Given a string of lowercase ASCII characters, find all distinct continuous palindromic sub-strings of it.
Input: str = "abaaa" Output: Below are 5 palindrome sub-strings a aa aaa aba b Input: str = "geek" Output: Below are 4 palindrome sub-strings e ee g k
Step 1: Finding all palindromes using modified Manacher’s algorithm:
Considering each character as a pivot, expand on both sides to find the length of both even and odd length palindromes centered at the pivot character under consideration and store the length in the 2 arrays (odd & even).
Time complexity for this step is O(n^2)
Step 2: Inserting all the found palindromes in a HashMap:
Insert all the palindromes found from the previous step into a HashMap. Also insert all the individual characters from the string into the HashMap (to generate distinct single letter palindromic sub-strings).
Time complexity of this step is O(n^3) assuming that the hash insert search takes O(1) time. Note that there can be at most O(n^2) palindrome sub-strings of a string. In below C++ code ordered hashmap is used where the time complexity of insert and search is O(Logn). In C++, ordered hashmap is implemented using Red Black Tree.
Step 3: Printing the distinct palindromes and number of such distinct palindromes:
The last step is to print all values stored in the HashMap (only distinct elements will be hashed due to the property of HashMap). The size of the map gives the number of distinct palindromic continuous sub-strings.
Below is the implementation of the above idea.
Below are 5 palindrome sub-strings a aa aaa aba b
Count All Palindrome Sub-Strings in a String
- Find distinct characters in distinct substrings of a string
- Rearrange the string to maximize the number of palindromic substrings
- Minimum changes to a string to make all substrings distinct
- Distinct palindromic sub-strings of the given string using Dynamic Programming
- Count of distinct substrings of a string using Suffix Trie
- Count of distinct substrings of a string using Suffix Array
- Find the count of palindromic sub-string of a string in its sorted form
- Minimum cuts required to convert a palindromic string to a different palindromic string
- Find a palindromic string B such that given String A is a subsequense of B
- Find all palindromic sub-strings of a given string | Set 2
- Count of Palindromic substrings in an Index range
- Count all Prime Length Palindromic Substrings
- Find the lexicographically largest palindromic Subsequence of a String
- Queries to find the count of vowels in the substrings of the given string
- Make palindromic string non-palindromic by rearranging its letters