PYTHON - ADJACENCY LIST CODE

JAVA PYTHON GO KOTLIN C# RUBY C++ Java Script

Example :

def insertVertex(vertices, vertex):
	vertices.append(vertex)

def constructAdjacencyList(adjcList, u, val):
	adjcList.append([])
	adjcList[u].append(val)

def printAdjacencyList(adjcList, vertices):
	i = 0
	for vtx in vertices:
		print("The Adjacency List for vertex", vtx, "at index", i, ":", end = " ")
		for j in range(len(adjcList[i])):
			print(adjcList[i][j], end = " --> ")
		print('\b\b\b\b', end = '    \n')
		i+=1	


vertices = []

adjacencyList = [[]]

# Insert Vertices
insertVertex(vertices, "a")
insertVertex(vertices, "b")
insertVertex(vertices, "c")
insertVertex(vertices, "d")
insertVertex(vertices, "e")

# Create Adjacency List

constructAdjacencyList(adjacencyList, 0, "b")
constructAdjacencyList(adjacencyList, 0, "c")
constructAdjacencyList(adjacencyList, 0, "d")
        
constructAdjacencyList(adjacencyList, 1, "a")
constructAdjacencyList(adjacencyList, 1 ,"e")
        
constructAdjacencyList(adjacencyList, 2, "a")
constructAdjacencyList(adjacencyList, 2, "d")
constructAdjacencyList(adjacencyList, 2, "e")
        
constructAdjacencyList(adjacencyList, 3, "a")
constructAdjacencyList(adjacencyList, 3 ,"c")
constructAdjacencyList(adjacencyList, 3, "e")
        
constructAdjacencyList(adjacencyList, 4, "b")
constructAdjacencyList(adjacencyList, 4, "c")
constructAdjacencyList(adjacencyList, 4, "d")

printAdjacencyList(adjacencyList, vertices)

Output :

The Adjacency List for vertex a at index 0 : b --> c --> d
The Adjacency List for vertex b at index 1 : a --> e
The Adjacency List for vertex c at index 2 : a --> d --> e
The Adjacency List for vertex d at index 3 : a --> c --> e
The Adjacency List for vertex e at index 4 : b --> c --> d

Code explanation for Adjacency List Data Structure

There are two methods in the above code :

def insertVertex(vertices, vertex)

def constructAdjacencyList(adjcList, u, val)

While the first method is quite simple.

Explanation of 'def insertVertex(vertices, vertex)' method :

def insertVertex(vertices, vertex):
	vertices.append(vertex)

As the name of the method def insertVertex(...) suggests. The method is used to add vertices to the Linked List.

Let us take the example to add the vertex a to the Linked List.

So, we have created a Linked List to hold the vertices.

vertices = []

Then we call the def insertVertex(...) method and pass the Linked List vertices and the vertex a to the method.

insertVertex(vertices, "a")

Now, if we go to the definition of the def insertVertex(...) method. We can see, there is just one line in it,

vertices.append(vertex)

That takes the vertex (a in this case) and adds it to the vertices Linked List.

Next, let us come to the next method that creates the Adjacency List.

Explanation of 'def constructAdjacencyList(adjcList, u, val)' method :

def constructAdjacencyList(adjcList, u, val):
	adjcList.append([])
	adjcList[u].append(val)

Let's start from the beginning. Where we have defined a 2D Linked List to hold the Adjacency List.

adjacencyList = [[]]

But why do we need a 2D Linked List ?

Let us look at the below diagram to get it clarified.

Vertex a is at index 0. Similarly, vertex b is at index 1 and so on.

Now, we can consider the above as a 2D Linked List.

But How ?

Let us consider vertex 'a' at index '0'

Let us take vertex a at index 0. Then take its Adjacent Vertices and pass it to def constructAdjacencyList(...) method.

constructAdjacencyList(adjacencyList, 0, "b")

The first adjacent vertex of a at index 0 is b. So, we pass the index i.e. 0 and its adjacent vertex i.e. b.

Now let's go to the def constructAdjacencyList(...) method definition.

And we come across the first line :

adjcList.append([])

Now, since adjcList is a 2D Linked List, we need to initialise the first row(As mentioned in the diagram) with a Linked List (i.e. [])

And this row will hold the Adjacent vertices of vertex a at index 0 (i.e. b, c & d)

And then comes the line that will be adding elements to the above created Linked List.

adjcList[u].append(val)

So, in the above line, the first thing we do is, get the Linked List at index 0

adjcList[u] 		[Since the value of 'u' is '0']

Then, add b to the Lined List.

adjcList[0].append("b")		[Since, the value of val is b].

And the below Linked List is formed.

Then, we come to the next line in the main program.

constructAdjacencyList(adjacencyList, 0, "c")

The second adjacent vertex of a at index 0 is c. So, we pass the index i.e. 0 and its adjacent vertex i.e. c.

Now let's come to the def constructAdjacencyList(...) method definition.

And we come across the first line :

adjcList.append([])

And then comes the line that will be adding elements to the above created Linked List.

adjcList[u].append(val)

So, in the above line, the first thing we do is, get the Linked List at index 0

adjcList[0] 		[Since the value of u is 0]

Then, add c to the Lined List.

adjcList[0].append("c") 	[Since, the value of val is c].

And the below Linked List is formed.

Similarly, we come to the next line in the main program.

constructAdjacencyList(adjacencyList, 0, "d")

The second adjacent vertex of a at index 0 is d. So, we pass the index i.e. 0 and its adjacent vertex i.e. d.

And the below Linked List is formed.

Next, let us consider vertex 'b' at index '1'

Now, us take vertex b at index 1. Then take its Adjacent Vertices and pass it to def constructAdjacencyList(...) method.

constructAdjacencyList(adjacencyList, 1, "a")

The first adjacent vertex of b at index 1 is a. So, we pass the index i.e. 1 and its adjacent vertex i.e. a.

Now let's go to the def constructAdjacencyList(...) method definition.

And we come across the first line :

adjcList.append([])

Now, since adjcList is a 2D Linked List, we need to initialise the 2nd row(As mentioned in the diagram) with a Linked List (i.e. [])

And this row will hold the Adjacent vertices of vertex b at index 1 (i.e. a & e).

And then comes the line that will be adding elements to the above created Linked List.

adjcList[u].append(val)

So, in the above line, the first thing we do is, get the Linked List at index 1

adjcList[1] 		[Since the value of u is 1]

Then, add 1 to the Lined List.

adjcList[1].append("a") 	[Since, the value of val is a].

And the below Linked List is formed.

And continuing this way we get the Adjacency List.

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