Algorithms
Algorithms
Notes for Professionals
Notes for Professionals
200+ pages
of professional hints and tricks
Disclaimer
GoalKicker.com This is an unocial free book created for educational purposes and is
not aliated with ocial Algorithms group(s) or company(s).
Free Programming Books All trademarks and registered trademarks are
the property of their respective owners
,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
, Chapter 29: Bubble Sort ........................................................................................................................................ 144
Section 29.1: Bubble Sort .......................................................................................................................................... 144
Section 29.2: Implementation in C & C++ ............................................................................................................... 144
Section 29.3: Implementation in C# ........................................................................................................................ 145
Section 29.4: Python Implementation ..................................................................................................................... 146
Section 29.5: Implementation in Java ..................................................................................................................... 147
Section 29.6: Implementation in Javascript ........................................................................................................... 147
Chapter 30: Merge Sort ......................................................................................................................................... 149
Section 30.1: Merge Sort Basics ............................................................................................................................... 149
Section 30.2: Merge Sort Implementation in Go .................................................................................................... 150
Section 30.3: Merge Sort Implementation in C & C# ............................................................................................. 150
Section 30.4: Merge Sort Implementation in Java ................................................................................................ 152
Section 30.5: Merge Sort Implementation in Python ............................................................................................. 153
Section 30.6: Bottoms-up Java Implementation ................................................................................................... 154
Chapter 31: Insertion Sort ..................................................................................................................................... 156
Section 31.1: Haskell Implementation ....................................................................................................................... 156
Chapter 32: Bucket Sort ........................................................................................................................................ 157
Section 32.1: C# Implementation ............................................................................................................................. 157
Chapter 33: Quicksort ............................................................................................................................................. 158
Section 33.1: Quicksort Basics .................................................................................................................................. 158
Section 33.2: Quicksort in Python ............................................................................................................................ 160
Section 33.3: Lomuto partition java implementation ............................................................................................. 160
Chapter 34: Counting Sort ................................................................................................................................... 162
Section 34.1: Counting Sort Basic Information ....................................................................................................... 162
Section 34.2: Psuedocode Implementation ............................................................................................................ 162
Chapter 35: Heap Sort ........................................................................................................................................... 164
Section 35.1: C# Implementation ............................................................................................................................. 164
Section 35.2: Heap Sort Basic Information ............................................................................................................. 164
Chapter 36: Cycle Sort ........................................................................................................................................... 166
Section 36.1: Pseudocode Implementation ............................................................................................................. 166
Chapter 37: Odd-Even Sort .................................................................................................................................. 167
Section 37.1: Odd-Even Sort Basic Information ...................................................................................................... 167
Chapter 38: Selection Sort ................................................................................................................................... 170
Section 38.1: Elixir Implementation .......................................................................................................................... 170
Section 38.2: Selection Sort Basic Information ...................................................................................................... 170
Section 38.3: Implementation of Selection sort in C# ............................................................................................ 172
Chapter 39: Searching ............................................................................................................................................ 174
Section 39.1: Binary Search ...................................................................................................................................... 174
Section 39.2: Rabin Karp .......................................................................................................................................... 175
Section 39.3: Analysis of Linear search (Worst, Average and Best Cases) ........................................................ 176
Section 39.4: Binary Search: On Sorted Numbers ................................................................................................. 178
Section 39.5: Linear search ...................................................................................................................................... 178
Chapter 40: Substring Search ........................................................................................................................... 180
Section 40.1: Introduction To Knuth-Morris-Pratt (KMP) Algorithm ..................................................................... 180
Section 40.2: Introduction to Rabin-Karp Algorithm ............................................................................................. 183
Section 40.3: Python Implementation of KMP algorithm ...................................................................................... 186
Section 40.4: KMP Algorithm in C ............................................................................................................................ 187
Chapter 41: Breadth-First Search .................................................................................................................... 190
Algorithms
Notes for Professionals
Notes for Professionals
200+ pages
of professional hints and tricks
Disclaimer
GoalKicker.com This is an unocial free book created for educational purposes and is
not aliated with ocial Algorithms group(s) or company(s).
Free Programming Books All trademarks and registered trademarks are
the property of their respective owners
,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
, Chapter 29: Bubble Sort ........................................................................................................................................ 144
Section 29.1: Bubble Sort .......................................................................................................................................... 144
Section 29.2: Implementation in C & C++ ............................................................................................................... 144
Section 29.3: Implementation in C# ........................................................................................................................ 145
Section 29.4: Python Implementation ..................................................................................................................... 146
Section 29.5: Implementation in Java ..................................................................................................................... 147
Section 29.6: Implementation in Javascript ........................................................................................................... 147
Chapter 30: Merge Sort ......................................................................................................................................... 149
Section 30.1: Merge Sort Basics ............................................................................................................................... 149
Section 30.2: Merge Sort Implementation in Go .................................................................................................... 150
Section 30.3: Merge Sort Implementation in C & C# ............................................................................................. 150
Section 30.4: Merge Sort Implementation in Java ................................................................................................ 152
Section 30.5: Merge Sort Implementation in Python ............................................................................................. 153
Section 30.6: Bottoms-up Java Implementation ................................................................................................... 154
Chapter 31: Insertion Sort ..................................................................................................................................... 156
Section 31.1: Haskell Implementation ....................................................................................................................... 156
Chapter 32: Bucket Sort ........................................................................................................................................ 157
Section 32.1: C# Implementation ............................................................................................................................. 157
Chapter 33: Quicksort ............................................................................................................................................. 158
Section 33.1: Quicksort Basics .................................................................................................................................. 158
Section 33.2: Quicksort in Python ............................................................................................................................ 160
Section 33.3: Lomuto partition java implementation ............................................................................................. 160
Chapter 34: Counting Sort ................................................................................................................................... 162
Section 34.1: Counting Sort Basic Information ....................................................................................................... 162
Section 34.2: Psuedocode Implementation ............................................................................................................ 162
Chapter 35: Heap Sort ........................................................................................................................................... 164
Section 35.1: C# Implementation ............................................................................................................................. 164
Section 35.2: Heap Sort Basic Information ............................................................................................................. 164
Chapter 36: Cycle Sort ........................................................................................................................................... 166
Section 36.1: Pseudocode Implementation ............................................................................................................. 166
Chapter 37: Odd-Even Sort .................................................................................................................................. 167
Section 37.1: Odd-Even Sort Basic Information ...................................................................................................... 167
Chapter 38: Selection Sort ................................................................................................................................... 170
Section 38.1: Elixir Implementation .......................................................................................................................... 170
Section 38.2: Selection Sort Basic Information ...................................................................................................... 170
Section 38.3: Implementation of Selection sort in C# ............................................................................................ 172
Chapter 39: Searching ............................................................................................................................................ 174
Section 39.1: Binary Search ...................................................................................................................................... 174
Section 39.2: Rabin Karp .......................................................................................................................................... 175
Section 39.3: Analysis of Linear search (Worst, Average and Best Cases) ........................................................ 176
Section 39.4: Binary Search: On Sorted Numbers ................................................................................................. 178
Section 39.5: Linear search ...................................................................................................................................... 178
Chapter 40: Substring Search ........................................................................................................................... 180
Section 40.1: Introduction To Knuth-Morris-Pratt (KMP) Algorithm ..................................................................... 180
Section 40.2: Introduction to Rabin-Karp Algorithm ............................................................................................. 183
Section 40.3: Python Implementation of KMP algorithm ...................................................................................... 186
Section 40.4: KMP Algorithm in C ............................................................................................................................ 187
Chapter 41: Breadth-First Search .................................................................................................................... 190
