When solving realworld coding problems, employers and recruiters are looking for both runtime and resource efficiency.
Knowing which data structure best fits the current solution will increase program performance and reduce the time required to make it. For this reason, most top companies require a strong understanding of data structures and heavily test them in their coding interview.
Hereâ€™s what weâ€™ll cover today:

What are data structures?

Arrays in Python

Queues in Python

Stacks in Python

Linked lists in Python

Circular linked lists in Python

Trees in Python

Graphs in Python

Hash tables in Python

What to learn next
What are data structures?
Data structures are code structures for storing and organizing data that make it easier to modify, navigate, and access information. Data structures determine how data is collected, the functionality we can implement, and the relationships between data.
Data structures are used in almost all areas of computer science and programming, from operating systems, to frontend development, to machine learning.
Data structures help to:

Manage and utilize large datasets

Quickly search for particular data from a database

Build clear hierarchical or relational connections between data points

Simplify and speed up data processing
Data structures are vital building blocks for efficient, realworld problemsolving. Data structures are proven and optimized tools that give you an easy frame to organize your programs. After all, thereâ€™s no need for you to remake the wheel (or structure) every time you need it.
Each data structure has a task or situation it is most suited to solve. Python has 4 builtin data structures, lists, dictionaries, tuples, and sets. These builtin data structures come with default methods and behindthescenes optimizations that make them easy to use.
Most data structures in Python have modified forms of these or use the builtin structures as their backbone.

List: Arraylike structures that let you save a set of mutable objects of the same type to a variable.

Tuple: Tuples are immutable lists, meaning the elements cannot be changed. Itâ€™s declared with parenthesis instead of square brackets.

Set: Sets are unordered collections, meaning that elements are unindexed and have no set sequence. Theyâ€™re declared with curly braces.

Dictionary (dict): Similar to hashmap or hash tables in other languages, a dictionary is a collection of key/value pairs. You initialize an empty dictionary with empty curly braces and fill it with colonseparated keys and values. All keys are unique, immutable objects.
Now, letâ€™s see how we can use these structures to create all the advanced structures interviewers are looking for.
Arrays (Lists) in Python
Python does not have a builtin array type, but you can use lists for all of the same tasks. An array is a collection of values of the same type saved under the same name.
Each value in the array is called an â€śelementâ€ť and indexing that represents its position. You can access specific elements by calling the array name with the desired elementâ€™s index. You can also get the length of an array using the len() method.
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Unlike programming languages like Java that have static arrays after declaration, Pythonâ€™s arrays automatically scale up or down when elements are added/subtracted.
For example, we could use the append() method to add an additional element on the end of an existing array instead of declaring a new array.
This makes Python arrays particularly easy to use and adaptable on the fly.
cars = ["Toyota", "Tesla", "Hyundai"]
print(len(cars))
cars.append("Honda")
cars.pop(1)
for x in cars:
print(x)
Advantages:

Simple to create and use data sequences

Automatically scale to meet changing size requirements

Used to create more complex data structures
Disadvantages:

Not optimized for scientific data (unlike NumPyâ€™s array)

Can only manipulate the rightmost end of the list
Applications:

Shared storage of related values or objects, i.e. myDogs

Data collections youâ€™ll loop through

Collections of data structures, such as a list of tuples
Common arrays interview questions in Python

Remove even integers from a list

Merge two sorted lists

Find the minimum value in a list

Maximum sum sublist

Print products of all elements
Queues in Python
Queues are a linear data structure that store data in a â€śfirstin, firstoutâ€ť (FIFO) order. Unlike arrays, you cannot access elements by index and instead can only pull the next oldest element. This makes it great for ordersensitive tasks like online order processing or voicemail storage.
You can think of a queue as a line at the grocery store; the cashier does not choose who to check out next but rather processes the person who has stood in line the longest.
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We could use a Python list with append() and pop() methods to implement a queue. However, this is inefficient because lists must shift all elements by one index whenever you add a new element to the beginning.
Instead, itâ€™s best practice to use the deque class from Python's collections module. Deques are optimized for the append and pop operations. The deque implementation also allows you to create doubleended queues, which can access both sides of the queue through the popleft() and popright() methods.
from collections import deque
# Initializing a queue
q = deque()
# Adding elements to a queue
q.append('a')
q.append('b')
q.append('c')
print("Initial queue")
print(q)
# Removing elements from a queue
print("\nElements dequeued from the queue")
print(q.popleft())
print(q.popleft())
print(q.popleft())
print("\nQueue after removing elements")
print(q)
# Uncommenting q.popleft()
# will raise an IndexError
# as queue is now empty
Advantages:

