Generate an N-length string having longest palindromic substring of length K

Given two integers N and K (K ≤ N), the task is to obtain a string of length N such that maximum length of a palindromic substring of this string is K.

Examples:

Input: N = 5, K = 3 
Output: “abacd” 
Explanation: Palindromic substrings are “a”, “b”, “c”, “d” and “aba”. Therefore, the longest palindromic substring from the given string is of length 3.

Input: N = 8, K = 4 
Output: “abbacdef” 
Explanation: Palindromic substrings are “a”, “b”, “c”, “d”, “e”, “f”, “bb”, “abba”. Therefore, the longest palindromic substring from the given string is of length 4.

Approach: The idea is based on the following observation that the string of any length made up of a single character is always palindromic, e.g. {‘a’, ‘bbbbb’, ‘ccc’}. So, in order to generate a string with required conditions, print ‘a’ K times such that it has a longest palindromic substring of length K fill the remaining N – K slots by a non-palindromic sequence.

Follow the steps below to solve the problem:

• Print ‘a’ exactly K times.
• Consider a non-palindromic sequence, say “bcd”.
• Print the string.

Below is the implementation of the above approach:

C++

// C++ program to implement the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to generate a string of
// length N having longest palindromic
// substring of length K
void string_palindrome(int N, int K)
{

    // Fill first K characters with 'a'
    for (int i = 0; i < K; i++)
        cout << "a";

    // Stores a non-palindromic sequence
    // to be repeated for N - k slots
    string s = "bcd";

    // Print N - k remaining characters
    for (int i = 0; i < N - K; i++)
        cout << s[i % 3];
}

// Driver Code
int main()
{

    // Given N and K
    int N = 5, K = 3;
    string_palindrome(N, K);

    return 0;
}

Java

// Java program to implement the above approach
import java.util.*;

class GFG
{

// Function to generate a String of
// length N having longest palindromic
// subString of length K
static void String_palindrome(int N, int K)
{

    // Fill first K characters with 'a'
    for (int i = 0; i < K; i++)
        System.out.print("a");

    // Stores a non-palindromic sequence
    // to be repeated for N - k slots
    String s = "bcd";

    // Print N - k remaining characters
    for (int i = 0; i < N - K; i++)
        System.out.print(s.charAt(i % 3));
}

// Driver Code
public static void main(String[] args)
{

    // Given N and K
    int N = 5, K = 3;
    String_palindrome(N, K);
}
}

// This code is contributed by 29AjayKumar

Python3

# Python3 program to implement the above approach

# Function to generate a string of
# length N having longest palindromic
# substring of length K
def string_palindrome(N, K):

    # Fill first K characters with 'a'
    for i in range(K):
        print("a", end = "")

    # Stores a non-palindromic sequence
    # to be repeated for N - k slots
    s = "bcd"

    # Print N - k remaining characters
    for i in range(N - K):
        print(s[i % 3], end = "")

# Driver Code
if __name__ == '__main__':

    # Given N and K
    N, K = 5, 3
    string_palindrome(N, K)

    # This code is contributed by mohit kumar 29

C#

// C# program to implement the above approach
using System;
class GFG
{

    // Function to generate a String of
    // length N having longest palindromic
    // subString of length K
    static void String_palindrome(int N, int K)
    {

        // Fill first K characters with 'a'
        for (int i = 0; i < K; i++)
            Console.Write("a");

        // Stores a non-palindromic sequence
        // to be repeated for N - k slots
        string s = "bcd";

        // Print N - k remaining characters
        for (int i = 0; i < N - K; i++)
            Console.Write(s[i % 3]);
    }

    // Driver Code
    public static void Main(string[] args)
    {

        // