Data Structures and Algorithms in Python

This lesson serves as a simple introduction to Python's data structures and algorithms. With the aid of practical and thoroughly explained illustrations, we will go over the built-in data structures like lists, sets, dictionaries, tuples, etc., as well as a few other user-defined data structures like linked trees, lists, and graphs, as well as some commonly used algorithms.

Lists

Likewise, arrays in other computer languages and lists in Python are collections of items arranged in any manner. It permits many data types of elements in the list. Python's version of lists is comparable to C++'s vectors or Java's array lists. As all the components must be relocated, adding or removing a member from the list's head is the most expensive operation. If the pre-allocated memory is all used up, insertion and deletion of an element at the end of the list may also become costly.

Code

# Python program to show how to create a Python List and some of its operations

# Creating a Python list
List = ["Python", "Data", "Structures", "Tutorial"]
print("The created Python list is: ")
print(List)
  
# Creating a multi-dimensional list using nested lists (list inside a list)
List_ = [["Python", "Data"], ["Structures", "Tutorial"]]
print("The multi-Dimensional list is: ")
print(List_)
  
# We can access the list of elements using the index of the element
print("Single element: ", List[1])
print("Multiple elements (slicing): ", List[0:2])
print("For nested lists: ", List_[1][0])
  
# We can access elements using negative indices also
      
# printing the last element of the list
print("Last element: ", List_[-1])
      
# Slicing the list using negative indexing
print("Last two elements: ", List[-1:-3:-1]) # Last first order

Output

The created Python list is: 
['Python', 'Data', 'Structures', 'Tutorial']
The multi-Dimensional list is: 
[['Python', 'Data'], ['Structures', 'Tutorial']]
Single element:  Data
Multiple elements (slicing):  ['Python', 'Data']
For nested lists:  Structures
Last element:  ['Structures', 'Tutorial']
Last two elements:  ['Tutorial', 'Structures']

Tuple

Lists and Python tuples are equivalent, but unlike lists, tuples are immutable, meaning that once formed, we cannot change them. A Tuple can include components of several types, just like a List.

Python tuples are made by grouping together a series of values. These values are delimited by a "comma", regardless of whether or not the parenthesis is used.

Code

# Python program to show how to create a Python Tuple and to access its elements

# Creating a Python tuple
Tuple = ("Python", "Data", "Structures", "Tutorial")
print("The Python tuple is: ")
print(Tuple)
      
# Create a tuple using a Python list
list = [3, 6, 2, 7, 4, 5, 3]
print("Tuple using a List: ")
Tuple_ = tuple(list)

# Accessing tuple elements using indices
print("Single element: ", Tuple[1])
print("Multiple elements (slicing): ", Tuple[0:2])
  
# Using negative indexing
      
# printing the last element of the list
print("Last element: ", Tuple[-1])
      
# Trying to modify a tuple
try:
    Tuple[1] = "Tuple"
    print(Tuple)
except Exception as e:
    print("Exception raised: ", e

Output

The Python tuple is: 
('Python', 'Data', 'Structures', 'Tutorial')
Tuple using a List: 
Single element:  Data
Multiple elements (slicing):  ('Python', 'Data')
Last element:  Tutorial
Exception raised:  'tuple' object does not support item assignment

Set

A Python set data structure is a non-duplicate data collection that is modifiable. Sets are mainly used for membership screening and removing redundant entries. These processes use the Hashing data structure, a popular method for traversal, insertion, and deletion of elements that typically takes O(1) time.

Code

# Python program to show how to create a Python Set and its operations

# Creating a Python set
Set = {"Python", "Data", "Structures", "Tutorial"}
print("The Python Set is: ")
print(Set)
  
# Accessing the set elements
for ind, i in enumerate(Set):
    print(ind, i)

# Finding the intersection of two sets
Set_ = {1, 2, "Python", "Data"}
print("Intersection: ", Set.intersection(Set_))

# Union of two sets
print("Union: ", Set.union(Set_))

Output

The Python Set is: 
{'Python', 'Data', 'Tutorial', 'Structures'}
0 Python
1 Data
2 Tutorial
3 Structures
Intersection:  {'Python', 'Data'}
Union:  {1, 2, 'Structures', 'Python', 'Tutorial', 'Data'}

Dictionary

A key-value pair-formatted data collection called a Python dictionary is used to store data. The temporal complexity of this data structure is O(1), much like hash tables in other coding languages. The Python Dictionary is indexed with the help of the keys. The values of keys can be of any type, i.e., a constant item like a string, integer, sequence, etc. We can build a dictionary using curly brackets {} or dictionary comprehension.

