Introduction to Analysis of Algorithms

In theoretical analysis of algorithms, it is common to estimate their complexity in the asymptotic sense, i.e., to estimate the complexity function for arbitrarily large input. The term "analysis of algorithms" was coined by Donald Knuth.

Algorithm analysis is an important part of computational complexity theory, which provides theoretical estimation for the required resources of an algorithm to solve a specific computational problem. Most algorithms are designed to work with inputs of arbitrary length. Analysis of algorithms is the determination of the amount of time and space resources required to execute it.

Usually, the efficiency or running time of an algorithm is stated as a function relating the input length to the number of steps, known as time complexity, or volume of memory, known as space complexity.

In this Section We are going to cover −

• Algorithms and Complexities
• Asymptotic analysis
• Asymptotic notations
• Amortized analysis
• Space Complexity
• Pseudo Polynomial Type Algorithm and PATS (Pseudo Polynomial Type Approximation Scheme)