Find the count of palindromic sub-string of a string in its sorted form

Given a string str consisting of lowercase English alphabets, the task is to find the total number of palindromic sub-strings present in the sorted form of str.

Examples:

Input: str = “acbbd”
Output: 6
All palindromic sub-string in it’s sorted form (“abbcd”) are “a”, “b”, “b”, “bb”, “c” and “d”.



Input: str = “abbabdbd”
Output: 16

Naive approach: One way is to sort the given string and then count the total number of sub-strings present which are palindromes. For finding number of palindromic sub-strings this approach can be used which has time complexity of O(n^2).

Optimized approach: An efficient way is to count the frequency of each character and then for each frequency total number of palindromes will (n*(n+1))/2 as all the palindromic sub-strings of a sorted string will consist of the same character.
For example, palindromic sub-string for the string “aabbbcd” will be “a”, “aa”, …, “bbb”, “c”, … etc. Time complexity for this approach will be O(n).

  • Create a hash table for storing the frequencies of each character of the string str.
  • Traverse the hash table and for each non-zero frequency add (hash[i] * (hash[i]+1)) / 2 to the sum.
  • Print the sum in the end.

Below is the implementation of the above approach:

C++

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// CPP program to find the count of palindromic sub-string
// of a string in it's ascending form
#include <bits/stdc++.h>
using namespace std;
  
const int MAX_CHAR = 26;
  
// function to return count of palindromic sub-string
int countPalindrome(string str)
{
    int n = str.size();
    int sum = 0;
  
    // calculate frequency
    int hashTable[MAX_CHAR];
    for (int i = 0; i < n; i++)
        hashTable[str[i] - 'a']++;
  
    // calculate count of palindromic sub-string
    for (int i = 0; i < 26; i++) {
        if (hashTable[i])
            sum += (hashTable[i] * (hashTable[i] + 1) / 2);
    }
  
    // return result
    return sum;
}
  
// driver program
int main()
{
    string str = "ananananddd";
  
    cout << countPalindrome(str);
    return 0;
}

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Java

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// Java program to find the count of palindromic sub-string 
// of a string in it's ascending form 
  
class GFG {
  
    final static int MAX_CHAR = 26;
  
// function to return count of palindromic sub-string 
    static int countPalindrome(String str) {
        int n = str.length();
        int sum = 0;
  
        // calculate frequency 
        int hashTable[] = new int[MAX_CHAR];
        for (int i = 0; i < n; i++) {
            hashTable[str.charAt(i) - 'a']++;
        }
  
        // calculate count of palindromic sub-string 
        for (int i = 0; i < 26; i++) {
            if (hashTable[i] != 0) {
                sum += (hashTable[i] * (hashTable[i] + 1) / 2);
            }
        }
  
        // return result 
        return sum;
    }
  
// driver program 
    public static void main(String[] args) {
        String str = "ananananddd";
  
        System.out.println(countPalindrome(str));
  
    }
}

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Python3

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# Python3 program to find the count of 
# palindromic sub-string of a string 
# in it's ascending form
MAX_CHAR = 26
  
# function to return count of 
# palindromic sub-string
def countPalindrome(str):
  
    n = len (str)
    sum = 0
  
    # calculate frequency
    hashTable = [0] * MAX_CHAR
    for i in range(n):
        hashTable[ord(str[i]) - 
                  ord('a')] += 1
  
    # calculate count of palindromic
    # sub-string
    for i in range(26) :
        if (hashTable[i]):
            sum += (hashTable[i] * 
                   (hashTable[i] + 1) // 2)
  
    # return result
    return sum
  
# Driver Code
if __name__ == "__main__":
  
    str = "ananananddd"
  
    print (countPalindrome(str))
  
# This code is contributed by ita_c

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C#

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// C# program to find the count of palindromic sub-string 
// of a string in it's ascending form 
using System;
                      
public class GFG{
   
    readonly static int MAX_CHAR = 26;
   
// function to return count of palindromic sub-string 
    static int countPalindrome(String str) {
        int n = str.Length;
        int sum = 0;
   
        // calculate frequency 
        int []hashTable = new int[MAX_CHAR];
        for (int i = 0; i < n; i++) {
            hashTable[str[i] - 'a']++;
        }
   
        // calculate count of palindromic sub-string 
        for (int i = 0; i < 26; i++) {
            if (hashTable[i] != 0) {
                sum += (hashTable[i] * (hashTable[i] + 1) / 2);
            }
        }
   
        // return result 
        return sum;
    }
   
// driver program 
    public static void Main() {
        String str = "ananananddd";
   
        Console.Write(countPalindrome(str));
   
    }
}
  
// This code is contributed by Rajput-Ji

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PHP

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<?php
// PHP program to find the count of 
// palindromic sub-string of a string
// in it's ascending form
$MAX_CHAR = 26;
  
// function to return count of 
// palindromic sub-string
function countPalindrome($str)
{
    global $MAX_CHAR;
    $n = strlen($str);
    $sum = 0;
  
    // calculate frequency
    $hashTable = array_fill(0, $MAX_CHAR, 0);
    for ($i = 0; $i < $n; $i++)
        $hashTable[ord($str[$i]) - ord('a')]++;
  
    // calculate count of palindromic sub-string
    for ($i = 0; $i < 26; $i++) 
    {
        if ($hashTable[$i])
            $sum += (int)($hashTable[$i] * 
                         ($hashTable[$i] + 1) / 2);
    }
  
    // return result
    return $sum;
}
  
// Driver Code
$str = "ananananddd";
  
echo countPalindrome($str);
  
// This code is contributed by mits
?>

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Output:

26


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