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The set ret can be saved efficiently by just storing the index i, which is the last character of the longest common substring (of size z) instead of S[(i-z)..i]. Thus all the longest common substrings would be, for each i in ret, S[(ret[i]-z)..(ret[i])]. The following tricks can be used to reduce the memory usage of an implementation:
In Unicode, characters can have a unique name. A character can also have one or more alias names. An alias name can be an abbreviation, a C0 or C1 control name, a correction, an alternate name or a figment. An alias too is unique over all names and aliases, and therefore identifying.
P denotes the string to be searched for, called the pattern. Its length is m. S[i] denotes the character at index i of string S, counting from 1. S[i..j] denotes the substring of string S starting at index i and ending at j, inclusive. A prefix of S is a substring S[1..i] for some i in range [1, l], where l is the length of S.
HTML and XML provide ways to reference Unicode characters when the characters themselves either cannot or should not be used. A numeric character reference refers to a character by its Universal Character Set/Unicode code point, and a character entity reference refers to a character by a predefined name. A numeric character reference uses the ...
A simple and inefficient way to see where one string occurs inside another is to check at each index, one by one. First, we see if there is a copy of the needle starting at the first character of the haystack; if not, we look to see if there's a copy of the needle starting at the second character of the haystack, and so forth.
The empty string is the unique string over Σ of length 0, and is denoted ε or λ. [25] [26] The set of all strings over Σ of length n is denoted Σ n. For example, if Σ = {0, 1}, then Σ 2 = {00, 01, 10, 11}. We have Σ 0 = {ε} for every alphabet Σ. The set of all strings over Σ of any length is the Kleene closure of Σ and is denoted Σ *.
Character references that are based on the referenced character's UCS or Unicode code point are called numeric character references. In HTML 4 and in all versions of XHTML and XML, the code point can be expressed either as a decimal (base 10) number or as a hexadecimal (base 16) number.
This would represent a unique suffix in the ternary tree corresponding to the key string. If there is no such path, this means that the key string is either fully contained as a prefix of another string, or is not in the search tree. Many implementations make use of an end of string character to ensure only the latter case occurs.