Coding Challenge
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:
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.
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(n³).
Quadratic Runtime Solutions
Is this the best we can do? No! There’s also an O(n²) 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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