Mastering Algorithms with C

Related Topics

Recurrences

Functions frequently used in the formal analysis of recursive algorithms. Recurrences are represented as recursive functions. A recursive function is a function that calls itself (see Chapter 3). Each successive call works on a more refined set of inputs, bringing us closer and closer to a solution. They are useful in describing the performance of recursive algorithms because they allow us to describe an algorithm’s performance in terms of invoking the algorithm on a more and more refined set of inputs.

Summation formulas

Mathematical formulas useful in simplifying summations that describe the running times of algorithms. Summations occur frequently as the result of analyzing iterative control structures.

Θ-notation, Ω-notation, o-notation, and w-notation

Additional notations used to represent information about an algorithm’s performance. Whereas O -notation expresses the upper bound of a function within a constant factor, Θ -notation expresses a bound from above and below. Ω -notation expresses strictly a lower bound within a constant factor. o -notation and w -notation are analogous to O -notation and Ω-notation but are more precise. O -notation often is used informally where other notations would be more specific.

NP-complete problems

A class of problems for which no polynomial-time algorithms are known, but for which no proof exists refuting the possibility either. Thus, NP-completeness has long been one of the most perplexing vexations in computer ...