Data Structures Last Updated : 15 Feb, 2023 Improve Improve Like Article Like Save Share Report Learn more about Data Structure in DSA Self Paced Course Practice Problems on all Data Structures Recent articles on Data Structures What is Data Structure: A data structure is a storage that is used to store and organize data. It is a way of arranging data on a computer so that it can be accessed and updated efficiently. A data structure is not only used for organizing the data. It is also used for processing, retrieving, and storing data. There are different basic and advanced types of data structures that are used in almost every program or software system that has been developed. So we must have good knowledge about data structures. Classification of Data Structure: Classification of Data Structure Linear data structure: Data structure in which data elements are arranged sequentially or linearly, where each element is attached to its previous and next adjacent elements, is called a linear data structure. Examples of linear data structures are array, stack, queue, linked list, etc. Static data structure: Static data structure has a fixed memory size. It is easier to access the elements in a static data structure. An example of this data structure is an array. Dynamic data structure: In dynamic data structure, the size is not fixed. It can be randomly updated during the runtime which may be considered efficient concerning the memory (space) complexity of the code. Examples of this data structure are queue, stack, etc. Non-linear data structure: Data structures where data elements are not placed sequentially or linearly are called non-linear data structures. In a non-linear data structure, we can’t traverse all the elements in a single run only. Examples of non-linear data structures are trees and graphs. For example, we can store a list of items having the same data-type using the array data structure. Array Data Structure This page contains detailed tutorials on different data structures (DS) with topic-wise problems. Introduction to Data Structures: What is Data Structure: Types, Classifications and Applications Introduction to Data Structures Common operations on various Data Structures Popular types of Data Structures: Array Linked List Stack Queue Binary Tree Binary Search Tree Heap Hashing Graph Matrix Misc Advanced Data Structure Overview: Overview of Data Structures | Set 1 (Linear Data Structures) Overview of Data Structures | Set 2 (Binary Tree, BST, Heap and Hash) Overview of Data Structures | Set 3 (Graph, Trie, Segment Tree and Suffix Tree) Abstract Data Types Linked List: Singly Linked List: 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 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 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 All Articles of Linked List Quiz on Linked List Coding Practice on Linked List Recent Articles on Linked List 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 Quiz on Stack All Articles on Stack Coding Practice on Stack Recent Articles on Stack 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? Quiz on Queue All Articles on Queue Coding Practice on Queue Recent Articles on Queue 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 Quiz on Binary Tree Quiz on Binary Tree Traversals All articles on Binary Tree Coding Practice on Binary Tree Recent Articles on Tree 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 Quiz on Binary Search Trees Quiz on Balanced Binary Search Trees All Articles on Binary Search Tree Coding Practice on Binary Search Tree Recent Articles on BST Heap: Binary Heap Why is Binary Heap Preferred over BST for Priority Queue? Binomial Heap Fibonacci Heap Heap Sort K’th Largest Element in an array Sort an almost sorted array/ Tournament Tree (Winner Tree) and Binary Heap All Articles on Heap Quiz on Heap Coding Practice on Heap Recent Articles on Heap 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 Quiz on Hashing All Articles on Hashing Coding Practice on Hashing Recent Articles on Hashing Graph: Introduction, DFS and BFS: 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 a an Undirected Graph Detect cycle in an undirected graph 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 All Articles on Graph Data Structure Quiz on Graph Quiz on Graph Traversals Quiz on Graph Shortest Paths Quiz on Graph Minimum Spanning Tree Coding Practice on Graph Recent Articles on Graph Advanced Data Structure: 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) 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) All articles on Segment Tree 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? All Articles on Trie 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 All Articles on Binary Indexed Tree 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 All Articles on Suffix Tree AVL Tree: AVL Tree | Set 1 (Insertion) AVL Tree | Set 2 (Deletion) AVL with duplicate keys Splay Tree: Splay Tree | Set 1 (Search) Splay Tree | Set 2 (Insert) B Tree: B-Tree | Set 1 (Introduction) B-Tree | Set 2 (Insert) B-Tree | Set 3 (Delete) Red-Black Tree: Red-Black Tree Introduction Red Black Tree Insertion. Red-Black Tree Deletion Program for Red Black Tree Insertion All Articles on Self-Balancing BSTs K Dimensional Tree: KD Tree (Search and Insert) K D Tree (Find Minimum) K D Tree (Delete) Others: 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. 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 All Articles on Array Coding Practice on Array Quiz on Array Coding Practice on Array Recent Articles on Array 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 All Articles on Matrix Coding Practice on Matrix Recent Articles on Matrix. Misc: Commonly Asked Data Structure Interview Questions | Set 1 A data structure for n elements and O(1) operations Expression Tree GeeksforGeeks Courses My Personal Notes arrow_drop_up Save Like Article Suggest improvement Next Introduction to Data Structures Share your thoughts in the comments Add Your Comment Please Login to comment...