Design and Analysis of Algorithms

Introduction to Algorithms

Algorithm vs. Program

Characteristics of an Algorithm

Significance of Algorithms

Decidable vs. Undecidable Problems in Algorithms

The Nature of Undecidable Problems

Posteriori vs. Priori Analysis

Algorithms - Rapid Fire Quiz 1

Importance of Algorithm Analysis

Importance of Growth Rate

Introduction to Big O Notation

Big O Notation and Binary Search

Formal Definition of Big O Notation

Big O Notation (Solved Problems) - Set 1

Big O Notation (Solved Problems) - Set 2

Big O Notation (Solved Problems) - Set 3

Big O Notation (Solved Problems) - Set 4

Common Big O Runtimes

Functions in Asymptotic Notations (Decrement Functions)

Functions in Asymptotic Notations (Constant Functions)

Functions in Asymptotic Notations (Logarithmic Functions)

Functions in Asymptotic Notations (Polynomial Functions)

Functions in Asymptotic Notations (Exponential Functions)

Functions in Asymptotic Notations (Solved Problem 1)

Functions in Asymptotic Notations (Solved Problem 2)

Functions in Asymptotic Notations (Solved Problem 3)

The Big Omega (Ω) Notation

The Big Theta (θ) Notation

Big Omega and Big Theta Notations (Solved Problems)

Properties of Asymptotic Notations (General Property)

Properties of Asymptotic Notations (Reflexive Property)

Properties of Asymptotic Notations (Symmetric Property)

Properties of Asymptotic Notations (Transpose Symmetric Property)

Properties of Asymptotic Notations (Transitive Property)

Properties of Asymptotic Notations (Addition and Multiplication)

The Little o Notation

The Little Omega (ω) Notation

Asymptotic Notations - Summary

Asymptotic Notations (Solved Problem 1)

Asymptotic Notations (Solved Problem 2)

Asymptotic Notations (Solved Problem 3)

Asymptotic Notations (Solved Problem 4)

Asymptotic Notations (Solved Problem 5)

Asymptotic Notations (Solved Problem 6)

Algorithms - Rapid Fire Quiz 2

Understanding the Time Complexity of an Algorithm

Understanding the Space Complexity of an Algorithm

Analysis of Algorithms (Logarithms and Summations)

Time Complexity of Single Loops (Introduction)

Time Complexity of Single Loops (Increment by a Constant)

Time Complexity of Single Loops (Decrement by a Constant)

Time Complexity of Single Loops (Multiplying the Update Expression)

Time Complexity of Single Loops (Dividing the Update Expression)

Time Complexity of Single Loops (Update Expression with Power)

Time Complexity of Single Loops (Conditional Statement with a Function)

Time Complexity of Single Loops (Initialization Statement with a Function)

Time Complexity of Nested Loops (Independent Loops)

Time Complexity of Nested Loops (Independent Loop Examples)

Time Complexity of Nested Loops (Dependent Loops)

Time Complexity of Nested Loops (Dependent Loop Examples)

Time Complexity of Loops (Solved Problem 1)

Time Complexity of Loops (Solved Problem 2)

Time Complexity of Loops (Solved Problem 3)

Time Complexity of Loops (Solved Problem 4)

Time Complexity of Loops (Solved Problem 5)

Time Complexity of Loops (Solved Problem 6)

Algorithms - Rapid Fire Quiz 3

Space Complexity of Recursive Algorithms (The Call Stack)

Space Complexity of Recursive Algorithms (A Recursive Function)

Finding the Space Complexity of Recursive Algorithms

Space Complexity of Recursive Algorithms (Factorial of n)

Space Complexity of Recursive Algorithms (nth Fibonacci Number)

Space Complexity of Recursive Algorithms (Solved Problem 1)

Space Complexity of Recursive Algorithms (Solved Problem 2)

Space Complexity of Recursive Algorithms (Solved Problem 3)

Space Complexity of Recursive Algorithms (Solved Problem 4)

Algorithms - Rapid Fire Quiz 4

Writing Recurrence Relations

Substitution Method to Solve Recurrence Relation of Time

Substitution Method to Solve Recurrence Relation of Return Value

Substitution Method to Solve Recurrence Relation of Multiplications

Solving Recurrences using Substitution Method (Solved Problem 1)

Solving Recurrences using Substitution Method (Solved Problem 2)

Solving Recurrences using Substitution Method (Solved Problem 3)

Solving Recurrences using Substitution Method (Solved Problem 4)

Solving Recurrences using Substitution Method (Solved Problem 5)

Solving Recurrences using Substitution Method (Solved Problem 6)

Solving Recurrences using Substitution Method (Solved Problem 7)

Solving Recurrences using Substitution Method (Solved Problem 8)

Solving Recurrences using Substitution Method (Solved Problem 9)

Introduction to Towers of Hanoi

Towers of Hanoi (Recursive Algorithm)

Towers of Hanoi (Implementation)

Towers of Hanoi (Recurrence Relation of Moves)

Algorithms - Rapid Fire Quiz 5