5 Best Ways to Find the Longest Substring Which Is a Prefix, Suffix, and Also Present Inside the String in Python

πŸ’‘ Problem Formulation: The challenge is to develop a Python function that finds the longest substring which fulfills three criteria: it’s a prefix, a suffix, and also appears at least once elsewhere inside the given string. For instance, in the string “abcpqrabcabc”, the substring “abc” is both a prefix, a suffix, and appears inside the string. Thus, “abc” is the longest such substring we aim to find.

Method 1: Brute Force Approach

A brute force approach involves checking each substring of the input string that is a prefix and verifying if it is also a suffix and appears inside the string. This method iterates over the length of the string and slices out potential substring candidates for further checks.

Here’s an example:

def longest_prefix_suffix(string):
    max_len = len(string) // 2
    for i in range(max_len, 0, -1):
        prefix = string[:i]
        if string.endswith(prefix) and string.find(prefix, 1, -1) != -1:
            return prefix
    return ''

print(longest_prefix_suffix("abcpqrabcabc"))

Output:

abc

This code snippet defines a function longest_prefix_suffix() that iterates from the half-length of the string downwards to find the longest substring that is a prefix, suffix, and also inside the string. It returns this substring or an empty string if there’s no such substring.

Method 2: KMP Algorithm

The Knuth-Morris-Pratt (KMP) algorithm can be adapted to solve this problem efficiently by using the longest proper prefix which is also suffix (LPS) array, which KMP uses to skip characters while matching a pattern.

Here’s an example:

def compute_LPS_array(string):
    lps = [0] * len(string)
    length = 0
    i = 1
    while i < len(string):
        if string[i] == string[length]:
            length += 1
            lps[i] = length
            i += 1
        else:
            if length != 0:
                length = lps[length-1]
            else:
                lps[i] = 0
                i += 1
    return lps

def longest_prefix_suffix_kmp(string):
    lps = compute_LPS_array(string)
    length = lps[-1]
    return string[:length]

print(longest_prefix_suffix_kmp("abcpqrabcabc"))

Output:

abc

This snippet employs the KMP pattern matching algorithm’s preprocessing phase to construct an array that captures the lengths of the longest proper prefix that is also a suffix at each index. The last value in this array represents the length of the desired substring.

Method 3: Using Regular Expressions

This method utilizes Python’s re (regular expression) module to search for the longest substring matching the criteria. We use an iterative process to build progressively smaller patterns that match the beginning and end of the string until we find a match.

Here’s an example:

import re

def longest_prefix_suffix_regex(string):
    for i in range(len(string) // 2, 0, -1):
        pattern = f"^(.{i}).*\\1$"
        match = re.search(pattern, string)
        if match:
            return match.group(1)
    return ''

print(longest_prefix_suffix_regex("abcpqrabcabc"))

Output:

abc

This code utilizes regular expressions to find the longest prefix that is also a suffix. The re.search() function looks for a pattern that matches the start, any sequence of characters in the middle, and then the same sequence at the end of the string. It iterates over possible lengths and uses capturing groups to extract the matching substring.

Method 4: Utilizing Python Slicing

Python’s powerful slicing capabilities can be used to simulate the brute force approach in a more concise manner. This method steps through potential substring lengths similar to Method 1 but leverages slicing for checks.

Here’s an example:

def longest_prefix_suffix_slicing(string):
    max_len = len(string) // 2
    for i in range(max_len, 0, -1):
        if string[:i] == string[-i:] and string.find(string[:i], 1, -1) != -1:
            return string[:i]
    return ''

print(longest_prefix_suffix_slicing("abcpqrabcabc"))

Output:

abc

The function longest_prefix_suffix_slicing() checks for the equal prefix and suffix in the string and leverages the built-in find() method to confirm it’s also inside the string. It returns the substring if found or an empty string if not.

Bonus One-Liner Method 5: Pythonic Approach Using List Comprehension

This one-liner method takes advantage of list comprehension and Python’s slicing to achieve the same goal in a concise and readable manner.

Here’s an example:

longest_sub = max([string[:i] for i in range(len(string)//2, 0, -1) if string[:i] == string[-i:] and string.find(string[:i], 1, -1) != -1], key=len, default='')

print(longest_sub)

Output:

abc

This one-liner uses list comprehension to build a list of all valid substrings, then selects the longest one using Python’s max() function with the key argument set to the length. If no valid substring is found, default='' ensures an empty string is returned.

Summary/Discussion

  • Method 1: Brute Force Approach. Straightforward and easy to understand. May be inefficient for large strings due to its O(n^2) time complexity.
  • Method 2: KMP Algorithm. Very efficient with O(n) time complexity. More complex to implement and understand than brute force.
  • Method 3: Using Regular Expressions. Expressive and can be quite concise. However, regex can be slower and less readable than other methods for those not familiar with regex syntax.
  • Method 4: Utilizing Python Slicing. Capitalizes on built-in Python features for readability. Similar performance drawbacks as the brute force method.
  • Method 5: Pythonic Approach Using List Comprehension. Elegant and concise one-liner. Offers the benefits and drawbacks of the slicing method, with added readability.