C++ Program to Find Single Source Shortest Path in DAG

This C++ program displays the shortest path traversal from a particular node to every other node present inside the graph relative to the former node.

Here is the source code of the C++ program of the Djikstra’s Algoritm of finding shortest paths from the first node in graph to every other node with the shortest path length displayed beside each pair of vertices.This C++ program is successfully compiled and run on DevCpp,a C++ compiler.The program output is given below.

```
/*
```

 * C++ Program to find SSSP(Single Source Shortest Path)

```
 * in DAG(Directed Acyclic Graphs)
```
```
 */
```
```
#include <iostream>
```
```
#include <conio.h>
```
```
using namespace std;
```
```
#define INFINITY 999
```
```
struct node
```
```
{
```
```
   int from;
```
```
}p[7];
```
```
int c = 0;
```

void djikstras(int *a,int b[][7],int *dv)

```
{
```
```
    int i = 0,j,min,temp;
```
```
    a[i] = 1;
```
```
    dv[i] = 0;
```
```
    p[i].from = 0;
```
```
    for (i = 0; i < 7;i++)
```
```
    {
```
```
        if (b[0][i] == 0)
```
```
        {
```
```
            continue;
```
```
        }
```
```
        else
```
```
        {
```
```
            dv[i] = b[0][i];
```
```
            p[i].from = 0;
```
```
        }
```
```
    }
```
```
    while (c < 6)
```
```
    {
```
```
        min = INFINITY;
```
```
        for (i = 0; i < 7; i++)
```
```
        {
```

            if (min <= dv[i] || dv[i] == 0 || a[i] == 1)

```
            {
```
```
                continue;
```
```
            }
```
```
            else if (min > dv[i])
```
```
            {
```
```
                min = dv[i];
```
```
            }
```
```
        }
```
```
        for (int k = 0; k < 7; k++)
```
```
        {
```
```
            if (min == dv[k])
```
```
            {
```
```
                temp = k;
```
```
                break;
```
```
            }
```
```
            else
```
```
            {
```
```
                continue;
```
```
    	    }
```
```
        }
```
```
        a[temp] = 1;
```
```
        for (j = 0; j < 7; j++)
```
```
        {
```

            if (a[j] == 1 || b[temp][j] == 0)

```
            {
```
```
                continue;
```
```
            }
```
```
            else if (a[j] != 1)
```
```
            {
```

                if (dv[j] > (dv[temp] + b[temp][j]))

```
                {
```

                    dv[j] = dv[temp] + b[temp][j];

```
                    p[i].from = temp;
```
```
                }
```
```
            }
```
```
        }
```
```
        c++;
```
```
    }  
```
```
    for (int i = 0; i < 7; i++)
```
```
    {
```

        cout<<"from node "<<p[i].from<<" cost is:"<<dv[i]<<endl;

```
    } 
```
```
}       
```
```
int main()
```
```
{
```
```
    int a[7];
```
```
    int dv[7];
```
```
    for(int k = 0; k < 7; k++)
```
```
    {
```
```
        dv[k] = INFINITY;
```
```
    }
```
```
    for (int i = 0; i < 7; i++)
```
```
    {
```
```
        a[i] = 0;
```
```
    }
```
```
    int b[7][7];
```
```
    for (int i = 0;i < 7;i++)
```
```
    {
```

        cout<<"enter values for "<<(i+1)<<" row"<<endl;

```
        for(int j = 0;j < 7;j++)
```
```
        {
```
```
            cin>>b[i][j];
```
```
        }
```
```
    }
```
```
    djikstras(a,b,dv);
```
```
    getch();
```
```
}
```

Output
enter values for 1 row
0
3
6
0
0
0
0
enter values for 2 row
3
0
2
4
0
0
0
enter values for 3 row
6
2
0
1
4
2
0
enter values for 4 row
0
4
1
0
2
0
4
enter values for 5 row
0
0
4
2
0
2
1
enter values for 6 row
0
0
2
0
2
0
1
enter values for 7 row
0
0
0
4
1
1
0
from node 0 to node 0 minimum cost is:0
from node 0 to node 1 minimum cost is:3
from node 0 to node 2 minimum cost is:5
from node 0 to node 3 minimum cost is:6
from node 0 to node 4 minimum cost is:8
from node 0 to node 5 minimum cost is:7
from node 0 to node 6 minimum cost is:8

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