Automatically orders data chronologically

Scales to meet size requirements

Timeefficient with deque class
Disadvantages:
 Can only access data on the ends
Applications:

Operations on a shared resource like a printer or CPU core

Serve as temporary storage for batch systems

Provides an easy default order for tasks of equal importance
Common queue interview questions in Python

Reverse first k elements of a queue

Implement a queue using a linked list

Implement a stack using a queue
Stacks in Python
Stacks are a sequential data structure that acts as the Lastin, Firstout (LIFO) version of queues. The last element inserted in a stack is considered at the top of the stack and is the only accessible element. To access a middle element, you must first remove enough elements to make the desired element at the top of the stack.
Many developers imagine stacks as a stack of dinner plates; you can add or remove plates to the top of the stack but must move the whole stack to place one at the bottom.
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Adding elements is known as a push, and removing elements is known as a pop. You can implement stacks in Python using the builtin list structure. With list implementation, push operations use the append() method, and pop operations use pop().
stack = []
# append() function to push
# element in the stack
stack.append('a')
stack.append('b')
stack.append('c')
print('Initial stack')
print(stack)
# pop() function to pop
# element from stack in
# LIFO order
print('\nElements popped from stack:')
print(stack.pop())
print(stack.pop())
print(stack.pop())
print('\nStack after elements are popped:')
print(stack)
# uncommenting print(stack.pop())
# will cause an IndexError
# as the stack is now empty
Advantages:

Offers LIFO data management thatâ€™s impossible with *Applications:*s or arrays

Automatic scaling and object cleanup

Simple and reliable data storage system
Disadvantages:

Stack memory is limited

Too many objects on the stack leads to a stack overflow error
Applications:

Used for making highly reactive systems

Memory management systems use stacks to handle the most recent requests first

Helpful for questions like parenthesis matching
Common stacks interview questions in Python

Implement a queue using stacks

Evaluate a Postfix expression with a stack

Next greatest element using a stack

Create a min() function using a stack
Linked lists in Python
Linked lists are a sequential collection of data that uses relational pointers on each data node to link to the next node in the list.
Unlike arrays, linked lists do not have objective positions in the list. Instead, they have relational positions based on their surrounding nodes.
The first node in a linked list is called the head node, and the final is called the tail node, which has a null pointer.
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Linked lists can be singly or doubly linked depending if each node has just a single pointer to the next node or if it also has a second pointer to the previous node.
You can think of linked lists like a chain; individual links only have a connection to their immediate neighbors but all the links together form a larger structure.
Python does not have a builtin implementation of linked lists and therefore requires that you implement a Node class to hold a data value and one or more pointers.
class Node:
def __init__(self, dataval=None):
self.dataval = dataval
self.nextval = None
class SLinkedList:
def __init__(self):
self.headval = None
list1 = SLinkedList()
list1.headval = Node("Mon")
e2 = Node("Tue")
e3 = Node("Wed")
# Link first Node to second node
list1.headval.nextval = e2
# Link second Node to third node
e2.nextval = e3
Linked lists are primarily used to create advanced data structures like graphs and trees or for tasks that require frequent addition/deletion of elements across the structure.
Advantages:

Efficient insertion and deletion of new elements

Simpler to reorganize than arrays

Useful as a starting point for advanced data structures like graphs or trees
Disadvantages:

Storage of pointers with each data point increases memory usage

Must always traverse the linked list from Head node to find a specific element
Applications:

