Algorithms Data Structures Presented by Abigail Atiwag Algorithms and data structures are fundamental concepts in computer science and software engineering Here s an overview of these topics Algorithms Algorithms An algorithm is a step by step procedure or set of rules used to solve a problem or perform a computation Algorithms are essential for efficient problem solving and are used in various applications such as sorting searching optimization machine learning and cryptography Algorithm Design Techniques Common algorithm design techniques include brute force divide and conquer dynamic programming greedy algorithms backtracking and graph algorithms e g breadth first search depth first search Complexity Analysis Algorithm complexity analysis involves evaluating the time and space requirements of an algorithm as a function of input size Big O notation is used to describe the worst case best case and average case performance of algorithms Sorting Algorithms Sorting algorithms arrange elements in a specific order e g ascending or descending Examples of sorting algorithms include bubble sort insertion sort selection sort merge sort quicksort heap sort and radix sort Searching Algorithms Searching algorithms find the location of a target element within a data structure Common searching algorithms include linear search binary search hash table hashing and tree based searches e g binary search tree AVL tree red black tree Graph Algorithms Graph algorithms deal with data structures that represent relationships between objects nodes through edges Graph algorithms include traversal algorithms e g depth first search breadth first search and algorithms for shortest paths e g Dijkstra s algorithm Bellman Ford algorithm minimum spanning trees e g Prim s algorithm Kruskal s algorithm and connectivity e g Tarjan s algorithm strongly connected components Data Structures Data Structures A data structure is a way of organizing and storing data to facilitate efficient operations such as insertion deletion search and retrieval Data structures are used to represent and manipulate data in computer programs Arrays Arrays are a basic data structure that stores a collection of elements of the same type in contiguous memory locations Operations on arrays include accessing elements by index updating elements and iterating through elements Linked Lists Linked lists are linear data structures consisting of nodes where each node contains a data element and a reference pointer to the next node in the sequence Linked lists can be singly linked doubly linked or circular linked Stacks A stack is a data structure that follows the Last In First Out LIFO principle It supports operations such as push add element to the top pop remove element from the top and peek view the top element without removing it Queues A queue is a data structure that follows the First In First Out FIFO principle It supports operations such as enqueue add element to the rear dequeue remove element from the front and peek view the front element without removing it Trees Trees are hierarchical data structures consisting of nodes where each node has a parent node and zero or more child nodes Common types of trees include binary trees binary search trees BST AVL trees red black trees and B trees Graphs Graphs are non linear data structures consisting of nodes vertices connected by edges They are used to represent networks relationships and interconnected data Graph data structures can be directed or undirected and may have weighted edges Hash Tables Hash tables hash maps are data structures that use a hash function to map keys to values allowing for efficient key value pair storage and retrieval Hash tables provide fast access to elements based on their keys Algorithmic Paradigms Greedy Algorithms Greedy algorithms make locally optimal choices at each step with the hope of finding a global optimum solution Examples include the greedy algorithm for activity selection and Huffman coding Divide and Conquer Divide and conquer algorithms divide a problem into smaller subproblems solve the subproblems recursively and combine the solutions to the subproblems to solve the original problem Examples include merge sort quicksort and binary search Randomized Algorithms Randomized algorithms use randomization or probability in their execution to achieve certain properties or improve efficiency Examples include randomized quicksort Monte Carlo algorithms and randomized primality testing Algorithm Analysis and Optimization Algorithm analysis involves evaluating the efficiency and performance of algorithms in terms of time complexity how long an algorithm takes to run and space complexity how much memory an algorithm requires Optimization techniques include algorithmic improvements algorithmic tuning and parallelization for faster execution Graphical Algorithms Graphical algorithms deal with algorithms used in computer graphics image processing computer vision geometric modeling and visualization Examples include rendering algorithms image processing filters geometric transformations and algorithms for 3D graphics rendering Understanding algorithms and data structures is essential for software engineers and computer scientists as they form the backbone of efficient and scalable software solutions across various domains and applications Mastery of these concepts enables developers to write optimized code solve complex problems and design robust software systems THANK YOU