Data structures and algorithms in Python are two of the most fundamental concepts in computer science. They are indispensable tools for any programmer. Data structures in Python deal with the organization and storage of data in the memory while a program is processing it. On the other hand, Python algorithms refer to the detailed set of instructions that helps in the processing of data for a specific purpose.
Alternately, it can be said that different data structures are logically utilized by algorithms to work out a particular problem of data analysis. Be it a realworld problem or a typical codingrelated question, an understanding of data structures and algorithms in Python is crucial if you want to come up with an accurate solution. In this article, you will find a detailed discussion of different Python algorithms and data structures.
Learn more: The Six Most Commonly Used Data Structures in R
What are data structures in Python?
Data structures are a way of organizing and storing data; they explain the relationship between data and various logical operations that can be performed on the data. There are many ways in which data structures can be classified. One way is to categorize them into primitive and nonprimitive data types.
While the primitive data types include Integers, Float, Strings and Boolean, the nonprimitive data types are Array, List, Tuples, Dictionary, Sets and Files. Some of these nonprimitive data types, such as List, Tuples, Dictionaries and Sets, are inbuilt in Python. There is another category of data structures in Python that is userdefined; that is, users define them. These include Stack, Queue, Linked List, Tree, Graph and HashMap.
Primitive data structures
These are the basic data structures in Python containing pure and simple data values and serve as the building blocks for manipulating data. Let us talk about the four primitive types of variables in Python:
 Integers – This data type is used to represent numerical data, that is, positive or negative whole numbers without a decimal point. Say, 1, 3, or 6.
 Float – Float signifies ‘floatingpoint real number.’ It is used to represent rational numbers, usually containing a decimal point like 2.0 or 5.77. Since Python is a dynamically typed programming language, the data type that an object stores is mutable, and there is no need to state the type of your variable explicitly.
 String – This data type denotes a collection of alphabets, words or alphanumeric characters. It is created by including a series of characters within a pair of double or single quotes. To concatenate two or more Strings, the ‘+’ operation can be applied to them. Repeating, splicing, capitalizing, and retrieving are some of the other String operations in Python. Example: ‘blue,’ ‘red,’ etc.
 Boolean – This data type is useful in comparison and conditional expressions and can take up the values TRUE or FALSE.
Know more: Data Frames in Python
Inbuilt nonprimitive data structures
In contrast to primitive data structures, nonprimitive data types not only store values, but a collection of values in different formats. Let us have a look at nonprimitive data structures in Python:

 Lists – This is the most versatile data structure in Python and is written as a list of commaseparated elements enclosed within square brackets. A List can consist of both heterogeneous and homogeneous elements. Some of the methods applicable on a List are index(), append(), extend(), insert(), remove(), pop(), etc. Lists are mutable; that is, their content can be changed, keeping the identity intact.
 Tuples – Tuples are similar to Lists but are immutable. Also, unlike Lists, Tuples are declared within parentheses instead of square brackets. The feature of immutability denotes that once an element has been defined in a Tuple, it cannot be deleted, reassigned or edited. It ensures that the declared values of the data structure are not manipulated or overridden.
 Dictionaries – Dictionaries consist of keyvalue pairs. The ‘key’ identifies an item, and the ‘value’ stores the value of the item. A colon separates the key from its value. The items are separated by commas, with the entire thing enclosed within curly brackets. While keys are immutable (numbers, Strings or Tuples), the values can be of any type.
 Sets – Sets are an unordered collection of unique elements. Like Lists, Sets are mutable and written within square brackets, but no two values can be the same. Some Set methods include count(), index(), any(), all(), etc.
 Lists vs. Arrays – There is no inbuilt concept of Arrays in Python. Arrays can be imported using the NumPy package before initializing them. To know more about NumPy one can checkout our python NumPy tutorial. Lists and Arrays are mostly similar except one difference – while Arrays are collections of only homogeneous elements, Lists include both homogeneous and heterogeneous items.
Userdefined data structures in Python
Next up in our discussion on data structures and algorithms in Python is a brief overview of the different userdefined data structures:
 Stacks – Stacks are linear data structures in Python. Storing items in Stacks is based on the principles of FirstIn/LastOut (FILO) or LastIn/FirstOut (LIFO). In Stacks, the addition of a new element at one end is accompanied by the removal of an element from the same end. The operations ‘push’ and ‘pop’ are used for insertions and deletions, respectively. Other functions related to Stack are empty(), size() and top(). Stacks can be implemented using modules and data structures from the Python library – list, collections.deque, and queue.LifoQueue.
 Queue – Similar to Stacks, Queues are linear data structures. However, items are stored based on the First In/ First Out (FIFO) principle. In a Queue, the item that is least recently added is removed first. Operations related to Queue include Enqueue (adding elements), Dequeue (deleting elements), Front and Rear. Like Stacks, Queues can be implemented using modules and data structures from the Python library – list, collections.deque, and queue.
