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Generate a Random Directed Acyclic Graph DAC for a Given Number of Edges

Generate a Random Directed Acyclic Graph DAC for a Given Number of Edges

- This algorithm generates a random directed acyclic graph for the given edges 'e'.
- The time complexity of this algorithm is O(e*v*e).

- This algorithm takes the input of the number of edges 'e' in the random DAG.
- It connects two random vertexes and checks for any cycle generated due to this edge.
- If yes discard this edge and generate random vertex pair again.
- Exit.

#include<iostream>
#include<stdlib.h>
 
// The maximum number of the vertex for the sample random graph.
#define NOV 20
 
using namespace std;
 
// A function to check for the cycle, on addition of a new edge in the random graph.
bool CheckAcyclic(int edge[][2], int ed, bool check[], int v)
{
	int i;
	bool value;
	// If the current vertex is visited already, then the graph contains cycle.
	if(check[v] == true)
	{
		return false;
	}
	else
	{
		check[v] = true;
		// For each vertex, go for all the vertex connected to it.
		for(i = ed; i >= 0; i--)
		{
			if(edge[i][0] == v)
			{
				return CheckAcyclic(edge, ed, check, edge[i][1]);
			}
		}
	}
	// In case, if the path ends then reassign the vertexes visited in that path to false again.
	check[v] = false;
 
	if(i == 0)
		return true;
}
 
// A function to generate random graph.
void GenerateRandGraphs(int e)
{
	int i, j, edge[e][2], count;
 
	bool check[21];
 
	// Build a connection between two random vertex.
	i = 0;
	while(i < e)
	{
		edge[i][0] = rand()%NOV+1;
		edge[i][1] = rand()%NOV+1;
 
		for(j = 1; j <= 20; j++)check[j] = false;
 
		if(CheckAcyclic(edge, i, check, edge[i][0]) == true)
			i++;
	}
 
	// Print the random graph.
	cout<<"\nThe generated random random graph is: ";
	for(i = 0; i < NOV; i++)
	{
		count = 0;
		cout<<"\n\t"<<i+1<<"-> { ";
		for(j = 0; j < e; j++)
		{
			if(edge[j][0] == i+1)
			{
				cout<<edge[j][1]<<"  ";
				count++;
			}
			else if(edge[j][1] == i+1)
			{
				count++;
			}
			else if(j == e-1 && count == 0)
				cout<<"Isolated Vertex!";
		}
		cout<<" }";
	}	
}
 
 
int main()
{
	int e;
 
	cout<<"Enter the number of edges for the random graphs: ";
	cin>>e;
 
	// A function to generate a random undirected graph with e edges.
	GenerateRandGraphs(e);
}