C Program to implement Topological Sorting Algorithm Example

By | 13.07.2017

Topological Sorting Algorithm


Write a C Program to implement Topological Sorting Algorithm Example. Here’s simple Program to implement Topological Sort Algorithm Example in C Programming Language.


Topological Sorting


Topological sorting or Topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge (u v) from vertex to vertex vu comes before v in the ordering.

For instance, the vertices of the graph may represent tasks to be performed, and the edges may represent constraints that one task must be performed before another; in this application, a topological ordering is just a valid sequence for the tasks.

A topological ordering is possible if and only if the graph has no directed cycles, that is, if it is a directed acyclic graph (DAG).

Any DAG has at least one topological ordering, and algorithms are known for constructing a topological ordering of any DAG in linear time.


Also Read : : C Program for Creating Minimum Spanning Tree using Prim’s Algorithm

Below is the source code for C Program to implement Topological Sorting Algorithm Example which is successfully compiled and run on Windows System to produce desired output as shown below :


SOURCE CODE : :


/* C Program to implement Topological Sorting Algorithm Example */

#include<stdio.h>
#include<stdlib.h>

#define MAX 100

int n;    /*Number of vertices in the graph*/
int adj[MAX][MAX]; /*Adjacency Matrix*/
void create_graph();

int queue[MAX], front = -1,rear = -1;
void insert_queue(int v);
int delete_queue();
int isEmpty_queue();

int indegree(int v);

int main()
{
        int i,v,count,topo_order[MAX],indeg[MAX];

        create_graph();

        /*Find the indegree of each vertex*/
        for(i=0;i<n;i++)
        {
                indeg[i] = indegree(i);
                if( indeg[i] == 0 )
                        insert_queue(i);
        }

        count = 0;

        while(  !isEmpty_queue( ) && count < n )
        {
                v = delete_queue();
        topo_order[++count] = v; /*Add vertex v to topo_order array*/
                /*Delete all edges going fron vertex v */
                for(i=0; i<n; i++)
                {
                        if(adj[v][i] == 1)
                        {
                                adj[v][i] = 0;
                                indeg[i] = indeg[i]-1;
                                if(indeg[i] == 0)
                                        insert_queue(i);
                        }
                }
        }

        if( count < n )
        {
                printf("\nNo topological ordering possible, graph contains cycle\n");
                exit(1);
        }
        printf("\nVertices in topological order are :\n");
        for(i=1; i<=count; i++)
                printf( "%d ",topo_order[i] );
        printf("\n");

        return 0;
}/*End of main()*/

void insert_queue(int vertex)
{
        if (rear == MAX-1)
                printf("\nQueue Overflow\n");
        else
        {
                if (front == -1)  /*If queue is initially empty */
                        front = 0;
                rear = rear+1;
                queue[rear] = vertex ;
        }
}/*End of insert_queue()*/

int isEmpty_queue()
{
        if(front == -1 || front > rear )
                return 1;
        else
                return 0;
}/*End of isEmpty_queue()*/

int delete_queue()
{
        int del_item;
        if (front == -1 || front > rear)
        {
                printf("\nQueue Underflow\n");
                exit(1);
        }
        else
        {
                del_item = queue[front];
                front = front+1;
                return del_item;
        }
}/*End of delete_queue() */

int indegree(int v)
{
        int i,in_deg = 0;
        for(i=0; i<n; i++)
                if(adj[i][v] == 1)
                        in_deg++;
        return in_deg;
}/*End of indegree() */

void create_graph()
{
        int i,max_edges,origin,destin;

        printf("\nEnter number of vertices : ");
        scanf("%d",&n);
        max_edges = n*(n-1);

        for(i=1; i<=max_edges; i++)
        {
                printf("\nEnter edge %d(-1 -1 to quit): ",i);
                scanf("%d %d",&origin,&destin);

                if((origin == -1) && (destin == -1))
                        break;

                if( origin >= n || destin >= n || origin<0 || destin<0)
                {
                        printf("\nInvalid edge!\n");
                        i--;
                }
                else
                        adj[origin][destin] = 1;
        }
}

OUTPUT : :


/* C Program to implement Topological Sorting Algorithm Example */

Enter number of vertices : 6

Enter edge 1(-1 -1 to quit): 0 1

Enter edge 2(-1 -1 to quit): 0 2

Enter edge 3(-1 -1 to quit): 0 3

Enter edge 4(-1 -1 to quit): 1 3

Enter edge 5(-1 -1 to quit): 2 4

Enter edge 6(-1 -1 to quit): 2 5

Enter edge 7(-1 -1 to quit): 3 5

Enter edge 8(-1 -1 to quit): 4 5

Enter edge 9(-1 -1 to quit): 1 5

Enter edge 10(-1 -1 to quit): -1 -1

Vertices in topological order are :
0 1 2 3 4 5

Process returned 0

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