 Tree – Trees are nonlinear data structures in Python and consist of nodes connected by edges. The properties of a Tree are one node is designated the root node, other than the root, every other node has an associated parent node, and each node can have an arbitrary number of children nodes. A binary Tree data structure is one whose elements have no more than two children.
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 Linked List – A series of data elements joined together via links is termed as a Linked List in Python. It is also a linear data structure. Each data element in a Linked List is connected to another using pointer. Since the Python library does not contain Linked Lists, they are implemented using the concept of nodes. Linked Lists have an advantage over Arrays in having a dynamic size, with ease of inserting/deleting elements.
 Graph – A Graph in Python pictorially represents a set of objects, with some object pairs connected by links. Vertices represent the objects that are interconnected, and the links that join the vertices are termed as edges. The Python dictionary data type can be used to present graphs. In essence, the ‘keys’ of the dictionary represent the vertices, and the ‘values’ indicate the connections or the edges between the vertices.
 HashMaps/Hash Tables – In this type of data structure, a Hash function generates the address or index value of the data element. The index value serves as the key to the data value allowing faster access of data. As in the dictionary data type, Hash Tables have keyvalue pairs, but a hashing function generates the key.
What are algorithms in Python?
Python algorithms are a set of instructions that are executed to get the solution to a given problem. Since algorithms are not languagespecific, they can be implemented in several programming languages. No standard rules guide the writing of algorithms. They are resource and problemdependent but share some common code constructs, such as flowcontrol (ifelse) and loops (do, while, for). In the following sections, we will briefly discuss Tree Traversal, Sorting, Searching, and Graph Algorithms.
Tree Traversal Algorithms
Traversal is a process of visiting all the nodes of a Tree, starting from the root node. A Tree can be traversed in three different ways:
– Inorder traversal involves visiting the subtree on the left first, followed by the root, and then the right subtree.
– In the preorder traversal, the first to be visited is the root node, followed by the left subtree, and finally, the right subtree.
– In the postorder traversal algorithm, the left subtree is visited first, then the right subtree is visited, with the root node being visited last.
Learn more: How to Create Perfect Decision Tree
Sorting Algorithms
Sorting algorithms denote the ways to arrange data in a particular format. Sorting ensures that data searching is optimized to a high level and that the data is presented in a readable format. Let us look at the five different types of Sorting algorithms in Python:
 Bubble Sort – This algorithm is based on comparison in which there is repeated swapping of adjacent elements if they are in an incorrect order.
 Merge Sort – Based on the divide and conquer algorithm, Merge sort divides the Array into two halves, sorts them, and then combines them.
 Insertion Sort – This sorting begins with comparing and sorting the first two elements. Then, the third element is compared with the two previously sorted elements and so on.
 Shell Sort – It is a form of Insertion sort, but here, far away elements are sorted. A large sublist of a given list is sorted, and the size of the list is progressively reduced until all the elements are sorted.
 Selection Sort – This algorithm begins by finding the minimum value from a list of elements and puts it into a sorted list. The process is then repeated for each of the remaining elements in the list which is unsorted. The new element entering the sorted list is compared with its existing elements and placed at the correct position. The process goes on until all the elements are sorted.
Searching Algorithms
Searching algorithms help in checking and retrieving an element from different data structures. One type of searching algorithm applies the method of sequential search where the list is sequentially traversed, and every element is checked (linear search). In another type, the interval search, elements are searched for in sorted data structures (binary search). Let us look at some of the examples:
 Linear Search – In this algorithm, each item is sequentially searched one by one.
 Binary Search – The search interval is repeatedly divided in half. If the element to be searched is lower than the central component of the interval, the interval is narrowed to the lower half. Otherwise, it is narrowed to the upper half. The process is repeated until the value is found.
Graph Algorithms
There are two methods of traversing graphs using their edges. These are:
 Depthfirst Traversal (DFS) – In this algorithm, a graph is traversed in a depthward motion. When any iteration faces a dead end, a stack is used to go to the next vertex and start a search. DFS is implemented in Python using the set data types.
 Breadthfirst Traversal (BFS) – In this algorithm, a graph is traversed in a breadthward motion. When any iteration faces a dead end, a queue is used to go to the next vertex and start a search. BFS is implemented in Python using the queue data structure.
Algorithm Analysis
 A Priori Analysis – This represents a theoretical analysis of the algorithm before its implementation. An algorithm’s efficiency is measured by presuming that factors, such as processor speed, are constant and have no consequence on the algorithm.
 A Posterior Analysis – This refers to the empirical analysis of the algorithm after its implementation. A programming language is used to implement the selected algorithm, followed by its execution on a computer. This analysis collects statistics, such as the time and space required for the algorithm to run.
Conclusion
Whether you are a veteran in programming or new to it, you cannot ignore data structures and algorithms in Python. These concepts are crucial when you are performing operations on data, and you need to optimize data processing. While data structures help in organizing information, algorithms provide the guidelines to solve the problem of data analysis. Together, they provide a way to computer scientists for processing the information given as input data.
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