Question

Data Structures, Write code in Java language:

2. Consider the graph below. Write a program that outputs the shortest distance from node 0 to every other node in the graph. 0 1 12 8 15 5 5 8 4 2

Answer 1

CODE

public class Main

{

// A utility function to find the vertex with minimum distance value,

// from the set of vertices not yet included in shortest path tree

static final int V = 6;

int minDistance(int dist[], Boolean sptSet[])

{

// Initialize min value

int min = Integer.MAX_VALUE, min_index=-1;

for (int v = 0; v < V; v++)

if (sptSet[v] == false && dist[v] <= min)

{

min = dist[v];

min_index = v;

}

return min_index;

}

// A utility function to print the constructed distance array

void printSolution(int dist[], int n)

{

System.out.println("Vertex Distance from Source");

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

System.out.println(i+" \t\t "+dist[i]);

}

// Funtion that implements Dijkstra's single source shortest path

// algorithm for a graph represented using adjacency matrix

// representation

void dijkstra(int graph[][], int src)

{

int dist[] = new int[V]; // The output array. dist[i] will hold

// the shortest distance from src to i

// sptSet[i] will true if vertex i is included in shortest

// path tree or shortest distance from src to i is finalized

Boolean sptSet[] = new Boolean[V];

// Initialize all distances as INFINITE and stpSet[] as false

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

{

dist[i] = Integer.MAX_VALUE;

sptSet[i] = false;

}

// Distance of source vertex from itself is always 0

dist[src] = 0;

// Find shortest path for all vertices

for (int count = 0; count < V-1; count++)

{

// Pick the minimum distance vertex from the set of vertices

// not yet processed. u is always equal to src in first

// iteration.

int u = minDistance(dist, sptSet);

// Mark the picked vertex as processed

sptSet[u] = true;

// Update dist value of the adjacent vertices of the

// picked vertex.

for (int v = 0; v < V; v++)

// Update dist[v] only if is not in sptSet, there is an

// edge from u to v, and total weight of path from src to

// v through u is smaller than current value of dist[v]

if (!sptSet[v] && graph[u][v]!=0 &&

dist[u] != Integer.MAX_VALUE &&

dist[u]+graph[u][v] < dist[v])

dist[v] = dist[u] + graph[u][v];

}

// print the constructed distance array

printSolution(dist, V);

}

// Driver method

public static void main (String[] args)

{

/* Let us create the example graph discussed above */

int graph[][] = new int[][]{{0, 3, 15, 4, 0, 0},

{0, 0, 5, 0, 8, 12},

{0, 0, 0, 0, 2, 0},

{0, 0, 0, 0, 0, 0},

{0, 0, 3, 0, 0, 8},

{0, 0, 0, 7, 0, 0}

};

Main t = new Main();

t.dijkstra(graph, 0);

}

}

OUTPUT

Vertex Distance from Source

0 0

1 3

2 8

3 4

4 10

5 15