Building block for advanced data structures

Solutions that call for frequent addition and removal of data
Common linked list interview questions in Python

Print the middle element of a given linked list

Remove duplicate elements from a sorted linked list

Check if a singly linked list is a palindrome

Merge K sorted linked lists

Find the intersection point of two linked lists
Circular linked lists in Python
The primary downside of the standard linked list is that you always have to start at the Head node. The circular linked list fixes this problem by replacing the Tail nodeâ€™s null pointer with a pointer back to the Head node. When traversing, the program will follow pointers until it reaches the node it started on.
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The advantage of this setup is that you can start at any node and traverse the whole list. It also allows you to use linked lists as a loopable structure by setting a desired number of cycles through the structure. Circular linked lists are great for processes that loop for a long time like CPU allocation in operating systems.
Advantages:

Can traverse the whole list starting from any node

Makes linked lists more suited to looping structures
Disadvantages:
 More difficult to find the Head and Tail nodes of the list without a null marker
Applications:
 Regularly looping solutions like CPU scheduling
Common circular linked list interview questions in Python

Detect loop in a linked lists

Reverse a circular linked list

Reverse circular linked list in groups of a given size
Trees in Python
Trees are another relationbased data structure, which specialize in representing hierarchical structures. Like a linked list, theyâ€™re populated with Node objects that contain a data value and one or more pointers to define its relation to immediate nodes.
Each tree has a root node that all other nodes branch off from. The root contains pointers to all elements directly below it, which are known as its child nodes. These child nodes can then have child nodes of their own. Binary trees cannot have nodes with more than two child nodes.
Any nodes on the same level are called sibling nodes. Nodes with no connected child nodes are known as leaf nodes.
The most common application of the binary tree is a binary search tree. Binary search trees excel at searching large collections of data, as the time complexity depends on the depth of the tree rather than the number of nodes.
Binary search trees have four strict rules:

The left subtree contains only nodes with elements lesser than the root.

The right subtree contains only nodes with elements greater than the root.

Left and right subtrees must also be a binary search tree. They must follow the above rules with the â€śrootâ€ť of their tree.

There can be no duplicate nodes, i.e. no two nodes can have the same value.
class Node:
def __init__(self, data): self.left = None self.right = None self.data = data def insert(self, data):
Compare the new value with the parent node
if self.data: if data < self.data: if self.left is None: self.left = Node(data) else: self.left.insert(data) elif data > self.data: if self.right is None: self.right = Node(data) else: self.right.insert(data) else: self.data = data
Print the tree
def PrintTree(self): if self.left: self.left.PrintTree() print( self.data), if self.right: self.right.PrintTree()
Use the insert method to add nodes
root = Node(12) root.insert(6) root.insert(14) root.insert(3)
root.PrintTree()
Advantages:

Good for representing hierarchical relationships

Dynamic size, great at scale

Quick insert and delete operations

In a binary search tree, inserted nodes are sequenced immediately.

Binary search trees are efficient at searches; length is only O(height).
Disadvantages:
Time expensive, O(logn), to modify or â€śbalanceâ€ť trees or retrieve elements from a known location

Child nodes hold no information on their parent node and can be hard to traverse backward

Only works for lists that are sorted. Unsorted data degrades into linear search.
Applications:

Great for storing hierarchical data such as a file location

Used to implement top searching and sorting algorithms like binary search trees and binary heaps
Common tree interview questions in Python