Code

# Python program to show how to create a Python Dictionary and its operations

# Creating a Python Dictionary
Dict = {"1": "Python", "2": "Data", "3": "Structures", "4": "Tutorial"}
print("The Python Dictionary is: ")
print(Dict)
  
# accessing the dictionary element using the keys
print("Value of key 2 is: ", Dict["2"])
  
# accessing the elements using the built-in get method
print("Using the get method: ", Dict.get("2"))

Output

The Python Dictionary is: 
{'1': 'Python', '2': 'Data', '3': 'Structures', '4': 'Tutorial'}
Value of key 2 is:  Data
Using the get method:  Data

Linked List

A linear data structure called a linked list has elements that are not kept in consecutive locations in memory. A linked list's elements are connected via pointers.

A pointer to the first node of the linked list serves as the representation of a linked list. The head refers to the top node. The head's value is NULL if the linked list is empty. In a list, each node has at least two components:

Data
Pointer (Or Reference) to the next node

Code

# Python program to show the implementation of the linked list

# Creating a node class
class Node:
    def __init__(self, value):
        self.value = value
        self.next = None

# Creating a linked list class
class LinkedList:
    def __init__(self):
        self.head = None

# Initializing a linked list
list_ = LinkedList()

# Creating the nodes
list_.head = Node("Python")
second_node = Node("Tutorial")
third_node = Node("Data Structures")

# Connecting the nodes
list_.head.next = second_node
second_node.next = third_node

# Printing the linked list
while list_.head != None:
    print(list_.head.value, end = "\n")
    list_.head = list_.head.next

Output

Python
Tutorial
Data Structures

Linked lists are important data structures. Here are a few essential operations of the linked list.

Code

# Python programs to show linked list operations 

# Creating a node class
class Node:
    def __init__(self, value):
        self.value = value
        self.next = None

# Creating a linked list class
class Linked_List:
    def __init__(self):
        self.head = None

    # Inserting a node at the beginning of the list
    def insertInBeginning(self, value):
        insertion_node = Node(value)
        insertion_node.next = self.head
        self.head = insertion_node

    # Inserting a node after a particular node
    def insertAfterNode(self, previous_node, value):
        if previous_node is None:
            print("There is no previous node. Make a new head.")
            return

        insertion_node = Node(value)
        insertion_node.next = previous_node.next
        previous_node.next = insertion_node

    # Inserting the node at the end of the list
    def insertInEnd(self, value):
        insertion_node = Node(value)

        if self.head is None:
            self.head = insertion_node
            return

        last_node = self.head
        while (last_node.next):
            last_node = last_node.next

        last_node.next = insertion_node

    # Deleting a particular node 
    def deleteANode(self, pos):

        if self.head is None:
            return

        temporary = self.head

        if pos == 0:
            self.head = temporary.next
            temporary = None
            return

        # Finding the key which is to be deleted
        for i in range(pos - 1):
            temporary = temporary.next
            if temporary is None:
                break

        # If the key is not in the list
        if temporary is None:
            return

        if temporary.next is None:
            return

        next_ = temporary.next.next

        temporary.next = None

        temporary.next = next_

    # Searching an element in the list
    def search(self, key):

        current_node = self.head

        while current_node is not None:
            if current_node.value == key:
                return True

            current_node = current_node.next

        return False

    # Sorting the linked list
    def sortList(self, head):
        current_node = head
        index_node = Node(None)

        if head is None:
            return
        else:
            while current_node is not None:
                index_node = current_node.next

                while index_node is not None:
                    if current_node.value > index_node.value:
                        current_node.value, index_node.value = index_node.value, current_node.value

                    index_node = index_node.next
                current_node = current_node.next

    # Printing the linked list
    def printLinkedList(self):
        temporary = self.head
        while (temporary):
            print(str(temporary.value) + " ", end = "")
            temporary = temporary.next


if __name__ == '__main__':

    listt = Linked_List()
    listt.insertInEnd(7)
    listt.insertInBeginning(4)
    listt.insertInBeginning(9)
    listt.insertInEnd(2)
    listt.insertAfterNode(listt.head.next, 8)

    print('Linked list:')
    listt.printLinkedList()

    print("\nAfter deleting a node:")
    listt.deleteANode(2)
    listt.printLinkedList()

    value_to_find = 4
    if listt.search(value_to_find):
        print("\n", value_to_find, "is found in the list")
    else:
        print("\n", value_to_find, " is not found in the list")

    listt.sortList(listt.head)
    print("Sorted Linked List: ")
    listt.printLinkedList()

Output

Linked list:
9 4 8 7 2 
After deleting a node:
9 4 7 2 
 4 is found in the list
Sorted Linked List: 
2 4 7 9

Stack

A stack is a linear data structure that uses either first-in and last-out (FILO) or last-in and first-out (LIFO) ordering to store objects. In a stack, an item is deleted only from one end while a new item is put to the other. Push and pop are common names for the actions of insert and deletion.

