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Z-function and its calculation Suppose we are given a string of length . The Z-function for this string is an array of length where the -th element is equal to the greatest number of characters starting from the position that coincide with the first characters In other words, is the length of the longest string that is, at the same time, a prefix of and a prefix of the suffix of starting Note. In this article, to avoid ambiguity, we assume -based indexes; that is: the first character of has index and the last one has index The first element of Z-function, is generally not well defined. In this article we will assume it is zero (although it doesn't change anything in the algorithm implementation). This article presents an algorithm for calculating the Z-function in time, as well as various of its applications.
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Z-function and its calculation
Suppose we are given a string
of length . The Z-function for this string is an array of length where the -th element is equal to the greatest number of characters starting from the position that coincide with the first characters In other words,
is the length of the longest string that is, at the same time, a prefix of and a prefix of the suffix of starting Note. In this article, to avoid ambiguity, we assume -based indexes; that is: the first character of has index and the last one has index The first element of Z-function, is generally not well defined. In this article we will assume it is zero (although it doesn't change anything in the algorithm implementation). This article presents an algorithm for calculating the Z-function in time, as well as various of its applications.