Algorithm of the day -

The Ukkonen's Suffix Tree Construction Algorithm

Summary

A method for constructing a suffix tree in linear time, allowing for efficient string matching and other operations

Use Case

Ukkonen's algorithm can be used in a text editor to provide instant feedback on substring searches, or in a bioinformatics application to quickly identify patterns in large genomic sequences

Steps

  1. Preprocess the input string by appending a unique sentinel character
  2. Initialize the suffix tree with the root node
  3. Iterate over the characters in the input string, adding suffixes to the tree and updating the tree structure as necessary
  4. Use a combination of implicit and explicit suffix links to efficiently navigate the tree and reduce construction time

Complexity

The time complexity of Ukkonen's algorithm is O(n), where n is the length of the input string, and the space complexity is also O(n)

Code Example

def ukkonen_suffix_treeConstruction(string):
    string += '$'
    tree = {}
    for i in range(len(string)):
        suffix = string[i:]
        node = tree
        for char in suffix:
            if char not in node:
                node[char] = {}
            node = node[char]
    return tree

# Example usage:
string = "banana"
tree = ukkonen_suffix_treeConstruction(string)
print(tree)