How to Find All Palindromes in a Python String?

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Coding Challenge

šŸ’¬ Challenge: Given a string. How to find all palindromes in the string?

For comprehensibility, allow me to quickly add a definition of the term palindrome:

šŸ’” Definition: A palindrome is a sequence of characters that reads the same backward as forward such as 'madam', 'anna', or '101'.

This article wants to give you a quick and easy solution in Python. First, we’ll solve the easier but important problem of checking if a substring is a palindrome in the first place:

How to Check If String is Palindrome

You can easily check if a string is a palindrome by using the slicing expression word == word[::-1] that evaluates to True if the word is the same forward and backward, i.e., it is a palindrome.

šŸ‘‰ Recommended Tutorial: Python Palindromes One-Liner

Next, we’ll explore how to find all substrings in a Python string that are also palindromes. You can find our palindrome checker in the code solution (highlighted):

Find All Substrings That Are Palindrome

The brute-force approach to finding all palindromes in a string is to iterate over all substrings in a nested for loop. Then check each substring if it is a palindrome using word == word[::-1]. Keep track of the found palindromes using the list.append() method. Return the final list after traversing all substrings.

Here’s the full solution:

def find_palindromes(s):
    palindromes = []
    n = len(s)
    for i in range(n):
        for j in range(i+1,n+1):
            word = s[i:j]
            if word == word[::-1]:
                palindromes.append(word)          
    return palindromes


print(find_palindromes('locoannamadam'))
# ['l', 'o', 'oco', 'c', 'o', 'a', 'anna',
#  'n', 'nn', 'n', 'a', 'ama', 'm', 'madam',
#  'a', 'ada', 'd', 'a', 'm']

print(find_palindromes('anna'))
# ['a', 'anna', 'n', 'nn', 'n', 'a']

print(find_palindromes('abc'))
# ['a', 'b', 'c']

Runtime Complexity

This has cubic runtime complexity, i.e., for a string with length n, we need to check O(n*n) different words. Each word may have up to n characters, thus the palindrome check itself is O(n). Together, this yields runtime complexity of O(n*n*n) = O(nĀ³).

Quadratic Runtime Solutions

Is this the best we can do? No! There’s also an O(nĀ²) time solution!

Here’s a quadratic-runtime solution to find all palindromes in a given string that ignores the trivial one-character palindromes (significantly modified from source):

def find_palindromes(s, j, k):
    ''' Finds palindromes in substring between indices j and k'''
    palindromes = []
    while j >= 0 and k < len(s):
        if s[j] != s[k]:
            break
        palindromes.append(s[j: k + 1])
        j -= 1
        k += 1
    return palindromes


def find_all(s):
    '''Finds all palindromes (non-trivial) in string s'''
    palindromes = []
    for i in range(0, len(s)):
        palindromes.extend(find_palindromes(s, i-1, i+1))
        palindromes.extend(find_palindromes(s, i, i+1))
    return palindromes


print(find_all('locoannamadam'))
# ['oco', 'nn', 'anna', 'ama', 'ada', 'madam']

print(find_all('anna'))
# ['nn', 'anna']

print(find_all('abc'))
# []

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