Graph Representation using Adjacency List in C++

This is a C++ program to represent graph using adjacency list.

Problem Description

1. This algorithm represents a graph using adjacency list.
2. This method of representing graphs is not efficient.
3. The time complexity of this algorithm is O(v*e).

Problem Solution

1. This algorithm takes the input of the number of vertex and edges.
2. Take the input of connected vertex pairs.
3. Print the adjacency list.
4. Exit.

Program/Source Code

C++ program to represent graph using adjacency list.
This program is successfully run on Dev-C++ using TDM-GCC 4.9.2 MinGW compiler on a Windows system.

#include<iostream>
 
using namespace std;
 
int main()
{
	int i, v, e, j, count;
 
	// take the input of the number of vertex and edges.
	cout<<"Enter the number of vertexes of the graph: ";
	cin>>v;
	cout<<"\nEnter the number of edges of the graph: ";
	cin>>e;
	int edge[e][2];
 
	// Take the input of the adjacent vertex pairs of the given graph.
	for(i = 0; i < e; i++)
	{
		cout<<"\nEnter the vertex pair for edge "<<i+1;
		cout<<"\nV(1): ";
		cin>>edge[i][0];
		cout<<"V(2): ";
		cin>>edge[i][1];
	}
 
	// Print the adjacency list representation of the graph.
	cout<<"\n\nThe adjacency list representation for the given graph: ";
	for(i = 0; i < v; i++)
	{
		count = 0;
		// For each vertex print, its adjacent vertex.
		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)
			{
				cout<<edge[j][0]<<"  ";
				count++;
			}
			else if(j == e-1 && count == 0)
				cout<<"Isolated Vertex!";
		}
		cout<<" }";
	}
}

Program Explanation

1. Take the input of the number of vertex ‘v’ and edges ‘e’.
2. Take the input of ‘e’ pairs of vertexes of the given graph in edge[][].
3. For each vertex, search the vertex in the edge[][] matrix and print the corresponding vertex connected to this vertex.
4. Exit.

Runtime Test Cases

Case 1:
Enter the number of vertexes of the graph: 5
 
Enter the number of edges of the graph: 8
 
Enter the vertex pair for edge 1
V(1): 1
V(2): 3
 
Enter the vertex pair for edge 2
V(1): 1
V(2): 4
 
Enter the vertex pair for edge 3
V(1): 1
V(2): 5
 
Enter the vertex pair for edge 4
V(1): 2
V(2): 3
 
Enter the vertex pair for edge 5
V(1): 2
V(2): 5
 
Enter the vertex pair for edge 6
V(1): 3
V(2): 4
 
Enter the vertex pair for edge 7
V(1): 3
V(2): 5
 
Enter the vertex pair for edge 8
V(1): 4
V(2): 5
 
 
The adjacency list representation for the given graph:
        1-> { 3  4  5   }
        2-> { 3  5   }
        3-> { 1  2  4  5   }
        4-> { 1  3  5   }
        5-> { 1  2  3  4   }
 
Case 2:
Enter the number of vertexes of the graph: 4
 
Enter the number of edges of the graph: 6
 
Enter the vertex pair for edge 1
V(1): 1
V(2): 2
 
Enter the vertex pair for edge 2
V(1): 1
V(2): 3
 
Enter the vertex pair for edge 3
V(1): 1
V(2): 4
 
Enter the vertex pair for edge 4
V(1): 2
V(2): 3
 
Enter the vertex pair for edge 5
V(1): 2
V(2): 4
 
Enter the vertex pair for edge 6
V(1): 3
V(2): 4
 
 
The adjacency list representation for the given graph:
        1-> { 2  3  4   }
        2-> { 1  3  4   }
        3-> { 1  2  4   }
        4-> { 1  2  3   }

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