Longest biased interval and longest non-negative sum interval

摘要

Described is an algorithm to find the longest interval having at least a specified minimum bias in a sequence of characters (bases, amino acids), e.g. 'at least 0.95 (A+T)-rich'. It is based on an algorithm to find the longest interval having a non-negative sum in a sequence of positive and negative numbers. In practice, it runs in linear time; this can be guaranteed if the bias is rational.