                            }
                        System.out.println();
                    }
                else
                    System.out.println("No wire from " + i + " to " + start);
            }
    }

    public static void displayGraph()
    {
        for (int i = 0; i < n; i++)
            {
                System.out.print(i + ": ");
                ListIterator nbrs = graph[i].listIterator(0);
                while (nbrs.hasNext())
                    {
                        Node nd = (Node) nbrs.next();
                        System.out.print(nd.label + "(" + nd.weight + ") ");
                    }
                System.out.println();
            }
    }
}

/*
Enter the number of components and wires in a circuit:
4 3
Mention the wire between components and its length:
0 1 2
1 3 3
1 2 2
Enter the start and end for which length is to be minimized:
0 1
0: 1(2)
1: 0(2) 3(3) 2(2)
2: 1(2)
3: 1(3)
Wire from 0 to 0 with length 0:
Wire from 1 to 0 with length 2: 0
Wire from 2 to 0 with length 4: 1 0
Wire from 3 to 0 with length 5: 1 0