Question

Dijstra Shortest path

3. Implement Dijkstra Shortest Path algorithm for any input graph. Implementation will be checked with a number of test cases. Sample test case, Number of nodes 5 Edge table: 0, 1,1 0, 2,4 1, 2, 5 1, 3, 3 1, 4,2 3, 2, 5 3, 1,1 4, 3, 3 Source node 0 Vertex Distance from Source 2 4 4 3 4

Answer 1

comments have been used to explain working of the code.

#include <bits/stdc++.h>
#define V 5 // update NO of vertices according to question.
using namespace std;  

// 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 Source"<<endl;
for (int i = 0; i < V; i++)
cout<<i<<" "<<dist[i]<<endl;
}

// Function 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 the 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);
}

// driver program to test above function
int main()
{
int src, des,weight;
int graph[V][V];
memset(graph,0,sizeof(graph));
char ch;
cout<<"Enter the edges and weigths"<<endl;
while(1){
cin>>src>>des>>weight; // adding edges in a egde table
graph[src][des]=weight;
graph[des][src]=weight;
cout<<"More edges(Y for yes and N for no) :"<<endl;
cin>>ch;
if(ch!='Y'){
break;
}
  
}
dijkstra(graph, 0);

return 0;
}

output