Coding Challenge
π¬ Challenge: Given a string. How to find the longest palindrome in the string?

'locoannamadam'
contains multiple palindromes. The longest palindrome is 'madam'
.For comprehensibility, allow me to quickly add a definition of the term palindrome:
π‘ 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:
Check If Substring is Palindrome
You can easily check if a substring 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.
π 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 if
condition.
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
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(nΒ³)
.
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[i]
and s[j]
are the same. Set the cell to False
or True
accordingly. Initialize the data structure with diagonal values (i,i) == True
.
Note we do NOT use Python indexing in this description, i.e., the end index of a slice is included.
Here’s a quick overview of this idea:
π§© Exercise: Implement this idea in Python code and send it to me!

While working as a researcher in distributed systems, Dr. Christian Mayer found his love for teaching computer science students.
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