# Count all Prime Length Palindromic Substrings

Given a string str, the task is to count all the sub-strings of str which are palindromes and their length is prime.

Examples:

Input: str = “geeksforgeeks”
Output: 2
“ee” and “ee” are the only valid sub-strings

Input: str = “abccc”
Output: 3

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: Using Sieve of Eratosthenes, find all the primes till the length of str because that is the maximum length a sub-string of str can have. Now starting from the smallest prime i.e. j = 2 till j ≤ len(str). If j is prime then count all the palindromic sub-strings of str whose length = j. Print the total count in the end.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function that returns true if sub-string ` `// starting at i and ending at j in str is a palindrome ` `bool` `isPalindrome(string str, ``int` `i, ``int` `j) ` `{ ` `    ``while` `(i < j) { ` `        ``if` `(str[i] != str[j]) ` `            ``return` `false``; ` `        ``i++; ` `        ``j--; ` `    ``} ` ` `  `    ``return` `true``; ` `} ` ` `  `// Function to count all palindromic substring ` `// whose lwngth is a prime number ` `int` `countPrimePalindrome(string str, ``int` `len) ` `{ ` ` `  `    ``bool` `prime[len + 1]; ` `    ``memset``(prime, ``true``, ``sizeof``(prime)); ` ` `  `    ``// 0 and 1 are non-primes ` `    ``prime = prime = ``false``; ` `    ``for` `(``int` `p = 2; p * p <= len; p++) { ` ` `  `        ``// If prime[p] is not changed, then it is a prime ` `        ``if` `(prime[p]) { ` ` `  `            ``// Update all multiples of p greater than or ` `            ``// equal to the square of it ` `            ``// numbers which are multiple of p and are ` `            ``// less than p^2 are already been marked. ` `            ``for` `(``int` `i = p * p; i <= len; i += p) ` `                ``prime[i] = ``false``; ` `        ``} ` `    ``} ` ` `  `    ``// To store the required number of sub-strings ` `    ``int` `count = 0; ` ` `  `    ``// Starting from the smallest prime till  ` `    ``// the largest length of the sub-string possible ` `    ``for` `(``int` `j = 2; j <= len; j++) { ` ` `  `        ``// If j is prime ` `        ``if` `(prime[j]) { ` ` `  `            ``// Check all the sub-strings of length j ` `            ``for` `(``int` `i = 0; i + j - 1 < len; i++) { ` ` `  `                ``// If current sub-string is a palindrome ` `                ``if` `(isPalindrome(str, i, i + j - 1)) ` `                    ``count++; ` `            ``} ` `        ``} ` `    ``} ` ` `  `    ``return` `count; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``string s = ``"geeksforgeeks"``; ` `    ``int` `len = s.length(); ` ` `  `    ``cout << countPrimePalindrome(s, len); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach  ` `import` `java.util.Arrays; ` ` `  `class` `GfG ` `{ ` ` `  `    ``// Function that returns true if  ` `    ``// sub-string starting at i and  ` `    ``// ending at j in str is a palindrome  ` `    ``static` `boolean` `isPalindrome(String str, ``int` `i, ``int` `j)  ` `    ``{  ` `        ``while` `(i < j)  ` `        ``{  ` `            ``if` `(str.charAt(i) != str.charAt(j))  ` `                ``return` `false``;  ` `            ``i++;  ` `            ``j--;  ` `        ``}  ` `     `  `        ``return` `true``;  ` `    ``}  ` `     `  `    ``// Function to count all palindromic substring  ` `    ``// whose lwngth is a prime number  ` `    ``static` `int` `countPrimePalindrome(String str, ``int` `len)  ` `    ``{  ` `     `  `        ``boolean``[] prime = ``new` `boolean``[len + ``1``];  ` `        ``Arrays.fill(prime, ``true``);  ` `     `  `        ``// 0 and 1 are non-primes  ` `        ``prime[``0``] = prime[``1``] = ``false``;  ` `        ``for` `(``int` `p = ``2``; p * p <= len; p++)  ` `        ``{  ` `     `  `            ``// If prime[p] is not changed, ` `            ``// then it is a prime  ` `            ``if` `(prime[p]) ` `            ``{  ` `     `  `                ``// Update all multiples of p greater than or  ` `                ``// equal to the square of it  ` `                ``// numbers which are multiple of p and are  ` `                ``// less than p^2 are already been marked.  ` `                ``for` `(``int` `i = p * p; i <= len; i += p)  ` `                    ``prime[i] = ``false``;  ` `            ``}  ` `        ``}  ` `     `  `        ``// To store the required number of sub-strings  ` `        ``int` `count = ``0``;  ` `     `  `        ``// Starting from the smallest prime till  ` `        ``// the largest length of the sub-string possible  ` `        ``for` `(``int` `j = ``2``; j <= len; j++)  ` `        ``{  ` `     `  `            ``// If j is prime  ` `            ``if` `(prime[j])  ` `            ``{  ` `     `  `                ``// Check all the sub-strings of length j  ` `                ``for` `(``int` `i = ``0``; i + j - ``1` `< len; i++)  ` `                ``{  ` `     `  `                    ``// If current sub-string is a palindrome  ` `                    ``if` `(isPalindrome(str, i, i + j - ``1``))  ` `                        ``count++;  ` `                ``}  ` `            ``}  ` `        ``}  ` `        ``return` `count;  ` `    ``}  ` `     `  `    ``// Driver code ` `    ``public` `static` `void` `main(String []args) ` `    ``{ ` `        ``String s = ``"geeksforgeeks"``;  ` `        ``int` `len = s.length();  ` ` `  `        ``System.out.println(countPrimePalindrome(s, len)); ` `    ``} ` `} ` ` `  `// This code is contributed by Rituraj Jain `

