C++ Program to Find the Shortest Path from Source Vertex to All Other Vertices in Linear Time using Dijkstra’a Shortestpath algorithm

C++ Program to find the shortest path in linear time. This can be done by using Dijkstra’a Shortest path algorithm. Here is source code of the C++ Program to Find the Shortest Path from Source Vertex to All Other Vertices in Linear Time. The C++ program is successfully compiled and run on a Linux system. The program output is also shown below…C++ Program to Find the Shortest Path from Source Vertex to All Other Vertices in Linear Time  using Dijkstra’a Shortestpath algorithm


#include <stdio.h>
#include <limits.h>
#include <iostream>

using namespace std;

// Number of vertices in the graph
#define V 9

// A utility function to find the vertex with minimum distance value, from
// the set of vertices not yet included in shortest path tree
int minDistance(int dist[], bool sptSet[])
{
// Initialize min value
int min = INT_MAX, min_index;

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
int printSolution(int dist[], int n)
{
cout << "Vertex Distance from Sourcen";
for (int i = 0; i < V; i++)
printf("%d tt %dn", i, dist[i]);
}

// Funtion that implements Dijkstra's single source shortest path algorithm
// for a graph represented using adjacency matrix representation
void dijkstra(int graph[V][V], int src)
{
int dist[V]; // The output array. dist[i] will hold the shortest
// distance from src to i

bool sptSet[V]; // sptSet[i] will true if vertex i is included in shortest
// path tree or shortest distance from src to i is finalized

// Initialize all distances as INFINITE and stpSet[] as false
for (int i = 0; i < V; i++)
dist[i] = INT_MAX, 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] && dist[u] != INT_MAX && dist[u]
+ graph[u][v] < dist[v])
dist[v] = dist[u] + graph[u][v];
}

// print the constructed distance array
printSolution(dist, V);
}

int main()
{
int graph[V][V] =
{ { 0, 4, 0, 0, 0, 0, 0, 8, 0 }, { 4, 0, 8, 0, 0, 0, 0, 11, 0 }, {
0, 8, 0, 7, 0, 4, 0, 0, 2 },
{ 0, 0, 7, 0, 9, 14, 0, 0, 0 }, { 0, 0, 0, 9, 0, 10, 0, 0,
0 }, { 0, 0, 4, 0, 10, 0, 2, 0, 0 }, { 0, 0, 0, 14,
0, 2, 0, 1, 6 }, { 8, 11, 0, 0, 0, 0, 1, 0, 7 }, {
0, 0, 2, 0, 0, 0, 6, 7, 0 } };

dijkstra(graph, 0);

return 0;
}



Output:

$ g++ LinearTimeShortestPath.cpp
$ a.out

Vertex Distance from Source
0 0
1 4
2 12
3 19
4 21
5 11
6 9
7 8
8 14

------------------
(program exited with code: 0)
Press return to continue
Post a Comment