Check if two binary trees are identical

Implement level order traversal of a binary tree

Print the perimeter of a binary search tree

Sum all nodes along a path

Connect all siblings of a binary tree
Graphs in Python
Graphs are a data structure used to represent a visual of relationships between data vertices (the Nodes of a graph). The links that connect vertices together are called edges.
Edges define which vertices are connected but do not indicate a direction flow between them. Each vertex has connections to other vertices which are saved on the vertex as a commaseparated list.
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There are also special graphs called directed graphs that define a direction of the relationship, similar to a linked list. Directed graphs are helpful when modeling oneway relationships or a flowchartlike structure.
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Theyâ€™re primarily used to convey visual webstructure networks in code form. These structures can model many different types of relationships like hierarchies, branching structures, or simply be an unordered relational web. The versatility and intuitiveness of graphs makes them a favorite for data science.
When written in plain text, graphs have a list of vertices and edges:
V = {a, b, c, d, e}
E = {ab, ac, bd, cd, de}
In Python, graphs are best implemented using a dictionary with the name of each vertex as a key and the edges list as the values.
# Create the dictionary with graph elements
graph = { "a" : ["b","c"],
"b" : ["a", "d"],
"c" : ["a", "d"],
"d" : ["e"],
"e" : ["d"]
}
# Print the graph
print(graph)
Advantages:

Quickly convey visual information through code

Usable for modeling a wide range of realworld problems

Simple to learn the syntax
Disadvantages:

Vertex links are difficult to understand in large graphs

Time expensive to parse data from a graph
Applications:

Excellent for modeling networks or weblike structures

Used to model social network sites like Facebook
Common graph interview questions in Python

Detect cycle in a directed graph

Find a â€śMother Vertexâ€ť in a directed graph

Count the number of edges in an undirected graph

Check if a path exists between two vertices

Find the shortest path between two vertices
Hash tables in Python
Hash tables are a complex data structure capable of storing large amounts of information and retrieving specific elements efficiently.
This data structure uses key/value pairs, where the key is the name of the desired element and the value is the data stored under that name.
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Each input key goes through a hash function that converts it from its starting form into an integer value, called a hash. Hash functions must always produce the same hash from the same input, must compute quickly, and produce fixedlength values. Python includes a builtin hash() function that speeds up implementation.
The table then uses the hash to find the general location of the desired value, called a storage bucket. The program then only has to search this subgroup for the desired value rather than the entire data pool.
Beyond this general framework, hash tables can be very different depending on the application. Some may allow keys from different data types, while some may have differently setup buckets or different hash functions.
Here is an example of a hash table in Python code:
import pprint
class Hashtable:
def __init__(self, elements):
self.bucket_size = len(elements)
self.buckets = [[] for i in range(self.bucket_size)]
self._assign_buckets(elements)
def _assign_buckets(self, elements):
for key, value in elements: #calculates the hash of each key
hashed_value = hash(key)
index = hashed_value % self.bucket_size # positions the element in the bucket using hash
self.buckets[index].append((key, value)) #adds a tuple in the bucket
def get_value(self, input_key):
hashed_value = hash(input_key)
index = hashed_value % self.bucket_size
bucket = self.buckets[index]
for key, value in bucket:
if key == input_key:
return(value)
return None
def __str__(self):
return pprint.pformat(self.buckets) # pformat returns a printable representation of the object
if __name__ == "__main__":
capitals = [
('France', 'Paris'),
('United States', 'Washington D.C.'),
('Italy', 'Rome'),
('Canada', 'Ottawa')
]
hashtable = Hashtable(capitals)
print(hashtable)
print(f"The capital of Italy is {hashtable.get_value('Italy')}")
Advantages:

Can covert keys in any form to integer indices

Extremely effective for large data sets

Very effective search function

Constant number of steps for each search and constant efficiency for adding or deleting elements

Optimized in Python 3
Disadvantages:

Hashes must be unique, two keys converting to the same hash causes a collision error

Collision errors require a full overhaul of the hash function

Difficult to build for beginners
Applications:

Used for large, frequentlysearched databases

Retrieval systems that use input keys
Common hash table interview questions in Python

Build a hash table from scratch (without builtin functions)

Word formation using a hash table

Find two numbers that add up to â€śkâ€ť

Implement open addressing for collision handling

Detect if a list is cyclical using a hash table
What to learn next
There are dozens of interview questions and formats for each of these 8 data structures. The best way to prepare yourself for the interview process is to keep trying handson practice problems.
Hereâ€™s some beginner questions to get you started:

Reverse a string in Python

Check if a Python string contains another substring

Implement breadthfirst search of a binary tree

Merge two sorted lists

Find the first nonrepeating element in a list of integers
Happy learning!