PYTHON - DEPTH FIRST SEARCH CODE RECURSIVE

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

We will be seeing the Recursive way for implementing Depth First Search (DFS).

In the Recursive code we don't have to create the stack and maintain it as Python will do the job for us. And the stack will be hidden from us.

DFS - Depth First Search code for Undirected Graph - Recursive approach

Example :

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

def constructAdjacencyList(vtx, adjcVertex):
	vtxIndex = vertices.index(vtx)
	adjacencyList.append([])
	adjacencyList[vtxIndex].append(adjcVertex)

def depthFirstSearch(source):
	sourceIndex = vertices.index(source)
	visited[sourceIndex] = True
	print(source, end = "   ")
	for iter in adjacencyList[sourceIndex]:
		str = iter
		i = vertices.index(str)
		if (visited[i] == False):
			visited[i] = True
			depthFirstSearch(str)

V = 6
visited = [False]*V
adjacencyList = [[]]
vertices = []

# Insert Vertices

insertVertex("a")
insertVertex("b")
insertVertex("c")
insertVertex("d")
insertVertex("e")
insertVertex("f")

constructAdjacencyList("a", "c")
constructAdjacencyList("a", "d")

constructAdjacencyList("b", "d")
constructAdjacencyList("b" ,"e")
constructAdjacencyList("b" ,"c")

constructAdjacencyList("c", "a")
constructAdjacencyList("c", "b")
constructAdjacencyList("c", "e")

constructAdjacencyList("d", "a")
constructAdjacencyList("d" ,"b")
constructAdjacencyList("d", "e")
constructAdjacencyList("d", "f")

constructAdjacencyList("e", "b")
constructAdjacencyList("e", "c")
constructAdjacencyList("e", "d")
constructAdjacencyList("e", "f")

constructAdjacencyList("f", "d")
constructAdjacencyList("f", "e")

depthFirstSearch("a")

print()

Output :

a c b d e f

Code Explanation

We have implemented Depth First Search (DFS) on the below graph :

We can take various ways to navigate the graph using Depth First Search (DFS). Just remember our main intension is to visit all the vertices.

In this case we have covered the graph in the following path :

a --> c --> b --> d --> e --> f

Let us see how ?

Code Explanation for DFS - Depth First Search - Recursive :

Below code explains the `methods` :

def constructAdjacencyList(vtx, adjcVertex)

def insertVertex(vertex)

Almost the same we have discussed in DFS - Depth First Search - Iterative approach. You can skip it if you wane to.

Click Here - To understand the details of the methods 'def constructAdjacencyList(vtx, adjcVertex)' and 'def insertVertex(vertex)'.

Let's list out, what all do we need to support Depth First Search Data Structure.

We need a Linked List to store the vertices.

We need a doubly Linked List to store the adjacency linked list.

We need a Queue and an array to store its Levels.

We need a boolean array to store the Vertices that are already visited.

Now, let us see the above code.

We have a Linked List to store the Vertices.

vertices

We also have a doubly Linked List to store the Adjacency List.

adjacencyList

Similarly, we have a stack defined inside the method depthFirstSearch(...).

stack = []

And, there is a boolean array to store the Vertices that are visited.

visited

So, the first thing we will do is, insert the Vertices to the LinkedList vertices Linked List.

vertices = []

# Insert Vertices

insertVertex("a")
insertVertex("b")
insertVertex("c")
insertVertex("d")
insertVertex("e")
insertVertex("f")

Explanation of 'def insertVertex(vertex)' method

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

def insertVertex(vertex) is quite simple.

There is just one statement in it.

vertices.append(vertex)

It accepts String vertex as a parameter and adds it to the Linked List, vertices.

The next thing we will do is, create an Adjacency List to track the Adjacent Vertices.

Let us take the example of vertex a, to explain the creation of Adjacency List.

As we have seen, a has two adjacent vertices(i.e. c and d). And we have used the constructAdjacencyList(...) method to construct the Adjacency Matrix.

constructAdjacencyList("a", "c")
constructAdjacencyList("a", "d")

Note : Just remember, creating an Adjacency List above is same as creating an Edge. As the Adjacency List is actually a group of Edges.

