Data Structures Tutorial

Data structures are essential components that help organize and store data efficiently in computer memory. They provide a way to manage and manipulate data effectively, enabling faster access, insertion, and deletion operations.

Common data structures include arrays, linked lists, stacks, queues, trees, and graphs , each serving specific purposes based on the requirements of the problem. Understanding data structures is fundamental for designing efficient algorithms and optimizing software performance.

What is a Data Structure?

A data structure is a way of organizing and storing data in a computer so that it can be accessed and used efficiently. It defines the relationship between the data and the operations that can be performed on the data

Why are Data Structures Important?

Data structures are essential for the following reasons:

• Efficient Data Management: They enable efficient storage and retrieval of data, reducing processing time and improving performance.
• Data Organization: They organize data in a logical manner, making it easier to understand and access.
• Data Abstraction: They hide the implementation details of data storage, allowing programmers to focus on the logical aspects of data manipulation.
• Reusability: Common data structures can be reused in multiple applications, saving time and effort in development.
• Algorithm Optimization: The choice of the appropriate data structure can significantly impact the efficiency of algorithms that operate on the data.

Classification of Data Structures

Data structures can be classified into two main categories:

• Linear Data Structures: These structures store data in a sequential order this allowing for easy insertion and deletion operations. Examples include arrays, linked lists, and queues.
• Non-Linear Data Structures: These structures store data in a hierarchical or interconnected manner this allowing for more complex relationships between data elements. Examples include trees, graphs, and hash tables.

Types of Data Structures

Basically, data structures are divided into two categories:

Linear Data Structures:

• Array: A collection of elements of the same type stored in contiguous memory locations.
• Linked List: A collection of elements linked together by pointers, allowing for dynamic insertion and deletion.
• Queue: A First-In-First-Out (FIFO) structure where elements are added at the end and removed from the beginning.
• Stack: A Last-In-First-Out (LIFO) structure where elements are added and removed from the top.

Non-Linear Data Structures:

• Tree: A hierarchical structure where each node can have multiple child nodes.
• Graph: A collection of nodes connected by edges, representing relationships between data elements.
• Hash Table: A data structure that uses a hash function to map keys to values, allowing for fast lookup and insertion.

Applications of Data Structures

Data structures are widely used in various applications, including:

• Database Management Systems: To store and manage large amounts of structured data.
• Operating Systems: To manage memory, processes, and files.
• Compiler Design: To represent source code and intermediate code.
• Artificial Intelligence: To represent knowledge and perform reasoning.
• Graphics and Multimedia: To store and process images, videos, and audio data.

Learn Basics of Data Structure:

• Introduction to Linear Data Structures
• Introduction to Hierarchical Data Structure
• Overview of Data Structures | Set 3 (Graph, Trie, Segment Tree and Suffix Tree)
• Abstract Data Types

Most Popular Data Structures:

Below are some most popular Data Structure:

1. Array:

Array is a linear data structure that stores a collection of elements of the same data type. Elements are allocated contiguous memory, allowing for constant-time access. Each element has a unique index number.

Important articles on Array:

• Search, insert and delete in an unsorted array
• Search, insert and delete in a sorted array
• Write a program to reverse an array
• Leaders in an array
• Given an array A[] and a number x, check for pair in A[] with sum as x
• Majority Element
• Find the Number Occurring Odd Number of Times
• Largest Sum Contiguous Subarray
• Find the Missing Number
• Search an element in a sorted and pivoted array
• Merge an array of size n into another array of size m+n
• Median of two sorted arrays
• Program for array rotation
• Reversal algorithm for array rotation
• Block swap algorithm for array rotation
• Maximum sum such that no two elements are adjacent
• Sort elements by frequency | Set 1
• Count Inversions in an array

Related articles on Array:

• All Articles on Array
• Coding Practice on Array
• Quiz on Array
• Coding Practice on Array
• Recent Articles on Array

2. Matrix:

A matrix is a two-dimensional array of elements, arranged in rows and columns. It is represented as a rectangular grid, with each element at the intersection of a row and column.

Important articles on Matrix:

• Search in a row wise and column wise sorted matrix
• Print a given matrix in spiral form
• A Boolean Matrix Question
• Print unique rows in a given boolean matrix
• Maximum size square sub-matrix with all 1s
• Print unique rows in a given boolean matrix
• Inplace M x N size matrix transpose | Updated
• Dynamic Programming | Set 27 (Maximum sum rectangle in a 2D matrix)
• Strassen’s Matrix Multiplication
• Create a matrix with alternating rectangles of O and X
• Print all elements in sorted order from row and column wise sorted matrix
• Given an n x n square matrix, find sum of all sub-squares of size k x k
• Count number of islands where every island is row-wise and column-wise separated
• Find a common element in all rows of a given row-wise sorted matrix

Related articles on Matrix:

• All Articles on Matrix
• Coding Practice on Matrix
• Recent Articles on Matrix.

