Count Palindromic Substrings 🎯

Welcome to this engaging and educational lesson on Counting Palindromic Substrings! This tutorial is designed for both beginners and intermediates, providing a comprehensive understanding of this fascinating concept. Let's dive right in!

What are Palindromic Substrings? 📝

A palindromic substring is a segment of a string that reads the same forward and backward. For example, in the string "racecar", "race", "car", and "r" are all palindromic substrings.

Why Count Palindromic Substrings? 💡

Counting palindromic substrings can be useful in various real-world applications, such as pattern matching, text processing, and data compression. In this lesson, we'll learn an efficient algorithm to count palindromic substrings.

Understanding the Algorithm 🎯

The algorithm we'll discuss is based on the observation that if a center of a palindrome (the middle character) is odd, the palindrome length is always odd, and if the center is even, the palindrome length can be either odd or even.

Here's a step-by-step breakdown:

Initialize an array p[] of size n+1, where n is the string length, and fill it with zeros. p[i] will hold the length of the largest palindrome ending at the ith character.
Iterate through the string from 1 to n. For each character, check for all possible starting indices from i-p[i] to i-1, and if the substring is palindromic, update p[i].
To check for a palindrome, we'll use a simple function: if the substring is s[i - l] to s[i] and s[i - l + 1] to s[i + 1] are the same, then the substring is palindromic.
After iterating through the string, the p[] array will contain the lengths of the longest palindromic substrings ending at each position. To get the total count of palindromic substrings, sum up the elements in p[] array.

Code Example 💡

Here's a Python implementation of the algorithm:

python

def count_palindromes(s):
    p = [0] * len(s)
    count = 0

    for i in range(1, len(s)):
        for j in range(i - p[i], i - 1):
            if s[j] == s[i] and (i - j <= 2 or p[j + 1]):
                p[i] = j + 1
                count += 1

    return count

Practice Time 💡

Now that you've learned the algorithm, let's test your understanding with a quiz:

Happy coding! 🎉🥳