Explanation of 'def constructAdjacencyList(vtx, adjcVertex)' method

def constructAdjacencyList(vtx, adjcVertex):
	vtxIndex = vertices.index(vtx)
	adjacencyList.append([])
	adjacencyList[vtxIndex].append(adjcVertex)

Although, the above method is explained in Adjacency List Code tutorial. I will give a brief explanation in this tutorial.

When a method call is made,

The variable vtx is assigned with value "a" and adjcVertex is assigned with "b".

Now, the first line,

vtxIndex = vertices.index(vtx)

Calculates the index/position of Vertex a. And as we can see the index a is 0.

Now, in the next line,

adjacencyList.append([])

We are initialising the first row of the 2D Linked List, adjacencyList.

But with what ?

We are initialising it with a Linked List [],

adjacencyList.append([])

So that the first row can hold the Adjacency List for vertex a.

a   ---   c ---> d

Similarly, the second row should hold the Adjacency List for vertex b and so on.

And in this iteration, our target is to find out the first row(To create an Adjacency List for vertex a) and insert vertex b to it.

And the below code does that.

adjacencyList[vtxIndex].append(adjcVertex)

We get the index of vertex a

vtxIndex = vertices.index(vtx)

As we know vtx is a.

Then add adjcVertex(That contains vertex c) to the 0th index of adjacencyList.

adjacencyList[0].append("c")

And following it we form the Adjacency List.

Now, we come across the most important method void depthFirstSearch(String source) that performs the Depth First Search (DFS).

Explanation of 'def depthFirstSearch(source)' method

sourceIndex = vertices.index(source)
visited[sourceIndex] = True
print(source, end = "   ")
for iter in adjacencyList[sourceIndex]:
	str = iter
	i = vertices.index(str)
	if (visited[i] == False):
		visited[i] = True
		depthFirstSearch(str)

We have called the def depthFirstSearch(source) from the main method passing a as the parameter.

depthFirstSearch("a")

So, the first thing we will do is, take the index of a,

sourceIndex = vertices.index(source)

Now, if we see the List of vertices,

We can see that a lies in index 0.

Next, we mark a as visited,

visited[sourceIndex] = True

in the visited[] array,

visited[0] = True

Then we print the vertex a.

print(source, end = "   ")

Output :

Then comes the for(...) loop, where we find the adjacent vertices of the top element(i.e. a).

for iter in adjacencyList[sourceIndex]:
	str = iter
	i = vertices.index(str)
	if (visited[i] == False):
		visited[i] = True
		depthFirstSearch(str)

The first statement of the for loop (i.e. The initialisation section of the loop),

iter

is where we get the Adjacent Vertices of vertex c in the Iterator iter.

The adjacencyList is a 2D Linked List that stores the adjacent vertices.

adjacencyList[sourceIndex]

As we have seen, the sourceIndex is 0 (Because the index of vertex a is 0).

And the iter variable of iter gets the adjacency list of vertex a in it.

iter variable of iter, stores the Adjacency List of vertex a in it.

So, iter has the elements c and d in it.

Now, str contains the first adjacent vertex c.

str = iter

Next, we find the index of vertex c,

i = vertices.index(str)

Now, if we see the List of vertices,

We can see that c lies in index 2.

So, we check if c is visited or not.

if (visited[i] == False):
	visited[i] = True
	depthFirstSearch(str)

Now, if we check the visited array,

We found that visited[2] = False and we get into the if statement.

And marked visited[2] = true,

visited[i] = true;

In the visited[] array,

And then comes the fun part. Where the depthFirstSearch(...) method calls itself.

depthFirstSearch(str)

So, internally what happens is, Python maintains an internal stack, that is hidden from you.

Now, since the method started from a, Python puts a to the stack. Then whenever it meets the statement,

depthFirstSearch(str)

It recognises a recursive call is made and pushes the content of variable str(i.e. c) to the stack.

Similarly, we repeat the same process until all the vertices are visited. And Python pushes all the values to the stack.

Now, since we have reached a place where all the adjacent vertices of vertex f are visited.

So, it's time for Python to backtrack. i.e. Start popping out all the elements from its internal queue.

So, it takes out f out of the queue and checks if there are any adjacent vertices of e that are not visited.

Continuing in the same way, all the elements are popped out of the Queue and the execution ends.

❮❮ PREV NEXT ❯❯