3. Linked List:

A linear data structure where elements are stored in nodes linked together by pointers. Each node contains the data and a pointer to the next node in the list. Linked lists are efficient for inserting and deleting elements, but they can be slower for accessing elements than arrays.

Types of Linked List:

a) Singly Linked List: Each node points to the next node in the list.

Important articles on Singly Linked Lis:

• Introduction to Linked List
• Linked List vs Array
• Linked List Insertion
• Linked List Deletion (Deleting a given key)
• Linked List Deletion (Deleting a key at given position)
• A Programmer’s approach of looking at Array vs. Linked List
• Find Length of a Linked List (Iterative and Recursive)
• How to write C functions that modify head pointer of a Linked List?
• Swap nodes in a linked list without swapping data
• Reverse a linked list
• Merge two sorted linked lists
• Merge Sort for Linked Lists
• Reverse a Linked List in groups of given size
• Detect and Remove Loop in a Linked List
• Add two numbers represented by linked lists | Set 1
• Rotate a Linked List
• Generic Linked List in C

b) Circular Linked List: The last node points back to the first node, forming a circular loop.

Important articles on Circular Linked List:

• Circular Linked List Introduction and Applications,
• Circular Singly Linked List Insertion
• Circular Linked List Traversal
• Split a Circular Linked List into two halves
• Sorted insert for circular linked list

c) Doubly Linked List: Each node points to both the next and previous nodes in the list.

Important articles on Doubly Linked List:

• Doubly Linked List Introduction and Insertion
• Delete a node in a Doubly Linked List
• Reverse a Doubly Linked List
• The Great Tree-List Recursion Problem.
• QuickSort on Doubly Linked List
• Merge Sort for Doubly Linked List

Related articles on Linked List:

• All Articles of Linked List
• Coding Practice on Linked List
• Recent Articles on Linked List

4. Stack:

Stack is a linear data structure that follows a particular order in which the operations are performed. The order may be LIFO(Last In First Out) or FILO(First In Last Out). LIFO implies that the element that is inserted last, comes out first and FILO implies that the element that is inserted first, comes out last.

Important articles on Stack:

• Introduction to Stack
• Infix to Postfix Conversion using Stack
• Evaluation of Postfix Expression
• Reverse a String using Stack
• Implement two stacks in an array
• Check for balanced parentheses in an expression
• Next Greater Element
• Reverse a stack using recursion
• Sort a stack using recursion
• The Stock Span Problem
• Design and Implement Special Stack Data Structure
• Implement Stack using Queues
• Design a stack with operations on middle element
• How to efficiently implement k stacks in a single array?
• Sort a stack using recursion

Related articles on Stack:

• All Articles on Stack
• Coding Practice on Stack
• Recent Articles on Stack

5. Queue:

A Queue Data Structure is a fundamental concept in computer science used for storing and managing data in a specific order. It follows the principle of “First in, First out” (FIFO), where the first element added to the queue is the first one to be removed

Important articles on Queue:

• Queue Introduction and Array Implementation
• Linked List Implementation of Queue
• Applications of Queue Data Structure
• Priority Queue Introduction
• Deque (Introduction and Applications)
• Implementation of Deque using circular array
• Implement Queue using Stacks
• Find the first circular tour that visits all petrol pumps
• Maximum of all subarrays of size k
• An Interesting Method to Generate Binary Numbers from 1 to n
• How to efficiently implement k Queues in a single array?

Related articles on Queue:

• All Articles on Queue
• Coding Practice on Queue
• Recent Articles on Queue

6. Binary Tree:

Binary Tree is a hierarchical data structure where each node has at most two child nodes, referred to as the left child and the right child. Binary trees are mostly used to represent hierarchical data, such as file systems or family trees.

Important articles on Binary Tree:

• Binary Tree Introduction
• Binary Tree Properties
• Types of Binary Tree
• Handshaking Lemma and Interesting Tree Properties
• Enumeration of Binary Tree
• Applications of tree data structure
• Tree Traversals
• BFS vs DFS for Binary Tree
• Level Order Tree Traversal
• Diameter of a Binary Tree
• Inorder Tree Traversal without Recursion
• Inorder Tree Traversal without recursion and without stack!
• Threaded Binary Tree
• Maximum Depth or Height of a Tree
• If you are given two traversal sequences, can you construct the binary tree?
• Clone a Binary Tree with Random Pointers
• Construct Tree from given Inorder and Preorder traversals
• Maximum width of a binary tree
• Print nodes at k distance from root
• Print Ancestors of a given node in Binary Tree
• Check if a binary tree is subtree of another binary tree
• Connect nodes at same level

Related articles on Binary Tree:

• All articles on Binary Tree
• Coding Practice on Binary Tree
• Recent Articles on Tree

7. Binary Search Tree:

A Binary Search Tree is a data structure used for storing data in a sorted manner. Each node in a Binary Search Tree has at most two children, a left child and a right child, with the left child containing values less than the parent node and the right child containing values greater than the parent node. This hierarchical structure allows for efficient searching, insertion, and deletion operations on the data stored in the tree.