Basic Operations of Stack

We may carry out various activities on a stack using a few fundamental operations.

Push: This method adds an item to the top of the stack

Pop: This method will remove an item from the top of the stack

IsEmpty: This method checks whether the stack is empty or not.

IsFull: This method checks whether the stack is full or not.

Peek: This method will return the top element but not remove it.

Code

# Python program to show how to create a stack and implement the operations

# Creating a stack
def create():
    new_stack = []
    return new_stack

# To check if it is an empty stack
def check(stack):
    if len(stack) == 0:
        return True
    else:
        return False


# Adding new elements to the stack
def push(stack, value):
    stack.append(value)
    print("New stack after pushing: ", stack)


# Eleminating an item from the stack
def pop(stack):
    if (check(stack)):
        return "Given Stack is Empty."
    stack.pop()
    print("New stack after popping: ", stack)
    
# Peeking into the stack
def peek(stack):
    print("Last element of the stack: ", stack[-1])

# Driver code for the above methods
stack = create()
push(stack, 2)
push(stack, 5)
push(stack, 3)
push(stack, 1)
pop(stack)
peek(stack)

Output

New stack after pushing:  [2]
New stack after pushing:  [2, 5]
New stack after pushing:  [2, 5, 3]
New stack after pushing:  [2, 5, 3, 1]
New stack after popping:  [2, 5, 3]
Last element of the stack:  3

Queue

The queue, which holds objects in a First In First Out (FIFO) order, is another linear data structure similar to a stack. A queue removes items in the order that we most recently added them. Any line of users waiting to access a service where the user who arrived first is serviced first is an excellent illustration of a queue.

Operations Linked to the Queue Include:

Enqueue: Adds a piece of content to the queue. Overflow conditions are defined as when the queue is filled. The time complexity of adding an element to a queue: O(1)

Dequeue: Takes something out of the queue. The things are popped in the same sequence that the values are enqueued. It's called an underflow condition if a queue is empty. Getting the first item of the queue has an O(1) time complexity.

Rear: Obtain the last item in the queue. The time complexity to get the last item of the queue is O(1).

Code

# Python program to create a queue and implement operations of a queue

# Creating a class for queue
class Queue:
    # Initializing a queue
    def __init__(self):
        self.queue = []

    # Adding an element to the queue
    def enqueue(self, element):
        self.queue.append(element)
        print("New queue after enqueuing: ", self.queue)
        
    # Removing an element to the queue
    def dequeue(self):
        if len(self.queue) == 0:
            return None
        else: return self.queue.pop(0)
        print("New queue after dequeuing: ", self.queue)
        
    def rear(self):
        print("Last element: ", self.queue[-1])

# Drivers code for the above methods
queue = Queue()
queue.enqueue(6)
queue.enqueue(3)
queue.dequeue()
queue.enqueue(9)
queue.rear()

Output

New queue after enqueuing:  [6]
New queue after enqueuing:  [6, 3]
New queue after enqueuing:  [3, 9]
Last element:  9

Heap

The heap data structure, which is mainly designed to describe a priority queue, is provided by the Python heapq module. The characteristic of the heap data structure is that anytime an item is popped, it always returns the smallest item (min-heap). Items are always pushed or popped while the heap structure is preserved. Additionally, the heap[0] item consistently returns the smallest value. It enables O(log n)-time retrieval and insertion of the lowest value element.

Heaps often come in two varieties:

Max-Heap: Max-Heap data structure's root node's key must rank highest amongst its child's keys. The same condition should be recursively true for every sub-tree in a Binary Tree.

Min-Heap: Min-Heap's root node's key should be the least common key of all of its child's keys. The same condition should be recursively true for every sub-tree in a Binary Tree.

