The Fundamental Of The Algorithm

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An algorithm is a sequence of well-defined instructions for completing a task or solving a problem. It can be described in a natural language, pseudocode, a flowchart, or even a programming language. For example, suppose we are interested in knowing whether a specific number is contained in a given sequence of numbers. By traversing the entire number sequence from a certain beginning number to a certain ending number, we use a search algorithm to find this specific number. 

A major criterion for a good algorithm is its efficiency—that is, how much time and memory are required to solve a particular problem. Intuitively, time and memory can be measured in real units such as seconds and megabytes. However, these measurements are not subjective for comparisons between algorithms, because they depend on the computing power of the specific machine and on the specific data set. To standardize the measurement of algorithm efficiency, the computational complexity theory was developed [Ullman 1984; Papadimitriou 1993, 1998; Wilf 2002]. This allows an algorithm’s efficiency to be estimated and expressed conceptually as a mathematical function of its input size.