Important articles on Binary Search Tree:

• Search and Insert in BST
• Deletion from BST
• Minimum value in a Binary Search Tree
• Inorder predecessor and successor for a given key in BST
• Check if a binary tree is BST or not
• Lowest Common Ancestor in a Binary Search Tree.
• Inorder Successor in Binary Search Tree
• Find k-th smallest element in BST (Order Statistics in BST)
• Merge two BSTs with limited extra space
• Two nodes of a BST are swapped, correct the BST
• Floor and Ceil from a BST
• In-place conversion of Sorted DLL to Balanced BST
• Find a pair with given sum in a Balanced BST
• Total number of possible Binary Search Trees with n keys
• Merge Two Balanced Binary Search Trees
• Binary Tree to Binary Search Tree Conversion

Related articles on Binary Search Tree:

• All Articles on Binary Search Tree
• Coding Practice on Binary Search Tree
• Recent Articles on BST

8. Heap:

A Heap is a complete binary tree data structure that satisfies the heap property: for every node, the value of its children is less than or equal to its own value. Heaps are usually used to implement priority queues, where the smallest (or largest) element is always at the root of the tree.

Important articles on Heap:

• Binary Heap
• Why is Binary Heap Preferred over BST for Priority Queue?
• Heap Sort
• K’th Largest Element in an array
• Sort an almost sorted array
• Binomial Heap
• Fibonacci Heap
• Tournament Tree (Winner Tree) and Binary Heap

Related articles on Heap:

• All Articles on Heap
• Coding Practice on Heap
• Recent Articles on Heap

9. Hashing:

Hashing is a technique that generates a fixed-size output (hash value) from an input of variable size using mathematical formulas called hash functions. Hashing is used to determine an index or location for storing an item in a data structure, allowing for efficient retrieval and insertion.

Important articles on Hashing:

• Hashing Introduction
• Separate Chaining for Collision Handling
• Open Addressing for Collision Handling
• Print a Binary Tree in Vertical Order
• Find whether an array is subset of another array
• Union and Intersection of two Linked Lists
• Find a pair with given sum
• Check if a given array contains duplicate elements within k distance from each other
• Find Itinerary from a given list of tickets
• Find number of Employees Under every Employee

Related articles on Hashing:

• All Articles on Hashing
• Coding Practice on Hashing
• Recent Articles on Hashing

10. Graph:

Graph is a collection of nodes connected by edges. Graphs are mostly used to represent networks, such as social networks or transportation networks.

Important articles on Graph:

• Graph and its representations
• Breadth First Traversal for a Graph
• Depth First Traversal for a Graph
• Applications of Depth First Search
• Applications of Breadth First Traversal
• Detect Cycle in a Directed Graph
• Detect Cycle in Graph using DSU
• Detect cycle in an Undirected Graph using DFS
• Longest Path in a Directed Acyclic Graph
• Topological Sorting
• Check whether a given graph is Bipartite or not
• Snake and Ladder Problem
• Minimize Cash Flow among a given set of friends who have borrowed money from each other
• Boggle (Find all possible words in a board of characters)
• Assign directions to edges so that the directed graph remains acyclic

Related articles on Graph:

• All Articles on Graph Data Structure
• Coding Practice on Graph
• Recent Articles on Graph

Advanced Data Structure:

Below are some advance Data Structure:

1. Advanced Lists:

Advanced Lists is a data structure that extends the functionality of a standard list. Advanced lists may support additional operations, such as finding the minimum or maximum element in the list, or rotating the list.

Important articles on Advanced Lists:

• Memory efficient doubly linked list
• XOR Linked List – A Memory Efficient Doubly Linked List | Set 1
• XOR Linked List – A Memory Efficient Doubly Linked List | Set 2
• Skip List | Set 1 (Introduction)
• Self Organizing List | Set 1 (Introduction)
• Unrolled Linked List | Set 1 (Introduction)

2. Segment Tree:

Segment Tree is a tree data structure that allows for efficient range queries on an array. Each node in the segment tree represents a range of elements in the array, and the value stored in the node is some aggregate value of the elements in that range.

Important articles on Segment Tree:

• Segment Tree | Set 1 (Sum of given range)
• Segment Tree | Set 2 (Range Minimum Query)
• Lazy Propagation in Segment Tree
• Persistent Segment Tree | Set 1 (Introduction)

Related articles on Segment Tree:

• All articles on Segment Tree

3. Trie:

Trie is a tree-like data structure that is used to store strings. Each node in the trie represents a prefix of a string, and the children of a node represent the different characters that can follow that prefix. Tries are often used for efficient string matching and searching.