Code

# Python program to implement a heap data structure in Python

# Defining a method to create a heap
def heapify(array, n, j):
    largest = j
    a = 2 * j + 1
    b = 2 * j + 2 
    
    if a < n and array[j] < array[a]:
        largest = a
    
    if b < n and array[largest] < array[b]:
        largest = b
    
    if largest != j:
        array[j],array[largest] = array[largest], array[j]
        heapify(array, n, largest)

def insert_element(array, value):
    s = len(array)
    if s == 0:
        array.append(value)
    else:
        array.append(value);
        for j in range((s//2)-1, -1, -1):
            heapify(array, s, j)

def delete(array, value):
    s = len(array)
    for j in range(0, s):
        if s == array[j]:
            break
        
    array[j], array[s - 1] = array[s - 1], array[j]

    array.remove(value)
    
    for j in range((len(array)//2)-1, -1, -1):
        heapify(array, len(array), j)

# Drivers code for the above methods
heap = []

insert_element(heap, 3)
insert_element(heap, 6)
insert_element(heap, 5)
insert_element(heap, 4)
insert_element(heap, 8)

print("Heap array: ", heap)

delete(heap, 5)
print("After deleting an item: ", heap)

Output

Heap array:  [6, 4, 5, 3, 8]
After deleting an item:  [8, 4, 6, 3]

Binary Tree

A nonlinear hierarchy data structure called a tree comprises nodes and edges.

A Python tree data structure known as a binary tree allows each parent node to have a maximum of two children. A binary tree has three components at each node:

A data element
An address of the left child
An address of the right child

Code

# Python program to show how to create a binary tree and traverse it in Python

# Creating a class for a Node of the tree
class Node:
    def __init__(self, value):
        self.left = None
        self.val = value
        self.right = None

    # Method to transverse in a pre-order manner
    def traverseAsPreOrder(self):
        print(self.val, end = ' ')
        if self.left != None:
            self.left.traverseAsPreOrder()
        if self.right != None:
            self.right.traverseAsPreOrder()

    # Method to transverse in an in-order manner
    def traverseAsInOrder(self):
        if self.left != None:
            self.left.traverseAsInOrder()
        print(self.val, end = ' ')
        if self.right != None:
            self.right.traverseAsInOrder()

    # Method to transverse in an post-order manner
    def traverseAsPostOrder(self):
        if self.left != None:
            self.left.traverseAsPostOrder()
        if self.right != None:
            self.right.traverseAsPostOrder()
        print(self.val, end = ' ')

# Drivers code for the above binary tree class
root_node = Node(4)

root_node.left = Node(5)
root_node.right = Node(7)
root_node.right.left = Node(2)
root_node.right.left.right = Node(9)
root_node.left.right = Node(0)
root_node.left.left = Node(10)
root_node.left.left.right = Node(1)

# Transferring the tree
print("Pre-order traversal of the tree: ", end = "")
root_node.traverseAsPreOrder()
print("\nIn-order traversal of the tree: ", end = "")
root_node.traverseAsInOrder()
print("\nPost-order traversal of the tree: ", end = "")
root_node.traverseAsPostOrder()

Output

Pre-order traversal of the tree: 4 5 10 1 0 7 2 9 
In-order traversal of the tree: 10 1 5 0 4 2 9 7 
Post-order traversal of the tree: 1 10 0 5 9 2 7 4

Bubble Sort Algorithm

A sorting method known as bubble sort analyses two nearby items and swaps those until the desired order is achieved.

Each item of the list moves to the end of the list in each iteration. This is similar to the behaviour of the air bubbles in the liquid that come to the surface. Consequently, it is known as a bubble sort.

Code

# Python program to implement Bubble Sort Algorithm 

# Creating a method to perform bubble sort
def bubbleSort(listt):
    
  # looping over each element of the list
  for c in range(len(listt)):

    # looping over remaining elements to compare with the current element
    for n in range(0, len(listt) - c - 1):

        # comparing the two adjacent elements
        # we are sorting in descending order 
        if listt[n] < listt[n + 1]:

            # Swapping the two elements if they are not in the correct order
            temporary = listt[n]
            listt[n] = listt[n + 1]
            listt[n + 1] = temporary

# Drivers code for the above method
listt = [3, 7, 9, 2, 5, 0]

bubbleSort(listt)

print('Sorted List in Descending Order:')
print(listt)

Output

Sorted List in Descending Order:
[9, 7, 5, 3, 2, 0]

Selection Sort Algorithm

A sorting algorithm known as selection sort chooses the maximum element of an unsorted list for every iteration and inserts it at the start of the list.

