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dijakstra_algorithum.cpp
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dijakstra_algorithum.cpp
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// A C++ program for Dijkstra's single source shortest path algorithm.
// The program is for adjacency matrix representation of the graph
#include <limits.h>
#include <stdio.h>
// Number of vertices in the graph
#define V 28
// 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[])
{
printf("Vertex \t\t Distance from Source\n");
for (int i = 0; i < V; i++)
printf("%d \t\t %d\n", i, dist[i]);
}
// 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 be 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);
}
// driver program to test above function
int main()
{
/* Let us create the example graph discussed above */
int src;
int graph[V][V] = {
{00,25,00,00,00,00,00,00,50,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00},
{25,00,30,05,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00},
{00,30,00,10,10,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,10,00},
{05,00,00,00,05,10,05,00,00,20,15,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00},
{00,10,00,05,00,05,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,10},
{00,00,05,10,00,00,05,05,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,05},
{00,00,00,05,00,05,00,05,00,00,00,00,00,00,00,00,40,00,00,00,00,00,00,00,00,00,00,00},
{00,00,00,00,00,05,05,00,00,00,23,00,00,00,00,00,00,20,00,00,00,00,00,00,00,00,00,00},
{05,00,00,00,05,10,05,00,00,20,15,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00},
{50,00,00,20,00,00,00,00,20,00,30,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00},
{00,00,00,15,00,00,00,00,15,30,00,10,70,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00},
{00,00,00,00,00,00,00,00,00,00,10,00,00,35,00,00,00,00,00,00,00,00,00,00,00,00,00,00},
{00,00,00,50,00,00,00,00,50,00,70,35,00,15,20,00,00,00,00,00,00,00,00,00,00,00,00,00},
{00,00,00,00,00,00,00,00,00,00,00,00,15,00,05,02,00,00,00,00,00,00,00,00,00,00,00,00},
{00,00,00,00,00,00,40,00,00,00,00,00,20,05,00,00,02,00,00,00,00,00,00,00,00,00,00,00},
{00,00,00,00,00,00,00,00,00,00,00,00,00,02,00,00,15,80,00,00,00,00,00,00,00,00,00,00},
{00,00,00,00,00,00,00,00,00,00,00,00,00,00,02,15,00,20,00,00,00,00,00,00,00,00,00,00},
{00,00,00,00,00,00,00,20,00,00,00,00,00,00,00,80,20,00,20,00,00,100,00,23,00,00,00,00},
{00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,20,00,70,00,00,00,00,00,00,00,00},
{00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,70,00,00,00,00,00,00,00,00,00},
{00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,15,00,00,00,00,00,00},
{00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,15,00,25,00,00,00,00,00},
{00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,25,00,00,00,00,00,00},
{00,00,00,00,00,00,00,10,00,00,00,00,00,00,00,00,23,00,00,00,00,00,00,00,05,00,00,00},
{00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,05,00,05,00,00},
{00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,05,00,00,00},
{00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00},
{00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00},
};
dijkstra(graph, 0);
return 0;
}