Important articles on Trie:

• Trie | (Insert and Search)
• Trie | (Delete)
• Longest prefix matching – A Trie based solution in Java
• Print unique rows in a given boolean matrix
• How to Implement Reverse DNS Look Up Cache?
• How to Implement Forward DNS Look Up Cache?

Related articles on Trie:

• All Articles on Trie

4. Binary Indexed Tree:

Binary Indexed Tree is a data structure that allows for efficient range queries and updates on an array. Binary indexed trees are often used to compute prefix sums or to solve range query problems.

Important articles on Binary Indexed Tree:

• Binary Indexed Tree
• Two Dimensional Binary Indexed Tree or Fenwick Tree
• Binary Indexed Tree : Range Updates and Point Queries
• Binary Indexed Tree : Range Update and Range Queries

Related articles on Binary Indexed Tree:

• All Articles on Binary Indexed Tree

5. Suffix Array and Suffix Tree:

Suffix Array and Suffix Tree is a data structures that are used to efficiently search for patterns within a string. Suffix arrays and suffix trees are mostly used in bioinformatics and text processing applications.

Important articles on Suffix Array and Suffix Tree:

• Suffix Array Introduction
• Suffix Array nLogn Algorithm
• kasai’s Algorithm for Construction of LCP array from Suffix Array
• Suffix Tree Introduction
• Ukkonen’s Suffix Tree Construction – Part 1
• Ukkonen’s Suffix Tree Construction – Part 2
• Ukkonen’s Suffix Tree Construction – Part 3
• Ukkonen’s Suffix Tree Construction – Part 4,
• Ukkonen’s Suffix Tree Construction – Part 5
• Ukkonen’s Suffix Tree Construction – Part 6
• Generalized Suffix Tree
• Build Linear Time Suffix Array using Suffix Tree
• Substring Check
• Searching All Patterns
• Longest Repeated Substring,
• Longest Common Substring, Longest Palindromic Substring

Related articles on Suffix Array and Suffix Tree:

• All Articles on Suffix Tree

6. AVL Tree:

AVL tree is a self-balancing binary search tree that maintains a balanced height. AVL trees are mostly used when it is important to have efficient search and insertion operations.

Important articles on AVL Tree:

• AVL Tree | Set 1 (Insertion)
• AVL Tree | Set 2 (Deletion)
• AVL with duplicate keys

7. Splay Tree:

Splay Tree is a self-balancing binary search tree that moves frequently accessed nodes to the root of the tree. Splay trees are mostly used when it is important to have fast access to recently accessed data.

Important articles on Splay Tree:

• Splay Tree | Set 1 (Search)
• Splay Tree | Set 2 (Insert)

8. B Tree:

B Tree is a balanced tree data structure that is used to store data on disk. B trees are mostly used in database systems to efficiently store and retrieve large amounts of data.

Important articles on B Tree:

• B-Tree | Set 1 (Introduction)
• B-Tree | Set 2 (Insert)
• B-Tree | Set 3 (Delete)

9. Red-Black Tree:

Red-Black Tree is a self-balancing binary search tree that maintains a balance between the number of black and red nodes. Red-black trees are mostly used when it is important to have efficient search and insertion operations.

Important articles on Red-Black Tree:

• Red-Black Tree Introduction
• Red Black Tree Insertion.
• Red-Black Tree Deletion
• Program for Red Black Tree Insertion

Related articles on Red-Black Tree:

• All Articles on Self-Balancing BSTs

10. K Dimensional Tree:

K Dimensional Tree is a tree data structure that is used to store data in a multidimensional space. K dimensional trees are mostly used for efficient range queries and nearest neighbor searches.

Important articles on K Dimensional Tree:

• KD Tree (Search and Insert)
• K D Tree (Find Minimum)
• K D Tree (Delete)

Others Data Structure:

• Treap (A Randomized Binary Search Tree)
• Ternary Search Tree
• Interval Tree
• Implement LRU Cache
• Sort numbers stored on different machines
• Find the k most frequent words from a file
• Given a sequence of words, print all anagrams together
• Tournament Tree (Winner Tree) and Binary Heap
• Decision Trees – Fake (Counterfeit) Coin Puzzle (12 Coin Puzzle)
• Spaghetti Stack
• Data Structure for Dictionary and Spell Checker?
• Cartesian Tree
• Cartesian Tree Sorting
• Sparse Set
• Centroid Decomposition of Tree
• Gomory-Hu Tree
• Recent Articles on Advanced Data Structures.

Misc:

• Commonly Asked Data Structure Interview Questions | Set 1
• A data structure for n elements and O(1) operations
• Expression Tree