# Top Ten String Algorithms created in Grasshopper for Rhino3D

# String_Algorithms

Top Ten String Algorithms created in Grasshopper for Rhino3D

Sure! Here are the top ten string algorithms, widely recognized for their importance and utility in various applications such as text processing, data compression, and bioinformatics:

**Knuth-Morris-Pratt (KMP) Algorithm**:

**Description**: An efficient string matching algorithm that preprocesses the pattern to create a partial match table (also known as the "lps" array) and uses this table to skip unnecessary comparisons.**Time Complexity**: O(n + m), where n is the length of the text and m is the length of the pattern.

**Rabin-Karp Algorithm**:

**Description**: Uses hashing to find any one of a set of pattern strings in a text. It computes a hash for the pattern and for each substring of the text, comparing these hashes to find matches.**Time Complexity**: Average case O(n + m), worst case O(nm).

**Boyer-Moore Algorithm**:

**Description**: A highly efficient string matching algorithm that preprocesses the pattern to determine how far to shift the pattern when a mismatch occurs, using two heuristics: the "bad character" rule and the "good suffix" rule.**Time Complexity**: O(n/m) in best cases, O(nm) in worst case.

**Aho-Corasick Algorithm**:

**Description**: Builds a finite state machine from a set of keywords and searches the text in a single pass. Useful for searching multiple patterns simultaneously.**Time Complexity**: O(n + m + z), where n is the length of the text, m is the total length of all patterns, and z is the number of pattern matches.

**Suffix Array**:

**Description**: A data structure that represents the suffixes of a string in lexicographical order. It is used in a variety of applications such as substring search, string matching, and text compression.**Time Complexity**: O(n log n) for construction, O(m log n) for pattern matching.

**Suffix Tree**:

**Description**: A compressed trie of all the suffixes of a given string. It provides efficient solutions for many string-related problems, such as finding the longest repeated substring and the longest common substring.**Time Complexity**: O(n) for construction, O(m) for pattern matching.

**Z Algorithm**:

**Description**: Computes the Z-array, which for a given string, provides the length of the longest substring starting from each position that matches the prefix of the string. Useful for pattern matching and string analysis.**Time Complexity**: O(n), where n is the length of the string.

**Manacher's Algorithm**:

**Description**: Finds the longest palindromic substring in linear time. It uses a clever way of expanding around potential centers of palindromes.**Time Complexity**: O(n), where n is the length of the string.

**Longest Common Subsequence (LCS)**:

**Description**: Finds the longest subsequence common to two sequences. Used in diff tools and bioinformatics for sequence alignment.**Time Complexity**: O(nm), where n and m are the lengths of the two sequences.

**Levenshtein Distance (Edit Distance)**:

**Description**: Measures the minimum number of single-character edits (insertions, deletions, substitutions) required to change one string into another. Used in spell checking, DNA sequencing, and natural language processing.**Time Complexity**: O(nm), where n and m are the lengths of the two strings.

These algorithms are fundamental tools in computer science and are widely applied in various domains.

- Aho-Corasick Algorithm .gh
- Boyer-Moore Algorithm .gh
- Knuth-Morris-Pratt (KMP) Algorithm .gh
- Levenshtein Distance (Edit Distance) .gh
- Longest Common Subsequence (LCS) .gh
- Manachers Algorithm .gh
- Rabin-Karp Algorithm .gh
- Suffix Array .gh
- Suffix Tree .gh
- Z Algorithm .gh