Code

# Python program to implement Selection Sort 

# Defining a method to perform Selection Sort
def selectionSort(listt, size):
   
    for s in range(size):
        max_index = s

        for i in range(s + 1, size):
         
            # We are sorting in descending order
            # Selecting the maximum element of the listt
            if listt[i] > listt[max_index]:
                max_index = i
         
        # putting the maximum value at the beginning of the list
        (listt[s], listt[max_index]) = (listt[max_index], listt[s])

# Drivers code
listt = [20, 35, 29, 85, 23, 97]
size = len(listt)
selectionSort(listt, size)
print('Sorted List in Descending Order:')
print(listt)

Output

Sorted List in Descending Order:
[97, 85, 35, 29, 23, 20]

Quicksort Algorithm

An array is split into smaller arrays using the divide-and-conquer strategy in the sorting algorithm known as Quicksort (item taken from the array).

When splitting the given array, the pivot component should be set so that items of value greater than the pivot component are located on the right side, and components with a value less than the pivot value are stored on the left side.

The same method is used to divide the right and left subarrays. This procedure is repeated until only one element remains in each subarray.

The elements have already been sorted at this point. The combination of the items creates a sorted array at the end.

Code

# Python program to perform Quick Sort Algorithm

# Defining a function to search for the pivoting position
def pivot(listt, low, high):

  # selecting the right-most element as a pivot
  pivot = listt[high]

  # the greater item
  g = low - 1

  # transversing through all the elements
  for i in range(low, high):
    if listt[i] <= pivot:
      # if the value of j is smaller, we will swap it with the pointer g
      g = g + 1

      # swap the elements at g and i
      (listt[g], listt[i]) = (listt[i], listt[g])

  # swapping the pivot with the element of greater value
  (listt[g + 1], listt[high]) = (listt[high], listt[g + 1])

  # returning the position from where the pivot is done
  return g + 1

# defining a function to perform Quick Sort
def quickSortAlgo(listt, low, high):
    if low < high:

        # searching the pivot for which elements on its left are smaller and elements on its right are greater
        p = pivot(listt, low, high)

        # calling left pivot recursively
        quickSortAlgo(listt, low, p - 1)

        # calling right pivot recursively
        quickSortAlgo(listt, p + 1, high)

# Drivers code
listt = [3, 7, 2, 4, 9, 1, 0, 8]

size = len(listt)

quickSortAlgo(listt, 0, size - 1)

print('Sorted List in Ascending Order:')
print(listt)

Output

Sorted List in Ascending Order:
[0, 1, 2, 3, 4, 7, 8, 9]

Counting Sort Algorithm

A sorting method known as counting sort arranges the given array of elements according to the number of times every distinct element appears in the given array. Sorting is done by mapping the count of the elements of the array as an index of another array made by us. This array stores the count of elements.

Code

# Python program to perform Counting Sort

# Defining a function to perform Counting Sort
def countingSort(listt):
    s = len(listt)
    o = [0] * size

    # Initializing the counting list
    c = [0] * 10

    # Creating a list of counts of the elements
    for i in range(0, s):
        c[listt[i]] += 1

    # Storing the cumulative count
    for j in range(1, 10):
        c[j] += c[j - 1]

    # Finding the indices of every item of the initial list in the count list
    # placing the elements in the counting list
    j = s - 1
    while j >= 0:
        o[c[listt[j]] - 1] = listt[j]
        c[listt[j]] -= 1
        j -= 1

    # Copying the sorted list elements into the original list
    for k in range(0, s):
        listt[k] = o[k]

# Drivers code
listt = [3, 7, 9, 2, 4, 7, 2, 8]
countingSort(listt)
print("Sorted list: ")
print(listt)

Output

Sorted list: 
[2, 2, 3, 4, 7, 7, 8, 9]

Binary Search Algorithm

Binary Search is a searching algorithm for finding an element's position in a sorted array.

In this approach, the element is always searched in the middle of a portion of an array.

Code

# Python program to perform the Binary Search

# Defining a function to perform Binary Search
def binarySearch(listt, e, l, h):

    # We will use two pointers iteration to find the element
    while l <= h:

        mid_element = l + (h - l)//2

        if listt[mid_element] == e:
            return mid_element

        elif listt[mid_element] < e:
            l = mid_element + 1

        else:
            h = mid_element - 1

    return -1

# Drivers code
listt = [4, 2, 7, 6, 7, 8, 1, 9, 0, 5]
e = 7

index = binarySearch(listt, e, 0, len(listt)-1)

if index != -1:
    print("The element we searched for is present at: " + str(index))
else:
    print("Not found")

Output

The element we searched for is present at: 4

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