## Python3

 `# Python3 implementation of the approach ` `import` `math as mt ` ` `  `# Function that returns True if sub-str1ing ` `# starting at i and ending at j in str1  ` `# is a palindrome ` `def` `isPalindrome(str1, i, j): ` ` `  `    ``while` `(i < j): ` `        ``if` `(str1[i] !``=` `str1[j]): ` `            ``return` `False` `        ``i ``+``=` `1` `        ``j ``-``=` `1` `     `  `    ``return` `True` `     `  `# Function to count all palindromic substr1ing ` `# whose lwngth is a prime number ` `def` `countPrimePalindrome(str1, ``Len``): ` ` `  `    ``prime ``=` `[``True` `for` `i ``in` `range``(``Len` `+` `1``)] ` ` `  `    ``# 0 and 1 are non-primes ` `    ``prime[``0``], prime[``1``] ``=` `False``, ``False` `    ``for` `p ``in` `range``(``2``, mt.ceil(mt.sqrt(``Len` `+` `1``))): ` ` `  `        ``# If prime[p] is not changed,  ` `        ``# then it is a prime ` `        ``if` `(prime[p]): ` ` `  `            ``# Update all multiples of p greater  ` `            ``# than or equal to the square of it ` `            ``# numbers which are multiple of p  ` `            ``# and are less than p^2 are already  ` `            ``# been marked. ` `            ``for` `i ``in` `range``(``2` `*` `p, ``Len` `+` `1``, p): ` `                ``prime[i] ``=` `False` `         `  `    ``# To store the required number  ` `    ``# of sub-str1ings ` `    ``count ``=` `0` ` `  `    ``# Starting from the smallest prime  ` `    ``# till the largest Length of the  ` `    ``# sub-str1ing possible ` `    ``for` `j ``in` `range``(``2``, ``Len` `+` `1``): ` ` `  `        ``# If j is prime ` `        ``if` `(prime[j]): ` ` `  `            ``# Check all the sub-str1ings of  ` `            ``# Length j ` `            ``for` `i ``in` `range``(``Len` `+` `1` `-` `j): ` ` `  `                ``# If current sub-str1ing is a palindrome ` `                ``if` `(isPalindrome(str1, i, i ``+` `j ``-` `1``)): ` `                    ``count ``+``=` `1` `             `  `    ``return` `count ` ` `  `# Driver Code ` `s ``=` `"geeksforgeeks"` `Len` `=` `len``(s) ` ` `  `print``( countPrimePalindrome(s, ``Len``)) ` ` `  `# This code is contributed by  ` `# Mohit kumar 29 `

## C#

 `// C# implementation of the approach  ` `using` `System; ` ` `  `class` `GfG ` `{ ` ` `  `// Function that returns true if  ` `// sub-string starting at i and  ` `// ending at j in str is a palindrome  ` `static` `bool` `isPalindrome(``string` `str,  ` `                         ``int` `i, ``int` `j)  ` `{  ` `    ``while` `(i < j)  ` `    ``{  ` `        ``if` `(str[i] != str[j])  ` `            ``return` `false``;  ` `        ``i++;  ` `        ``j--;  ` `    ``}  ` ` `  `    ``return` `true``;  ` `}  ` ` `  `// Function to count all palindromic  ` `// substring whose lwngth is a prime number  ` `static` `int` `countPrimePalindrome(``string` `str,  ` `                                ``int` `len)  ` `{  ` ` `  `    ``bool``[] prime = ``new` `bool``[len + 1];  ` `    ``Array.Fill(prime, ``true``);  ` ` `  `    ``// 0 and 1 are non-primes  ` `    ``prime = prime = ``false``;  ` `    ``for` `(``int` `p = 2; p * p <= len; p++)  ` `    ``{  ` ` `  `        ``// If prime[p] is not changed, ` `        ``// then it is a prime  ` `        ``if` `(prime[p]) ` `        ``{  ` ` `  `            ``// Update all multiples of p greater  ` `            ``// than or equal to the square of it  ` `            ``// numbers which are multiple of p  ` `            ``// and are less than p^2 are already ` `            ``// been marked.  ` `            ``for` `(``int` `i = p * p; i <= len; i += p)  ` `                ``prime[i] = ``false``;  ` `        ``}  ` `    ``}  ` ` `  `    ``// To store the required number ` `    ``// of sub-strings  ` `    ``int` `count = 0;  ` ` `  `    ``// Starting from the smallest prime  ` `    ``// till the largest length of the  ` `    ``// sub-string possible  ` `    ``for` `(``int` `j = 2; j <= len; j++)  ` `    ``{  ` ` `  `        ``// If j is prime  ` `        ``if` `(prime[j])  ` `        ``{  ` ` `  `            ``// Check all the sub-strings of  ` `            ``// length j  ` `            ``for` `(``int` `i = 0;  ` `                     ``i + j - 1 < len; i++)  ` `            ``{  ` ` `  `                ``// If current sub-string is a  ` `                ``// palindrome  ` `                ``if` `(isPalindrome(str, i, i + j - 1))  ` `                    ``count++;  ` `            ``}  ` `        ``}  ` `    ``}  ` `    ``return` `count;  ` `}  ` ` `  `// Driver code ` `public` `static` `void` `Main() ` `{ ` `    ``string` `s = ``"geeksforgeeks"``;  ` `    ``int` `len = s.Length;  ` ` `  `    ``Console.WriteLine(countPrimePalindrome(s, len)); ` `} ` `} ` ` `  `// This code is contributed by Code_Mech `

## PHP

 ` `

Output:

```2
```

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