LCP Array šŸŽÆ

beginner
19 min

LCP Array šŸŽÆ

Welcome to our deep dive into the fascinating world of LCP (Longest Common Prefix) Arrays! In this lesson, we'll explore this powerful data structure and learn how to solve problems using it.

What is an LCP Array? šŸ“

An LCP Array is a data structure that stores the Longest Common Prefix of each contiguous block of strings in a given array. It's incredibly useful for tasks like finding the longest common string in a set of words, or even for solving the "Longest Common Subsequence" problem more efficiently.

Why use an LCP Array? šŸ’”

Using an LCP Array can significantly speed up algorithms that require multiple comparisons between strings. By keeping track of the longest common prefixes, we can avoid comparing strings that share a common prefix, thus reducing the overall complexity of the algorithm.

Creating an LCP Array šŸŽÆ

Let's dive into a step-by-step process to create an LCP Array. We'll use a simple example to illustrate the concept.

Example: Given an array of strings ["flower", "flow", "flight"], the LCP Array would be [6, 3, 2].

Here's how we can create it:

  1. Initialize the LCP Array with all zeros.
  2. Iterate through the array from left to right, comparing each string with its successor.
  3. For each comparison, find the length of the common prefix.
  4. Update the LCP Array with the length of the common prefix for the corresponding indices.

Let's break it down with our example:

  • flower, flow: Common prefix is "fl" (length 2). Update LCP Array: [2, 2].
  • flow, flight: No common prefix, but we don't need to update our LCP Array since it's the last comparison.

Using an LCP Array šŸ’”

Now that we have our LCP Array, we can use it to solve problems more efficiently. Let's see how we can find the longest common string in a given array using our LCP Array.

  1. Initialize a variable maxLength to 0 (or the minimum possible length).
  2. Iterate through the LCP Array and update maxLength with the maximum value found so far.
  3. If maxLength is greater than 0, the longest common string is the first maxLength characters of the first string.

Example Code šŸŽÆ

Here's a simple implementation of an LCP Array and a function to find the longest common string using it:

python
def lcp_array(arr): n = len(arr) lcp = [0] * n for i in range(n): for j in range(i + 1, n): length = min(len(arr[i]), len(arr[j])) while length > 0 and arr[i][-length] == arr[j][-length]: length -= 1 lcp[i] = max(lcp[i], length) return lcp def longest_common_string(arr): lcp = lcp_array(arr) max_length = max(lcp) if max_length > 0: return arr[0][:max_length] arr = ["flower", "flow", "flight"] print(longest_common_string(arr)) # Output: "fl"

Quiz šŸŽÆ