Dijkstra's algorithm (or Dijkstra's Shortest path First algorithm, SPF algorithm) is an algorithm for finding the shortest paths between nodes in a graph, which may represent, for example, road networks. A widely used application of shortest path algorithm is network routing protocols, most notably IS-IS (Intermediate System to Intermediate System) and open Shortest path As a solution, he re-observed the algorithm known as Prim's minimal spanning tree algorithm (known earlier to Jarník, and also rediscovered by Prim). He designed the shortest path algorithm and later implemented it for ARMAC for a slightly simplified transportation map of 64 city in the Netherlands (64, so that 6 bits would be sufficient to encode the city number).What is the shortest manner to travel from Rotterdam to Groningen, in general: from given city to given city.

If the destination node has been marked visited (when planning a path between two specific nodes) or if the smallest tentative distance among the nodes in the unvisited set is infinity (when planning a complete traversal; happens when there is no connection between the initial node and remaining unvisited nodes), then stop. Otherwise, choose the unvisited node that is marked with the smallest tentative distance, put it as the new" current node", and go back to step 3. When planning a path, it is actually not necessary to wait until the destination node is" visited" as above: the algorithm can stop once the destination node has the smallest tentative distance among all" unvisited" nodes (and thus could be choose as the next" current").

```
#include <iostream>
#include <limits.h>
using namespace std;
//Wrapper class for storing a graph
class Graph
{
public:
int vertexNum;
int **edges;
//Constructs a graph with V vertices and E edges
Graph(const int V)
{
// initializes the array edges.
this->edges = new int *[V];
for (int i = 0; i < V; i++)
{
edges[i] = new int[V];
}
// fills the array with zeros.
for (int i = 0; i < V; i++)
{
for (int j = 0; j < V; j++)
{
edges[i][j] = 0;
}
}
this->vertexNum = V;
}
//Adds the given edge to the graph
void addEdge(int src, int dst, int weight)
{
this->edges[src][dst] = weight;
}
};
//Utility function to find minimum distance vertex in mdist
int minDistance(int mdist[], bool vset[], int V)
{
int minVal = INT_MAX, minInd = 0;
for (int i = 0; i < V; i++)
{
if (!vset[i] && (mdist[i] < minVal))
{
minVal = mdist[i];
minInd = i;
}
}
return minInd;
}
//Utility function to print distances
void print(int dist[], int V)
{
cout << "\nVertex Distance" << endl;
for (int i = 0; i < V; i++)
{
if (dist[i] < INT_MAX)
cout << i << "\t" << dist[i] << endl;
else
cout << i << "\tINF" << endl;
}
}
//The main function that finds the shortest path from given source
//to all other vertices using Dijkstra's Algorithm.It doesn't work on negative
//weights
void Dijkstra(Graph graph, int src)
{
int V = graph.vertexNum;
int mdist[V]; //Stores updated distances to vertex
bool vset[V]; // vset[i] is true if the vertex i included
// in the shortest path tree
//Initialise mdist and vset. Set distance of source as zero
for (int i = 0; i < V; i++)
{
mdist[i] = INT_MAX;
vset[i] = false;
}
mdist[src] = 0;
//iterate to find shortest path
for (int count = 0; count < V - 1; count++)
{
int u = minDistance(mdist, vset, V);
vset[u] = true;
for (int v = 0; v < V; v++)
{
if (!vset[v] && graph.edges[u][v] && mdist[u] + graph.edges[u][v] < mdist[v])
{
mdist[v] = mdist[u] + graph.edges[u][v];
}
}
}
print(mdist, V);
}
//Driver Function
int main()
{
int V, E, gsrc;
int src, dst, weight;
cout << "Enter number of vertices: ";
cin >> V;
cout << "Enter number of edges: ";
cin >> E;
Graph G(V);
for (int i = 0; i < E; i++)
{
cout << "\nEdge " << i + 1 << "\nEnter source: ";
cin >> src;
cout << "Enter destination: ";
cin >> dst;
cout << "Enter weight: ";
cin >> weight;
// makes sure source and destionation are in the proper bounds.
if (src >= 0 && src < V && dst >= 0 && dst < V)
{
G.addEdge(src, dst, weight);
}
else
{
cout << "source and/or destination out of bounds" << endl;
i--;
continue;
}
}
cout << "\nEnter source:";
cin >> gsrc;
Dijkstra(G, gsrc);
return 0;
}
```