Count of Palindromic Substrings
Explore how to count palindromic substrings in a string by starting with a naive recursive solution and progressing to optimized dynamic programming methods. Understand both top-down memoization and bottom-up tabulation techniques that efficiently solve the problem with improved time and space complexity. This lesson equips you with practical DP patterns applicable to palindromic substring problems in coding interviews.
Statement
Given a string str1, find the count of palindromic substrings in it.
A string is said to be a palindrome if it can be read the same backward and forward. For example, “madam” is a palindrome because it can be read the same from left to right and right to left.
A substring is a sequence of consecutive characters from a string. For example, “way” is a substring of “subway”.
For example, if we have a string “aaa”, the palindromic substrings and its count will be:
- “a”, “a”, “a”, “aa”, “aa”, “aaa”
- Count of palindromic substrings will be equal to
Note: This problem has a direct application in bioinformatics. It is used in the analysis of DNA and RNA.
Constraints:
-
str1.length str1consists of the same case English letters.
Examples
No. | str1 | Palindromic Substrings | Count of Palindromic Substrings |
1 | pqr | "p", "q", "r" | 3 |
2 | aaa | "a", "a", "a", "aa", "aa", "aaa" | 6 |
Try it yourself
Implement your solution in the following playground.
def count_palindromic_substring(str1):return 0
Note: If you clicked the “Submit” button and the code timed out, this means that your solution needs to be optimized in terms ...