Algorithms

1. Introduction to Algorithms

1.1 Priori Analysis and Posteriori Testing

1.2 Characteristics of Algorithm

1.3 How Write and Analyze Algorithm

1.4 Frequency Count Method

1.5.1 Time Complexity #1

1.5.2 Time Complexity Example #2

1.5.3 Time Complexity of While and if #3

1.6 Classes of functions

1.7 Compare Class of Functions

1.8.1 Asymptotic Notations Big Oh - Omega - Theta #1

1.8.2 Asymptotic Notations - Big Oh - Omega - Theta #2

1.9 Properties of Asymptotic Notations

1.10.1 Comparison of Functions #1

1.10.2 Comparison of Functions #2

1.11 Best Worst and Average Case Analysis

1.12 Disjoint Sets Data Structure - Weighted Union and Collapsing Find

2 Divide And Conquer

2.1.1 Recurrence Relation (T(n)= T(n-1) + 1) #1

2.1.2 Recurrence Relation (T(n)= T(n-1) + n) #2

2.1.3 Recurrence Relation (T(n)= T(n-1) + log n) #3

2.1.4 Recurrence Relation T(n)=2 T(n-1)+1 #4

2.2 Masters Theorem Decreasing Function

2.3.1 Recurrence Relation Dividing Function T(n)=T(n/2)+1 #1

2.3.2 Recurrence Relation Dividing [ T(n)=T(n/2)+ n]. #2

2.3.3 Recurrence Relation [ T(n)= 2T(n/2) +n] #3

2.4.1 Masters Theorem in Algorithms for Dividing Function #1

2.4.2 Examples for Master Theorem #2

2.5 Root function (Recurrence Relation)

2.6.1 Binary Search Iterative Method

2.6.2 Binary Search Recursive Method

2.6.3 Heap - Heap Sort - Heapify - Priority Queues

2.7.1 Two Way MergeSort - Iterative method

2.7.2. Merge Sort Algorithm

2.7.3 MergeSort in-depth Analysis

2.8.1 QuickSort Algorithm

2.8.2 QuickSort Analysis

2.9 Strassens Matrix Multiplication

3. Greedy Method - Introduction

3.1 Knapsack Problem - Greedy Method

3.2 Job Sequencing with Deadlines - Greedy Method

3.3 Optimal Merge Pattern - Greedy Method

3.4 Huffman Coding - Greedy Method

3.5 Prims and Kruskals Algorithms - Greedy Method

3.6 Dijkstra Algorithm - Single Source Shortest Path - Greedy Method

4 Principle of Optimality - Dynamic Programming introduction

4.1 MultiStage Graph - Dynamic Programming

4.1.1 MultiStage Graph (Program) - Dynamic Programming

4.2 All Pairs Shortest Path (Floyd-Warshall) - Dynamic Programming

4.3 Matrix Chain Multiplication - Dynamic Programming

[New] Matrix Chain Multiplication using Dynamic Programming Formula

4.3.1 Matrix Chain Multiplication (Program) - Dynamic Programming

4.4 Bellman Ford Algorithm - Single Source Shortest Path - Dynamic Programming

4.5 0/1 Knapsack - Two Methods - Dynamic Programming

4.5.1 0/1 Knapsack Problem (Program) - Dynamic Programming

4.6 Optimal Binary Search Tree (Successful Search Only) - Dynamic Programming

4.6.2 [New] Optimal Binary Search Tree Successful and Unsuccessful Probability - Dynamic Programming

4.7 [New] Traveling Salesman Problem - Dynamic Programming using Formula

4.8 Reliability Design - Dynamic Programming

4.9 Longest Common Subsequence (LCS) - Recursion and Dynamic Programming

5.1 Graph Traversals - BFS & DFS -Breadth First Search and Depth First Search

5.2 Articulation Point and Biconnected Components

6 Introduction to Backtracking - Brute Force Approach

6.1 N Queens Problem using Backtracking

6.2 Sum Of Subsets Problem - Backtracking

6.3 Graph Coloring Problem - Backtracking

6.4 Hamiltonian Cycle - Backtracking

7 Branch and Bound Introduction

7.1 Job Sequencing with Deadline - Branch and Bound

7.2 0/1 Knapsack using Branch and Bound

7.3 Traveling Salesman Problem - Branch and Bound

8. NP-Hard and NP-Complete Problems

8.1 NP-Hard Graph Problem - Clique Decision Problem

9.1 Knuth-Morris-Pratt KMP String Matching Algorithm

9.2 Rabin-Karp String Matching Algorithm

10.1 AVL Tree - Insertion and Rotations

10.2 B Trees and B+ Trees. How they are useful in Databases

Asymptotic Notations - Simplified

Hashing Technique - Simplified

Shortest Path Algorithms (Dijkstra and Bellman-Ford) - Simplified

BFS DFS - Simplified

Tower of Hanoi Problem - Made Easy

Row-Major and Column-Major Mapping

Merge Sort Algorithm - Hindi