C++ Program to Implement Adjacency List

The adjacency list representation of a graph is linked list representation. In this representation we have an array of lists The array size is V. Here V is the number of vertices. In other words, we can say that we have an array to store V number of different lists. If a list header is vertex u, then it signifies that it will hold all of the adjacent vertices of u.

The complexity of Adjacency List representation

• This representation takes O(V+2E) for undirected graph, and O(V+E) for directed graph. If the number of edges are increased, then the required space will also be increased.

Input:

Output:

Algorithm

add_edge(adj_list, u, v)

Input: The u and v of an edge {u,v}, and the adjacency list

Output: Adjacency List of the graph G

Begin
   Append v into the list at index u
   Append u into the list at index v
End

Example Code

#include<iostream>
#include<list>
#include<iterator>
using namespace std;
void displayAdjList(list<int> adj_list[], int v) {
   for(int i = 0; i<v; i++) {
      cout << i << "--->";
      list<int> :: iterator it;
      for(it = adj_list[i].begin(); it != adj_list[i].end(); ++it) {
         cout << *it << " ";
      }
      cout << endl;
   }
}
void add_edge(list<int> adj_list[], int u, int v) {    //add v into the list u, and u into list v
   adj_list[u].push_back(v);
   adj_list[v].push_back(u);
}
main(int argc, char* argv[]) {
   int v = 6;    //there are 6 vertices in the graph
   //create an array of lists whose size is 6
   list<int> adj_list[v];
   add_edge(adj_list, 0, 4);
   add_edge(adj_list, 0, 3);
   add_edge(adj_list, 1, 2);
   add_edge(adj_list, 1, 4);
   add_edge(adj_list, 1, 5);
   add_edge(adj_list, 2, 3);
   add_edge(adj_list, 2, 5);
   add_edge(adj_list, 5, 3);
   add_edge(adj_list, 5, 4);
   displayAdjList(adj_list, v);
}

Output

0--->4 3
1--->2 4 5
2--->1 3 5
3--->0 2 5
4--->0 1 5
5--->1 2 3 4