Data Structures and Algorithms

Welcome to the Data Structures and Algorithms repository! This repository is dedicated to providing a comprehensive understanding of various data structures and algorithms, essential for coding interviews and competitive programming.

Table of Contents

• Introduction
• Big O Notation
• Data Structures
  • Arrays
  • Linked Lists
  • Stacks
  • Queues
  • Trees
  • Heaps
  • Graphs
  • Hash Tables
• Algorithms
  • Sorting Algorithms
  • Search Algorithms
  • Dynamic Programming
  • Greedy Algorithms
  • Backtracking
  • Divide and Conquer
• Resources

Introduction

Data structures and algorithms form the fundamental building blocks of computer science. Understanding and applying these concepts is crucial for solving complex problems efficiently.

Big O Notation

Big O notation is used to describe the performance and complexity of algorithms. It provides insights into the worst-case scenario of an algorithm's runtime or space requirements.

Examples:

• O(1): Constant time
• O(n): Linear time
• O(log n): Logarithmic time
• O(n^2): Quadratic time

Data Structures

Arrays

• Definition: A collection of elements identified by their index.
• Operations: Access, insertion, deletion, traversal.

Linked Lists

• Definition: A linear data structure where elements are linked using pointers.
• Types: Singly linked list, doubly linked list, circular linked list.

Stacks

• Definition: A linear data structure that follows the Last In, First Out (LIFO) principle.
• Operations: Push, pop, peek.

Queues

• Definition: A linear data structure that follows the First In, First Out (FIFO) principle.
• Types: Simple queue, circular queue, priority queue.

Trees

• Definition: A hierarchical data structure with a root node and child nodes.
• Types: Binary tree, binary search tree, AVL tree, red-black tree.

Heaps

• Definition: A special tree-based data structure that satisfies the heap property.
• Types: Max heap, min heap.

Graphs

• Definition: A collection of nodes connected by edges.
• Types: Directed graph, undirected graph, weighted graph.

Hash Tables

• Definition: A data structure that stores key-value pairs.
• Operations: Insert, delete, search.

Algorithms

Sorting Algorithms

• Bubble Sort
• Selection Sort
• Insertion Sort
• Merge Sort
• Quick Sort
• Heap Sort

Search Algorithms

• Linear Search
• Binary Search

Dynamic Programming

• Concept: Solving problems by breaking them down into subproblems and storing the results.
• Examples: Fibonacci sequence, knapsack problem.

Greedy Algorithms

• Concept: Making the locally optimal choice at each stage.
• Examples: Dijkstra's algorithm, Huffman coding.

Backtracking

• Concept: Trying out all possibilities to find a solution.
• Examples: N-Queens problem, sudoku solver.

Divide and Conquer

• Concept: Breaking a problem into smaller subproblems, solving each subproblem, and combining the solutions.
• Examples: Merge sort, quick sort.

Resources

Here are some of the best resources to learn more about data structures and algorithms:

• GeeksforGeeks
• LeetCode
• HackerRank
• Coursera Data Structures & Algorithms Specialization
• MIT OpenCourseWare

Happy Coding! 🌟