💬 Challenge: Given a string. How to find the longest palindrome 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
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:
Check If Substring is Palindrome
👉 Recommended Tutorial: Python Palindromes One-Liner
Next, we’ll explore how to find the longest substring in a Python string that is also a Palindrome. You can find our palindrome checker in the code solution (highlighted):
Find Longest Substring That is Palindrome
The brute-force approach to finding the longest palindrome 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 longest palindrome using the
len() function in an
Here’s the full solution:
def find_longest_palindrome(s): longest = '' n = len(s) for i in range(n): for j in range(i+1,n+1): word = s[i:j] if word == word[::-1]: if len(word)>len(longest): longest = word return longest print(find_longest_palindrome('locoannamadam')) # madam print(find_longest_palindrome('anna')) # anna print(find_longest_palindrome('abc')) # a
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).
Discussion and Better Solutions
Is this the best we can do?
No! The best we can theoretically do is a linear runtime complexity and linear space complexity called Manacher’s Algorithm. The idea is to choose multiple “palindrome centers” and grow these centers one step at a time by adding characters to the left or the right.
However, you’re not expected to come up with this yourself in a coding interview.
Quadratic Programming Idea
What some interviewers may expect is to come up with a “dynamic programming” idea where you construct a Boolean matrix.
Data Structure: Each cell
(i,j) of the Boolean Matrix is
True if the string
s[i:j] is a Palindrome and
False otherwise. The cell that is
True and has the highest value for
j-i represents the longest Palindrome.
Algorithm: Fill the data structure with Boolean values. You can construct a cell
(i,j) from the smaller cells easily by checking if the smaller substring
s[i+1:j-1] is a Palindrome and the first and last characters
s[j] are the same. Set the cell to
True accordingly. Initialize the data structure with diagonal values
(i,i) == True.
Here’s a quick overview of this idea:
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