Algorithm Notes for Professionals
Algorithm Notes for Professionals is a comprehensive guide that provides professionals with a detailed understanding of algorithms and their practical applications. This resource aims to provide a clear and concise overview of various algorithms, their complexit...
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,Contents
About ................................................................................................................................................................................... 1
Chapter 1: Getting started with algorithms .................................................................................................... 2
Section 1.1: A sample algorithmic problem ................................................................................................................. 2
Section 1.2: Getting Started with Simple Fizz Buzz Algorithm in Swift ...................................................................... 2
Chapter 2: Algorithm Complexity ......................................................................................................................... 5
Section 2.1: Big-Theta notation .................................................................................................................................... 5
Section 2.2: Comparison of the asymptotic notations .............................................................................................. 6
Section 2.3: Big-Omega Notation ................................................................................................................................ 6
Chapter 3: Big-O Notation ........................................................................................................................................ 8
Section 3.1: A Simple Loop ............................................................................................................................................ 9
Section 3.2: A Nested Loop ........................................................................................................................................... 9
Section 3.3: O(log n) types of Algorithms ................................................................................................................. 10
Section 3.4: An O(log n) example .............................................................................................................................. 12
Chapter 4: Trees ......................................................................................................................................................... 14
Section 4.1: Typical anary tree representation ......................................................................................................... 14
Section 4.2: Introduction ............................................................................................................................................. 14
Section 4.3: To check if two Binary trees are same or not ..................................................................................... 15
Chapter 5: Binary Search Trees .......................................................................................................................... 18
Section 5.1: Binary Search Tree - Insertion (Python) ............................................................................................... 18
Section 5.2: Binary Search Tree - Deletion(C++) ..................................................................................................... 20
Section 5.3: Lowest common ancestor in a BST ...................................................................................................... 21
Section 5.4: Binary Search Tree - Python ................................................................................................................. 22
Chapter 6: Check if a tree is BST or not .......................................................................................................... 24
Section 6.1: Algorithm to check if a given binary tree is BST .................................................................................. 24
Section 6.2: If a given input tree follows Binary search tree property or not ....................................................... 25
Chapter 7: Binary Tree traversals ..................................................................................................................... 26
Section 7.1: Level Order traversal - Implementation ............................................................................................... 26
Section 7.2: Pre-order, Inorder and Post Order traversal of a Binary Tree .......................................................... 27
Chapter 8: Lowest common ancestor of a Binary Tree ......................................................................... 29
Section 8.1: Finding lowest common ancestor ......................................................................................................... 29
Chapter 9: Graph ......................................................................................................................................................... 30
Section 9.1: Storing Graphs (Adjacency Matrix) ....................................................................................................... 30
Section 9.2: Introduction To Graph Theory .............................................................................................................. 33
Section 9.3: Storing Graphs (Adjacency List) ........................................................................................................... 37
Section 9.4: Topological Sort ..................................................................................................................................... 39
Section 9.5: Detecting a cycle in a directed graph using Depth First Traversal .................................................. 40
Section 9.6: Thorup's algorithm ................................................................................................................................. 41
Chapter 10: Graph Traversals .............................................................................................................................. 43
Section 10.1: Depth First Search traversal function .................................................................................................. 43
Chapter 11: Dijkstra’s Algorithm .......................................................................................................................... 44
Section 11.1: Dijkstra's Shortest Path Algorithm ........................................................................................................ 44
Chapter 12: A* Pathfinding ..................................................................................................................................... 49
Section 12.1: Introduction to A* ................................................................................................................................... 49
Section 12.2: A* Pathfinding through a maze with no obstacles ............................................................................. 49
Section 12.3: Solving 8-puzzle problem using A* algorithm .................................................................................... 56
,Chapter 13: A* Pathfinding Algorithm ............................................................................................................... 59
Section 13.1: Simple Example of A* Pathfinding: A maze with no obstacles .......................................................... 59
Chapter 14: Dynamic Programming ................................................................................................................. 66
Section 14.1: Edit Distance ........................................................................................................................................... 66
Section 14.2: Weighted Job Scheduling Algorithm .................................................................................................. 66
Section 14.3: Longest Common Subsequence .......................................................................................................... 70
Section 14.4: Fibonacci Number ................................................................................................................................. 71
Section 14.5: Longest Common Substring ................................................................................................................ 72
Chapter 15: Applications of Dynamic Programming ................................................................................ 73
Section 15.1: Fibonacci Numbers ................................................................................................................................ 73
Chapter 16: Kruskal's Algorithm .......................................................................................................................... 76
Section 16.1: Optimal, disjoint-set based implementation ....................................................................................... 76
Section 16.2: Simple, more detailed implementation ............................................................................................... 77
Section 16.3: Simple, disjoint-set based implementation ......................................................................................... 77
Section 16.4: Simple, high level implementation ....................................................................................................... 77
Chapter 17: Greedy Algorithms ............................................................................................................................ 79
Section 17.1: Human Coding ..................................................................................................................................... 79
Section 17.2: Activity Selection Problem .................................................................................................................... 82
Section 17.3: Change-making problem ..................................................................................................................... 84
Chapter 18: Applications of Greedy technique ............................................................................................ 86
Section 18.1: Oine Caching ....................................................................................................................................... 86
Section 18.2: Ticket automat ...................................................................................................................................... 94
Section 18.3: Interval Scheduling ................................................................................................................................ 97
Section 18.4: Minimizing Lateness ............................................................................................................................ 101
Chapter 19: Prim's Algorithm .............................................................................................................................. 105
Section 19.1: Introduction To Prim's Algorithm ....................................................................................................... 105
Chapter 20: Bellman–Ford Algorithm ............................................................................................................ 113
Section 20.1: Single Source Shortest Path Algorithm (Given there is a negative cycle in a graph) ................. 113
Section 20.2: Detecting Negative Cycle in a Graph ............................................................................................... 116
Section 20.3: Why do we need to relax all the edges at most (V-1) times .......................................................... 118
Chapter 21: Line Algorithm ................................................................................................................................... 121
Section 21.1: Bresenham Line Drawing Algorithm .................................................................................................. 121
Chapter 22: Floyd-Warshall Algorithm .......................................................................................................... 124
Section 22.1: All Pair Shortest Path Algorithm ........................................................................................................ 124
Chapter 23: Catalan Number Algorithm ....................................................................................................... 127
Section 23.1: Catalan Number Algorithm Basic Information ................................................................................ 127
Chapter 24: Multithreaded Algorithms ......................................................................................................... 129
Section 24.1: Square matrix multiplication multithread ......................................................................................... 129
Section 24.2: Multiplication matrix vector multithread .......................................................................................... 129
Section 24.3: merge-sort multithread ..................................................................................................................... 129
Chapter 25: Knuth Morris Pratt (KMP) Algorithm ..................................................................................... 131
Section 25.1: KMP-Example ...................................................................................................................................... 131
Chapter 26: Edit Distance Dynamic Algorithm .......................................................................................... 133
Section 26.1: Minimum Edits required to convert string 1 to string 2 ................................................................... 133
Chapter 27: Online algorithms ........................................................................................................................... 136
Section 27.1: Paging (Online Caching) .................................................................................................................... 137
Chapter 28: Sorting ................................................................................................................................................. 143
Section 28.1: Stability in Sorting ............................................................................................................................... 143
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