# C++ Program to Implement Dijkstra’s Algorithm Using Set

C++ProgrammingServer Side Programming

This is a C++ Program to Implement Dijkstra’s Algorithm using Set. Here we need to have two sets. We generate a shortest path tree with given source node as root. One set contains vertices included in shortest path tree and other set includes vertices not yet included in shortest path tree. At every step, we find a vertex which is in the other set (set of not yet included) and has minimum distance from source.

## Algorithm:

Begin
function dijkstra() to find minimum distance:
1) Create a set Set that keeps track of vertices included in shortest
path tree, Initially, the set is empty.
2) A distance value is assigned to all vertices in the input graph.
Initialize all distance values as INFINITE. Distance value is assigned as
0 for the source vertex so that it is picked first.
3) While Set doesn’t include all vertices
a) Pick a vertex u which is not there in the Set and has minimum distance value.
b) Include u to Set.
c) Distance value is updated of all adjacent vertices of u.
For updating the distance values, iterate through all adjacent
vertices. if sum of distance value of u (from source) and weight of
edge u-v for every adjacent vertex v, is less than the distance value
of v, then update the distance value of v.
End

## Example Code

#include <iostream>
#include <climits>
#include <set>
using namespace std;
#define N 5
int minDist(int dist[], bool Set[])//calculate minimum distance
{
int min = INT_MAX, min_index;
for (int v = 0; v < N; v++)
if (Set[v] == false && dist[v] <= min)
min = dist[v], min_index = v;
return min_index;
}
int printSol(int dist[], int n)//print the solution
{
cout<<"Vertex Distance from Source\n";
for (int i = 0; i < N; i++)
cout<<" \t\t \n"<< i<<" \t\t "<<dist[i];
}
void dijkstra(int g[N][N], int src)
{
int dist[N];
bool Set[N];
for (int i = 0; i < N; i++)
dist[i] = INT_MAX, Set[i] = false;
dist[src] = 0;
for (int c = 0; c < N- 1; c++)
{
int u = minDist(dist, Set);
Set[u] = true;
for (int v = 0; v < N; v++)
if (!Set[v] && g[u][v] && dist[u] != INT_MAX && dist[u]
+ g[u][v] < dist[v])
dist[v] = dist[u] + g[u][v];
}
printSol(dist, N);
}
int main()
{
int g[N][N] = { { 0, 4, 0, 0, 0 },
{ 4, 0, 7, 0, 0 },
{ 0, 8, 0, 9, 0 },
{ 0, 0, 7, 0, 6 },
{ 0, 2, 0, 9, 0 }};
dijkstra(g, 0);
return 0;
}

## Output

Vertex Distance from Source
0 0
1 4
2 11
3 20
4 26