Analysis of Algorithms (AofA) is a field in computer science whose overall goal is an understanding of the complexity of algorithms. While an extremely large amount of research is devoted to worst-case evaluations, the focus in these pages is methods for average-case and probabilistic analysis. Properties of random strings, permutations, trees, and graphs are thus essential ingredients in the analysis of algorithms.
To analyze an algorithm is to determine the amount of resources (such as time and storage) necessary to execute it. Most algorithms are designed to work with inputs of arbitrary length. Usually the efficiency or complexity of an algorithm is stated as a function relating the input length to the number of steps (time complexity) or storage locations (space complexity).
Algorithm analysis is an important part of a broader computational complexity theory, which provides theoretical estimates for the resources needed by any algorithm which solves a given computational problem. These estimates provide an insight into reasonable directions of search of efficient algorithms.