Adjacency List in Python

Given the adjacency list and the number of vertices and edges of a graph, the task is to represent the adjacency list for a directed graph.

Examples:

Input:
V = 3
edges[][] = {{0, 1}, {1, 2}, {2, 0}}
Output:
0 -> 1
1 -> 2
2 -> 0
Explanation: The output represents the adjacency list for the given graph.

Input:
V = 4
edges[][] = {{0, 1}, {1, 2}, {1, 3}, {2, 3}, {3, 0}}
Output:
0 -> 1
1 -> 2 3
2 -> 3
3 -> 0
Explanation: The output represents the adjacency list for the given graph.

Adjacency List in Python Using Dictionary:

Use a dictionary where each key is a vertex, and the corresponding value is a list of its neighboring vertices.

Step-by-step algorithm:

• Initialize an empty dictionary.
• Add vertices to the dictionary.
• Add edges between vertices by updating the dictionary.
• Display the adjacency list.

Below is the implementation of the above approach:

def adjacency_list_dictionary(V, edges):
   
    
    adjacency_list = {}

    # Add vertices to the dictionary
    for i in range(V):
        adjacency_list[i] = []

    # Add edges to the dictionary
    for edge in edges:
        vertex1, vertex2 = edge
        adjacency_list[vertex1].append(vertex2)

    # Display the adjacency list
    for vertex, neighbors in adjacency_list.items():
        print(f"{vertex} -> {' '.join(map(str, neighbors))}")


# testcase 1
V1 = 3
edges1 = [[0, 1], [1, 2], [2, 0]]
adjacency_list_dictionary(V1, edges1)

# testcase 2
V2 = 4
edges2 = [[0, 1], [1, 2], [1, 3], [2, 3], [3, 0]]
adjacency_list_dictionary(V2, edges2)

0 -> 1
1 -> 2
2 -> 0
0 -> 1
1 -> 2 3
2 -> 3
3 -> 0

Time Complexity:

• Initialization: O(V)
• Adding edges: O(E)
• Display: O(V + E)

Auxiliary Space: O(V + E)

Adjacency List in Python Using defaultdict:

Use defaultdict from the collections module where each key is a vertex, and the corresponding value is a list of its neighboring vertices.

Step-by-step algorithm:

• Initialize a defaultdict with a list as the default value.
• Add edges between vertices by updating the defaultdict.
• Display the adjacency list.

Below is the implementation of the above approach:

from collections import defaultdict

def adjacency_list_defaultdict(V, edges):
  
    adjacency_list = defaultdict(list)

    # Add edges to the defaultdict
    for edge in edges:
        vertex1, vertex2 = edge
        adjacency_list[vertex1].append(vertex2)

    # Display the adjacency list
    for vertex, neighbors in adjacency_list.items():
        print(f"{vertex} -> {' '.join(map(str, neighbors))}")


# test case 1
V1 = 3
edges1 = [[0, 1], [1, 2], [2, 0]]
adjacency_list_defaultdict(V1, edges1)

# test case 2
V2 = 4
edges2 = [[0, 1], [1, 2], [1, 3], [2, 3], [3, 0]]
adjacency_list_defaultdict(V2, edges2)

0 -> 1
1 -> 2
2 -> 0
0 -> 1
1 -> 2 3
2 -> 3
3 -> 0

Time Complexity:

• Adding edges: O(E)
• Display: O(V + E)

Auxiliary Space: O(V + E)