Algorithm of the day -

The Longest Common Prefix (LCP) Array Algorithm of the Suffix Array with Suffix Array Construction

Summary

This algorithm constructs a suffix array and then uses it to find the longest common prefix between any two suffixes in a given string, allowing for efficient string matching and comparison.

Use Case

The algorithm can be used in a text editor to provide an auto-complete feature, where it suggests the most likely completion of a word based on the context of the surrounding text.

Steps

  1. Construct the suffix array for the given string, which is an array of indices of all suffixes in the string in lexicographical order.
  2. Initialize the LCP array with zeros, where the length of the LCP array is equal to the length of the suffix array.
  3. Compare adjacent suffixes in the suffix array and store the length of their common prefix in the corresponding index in the LCP array.
  4. Use the constructed LCP array to find the longest common prefix between any two suffixes in the string.

Complexity

The time complexity of the algorithm is O(n log n) and the space complexity is O(n), where n is the length of the input string.

Code Example

import numpy as np
def lcp_array(s):
    # Construct the suffix array
    suffix_array = np.argsort([s[i:] for i in range(len(s))])
    # Initialize the LCP array
    lcp = [0] * len(suffix_array)
    # Compare adjacent suffixes and store the length of their common prefix
    for i in range(1, len(suffix_array)):
        j = 0
        while j + suffix_array[i-1] < len(s) and j + suffix_array[i] < len(s) and s[j + suffix_array[i-1]] == s[j + suffix_array[i]]:
            j += 1
        lcp[i] = j
    return lcp
# Example usage:
s = 'banana'
print(lcp_array(s))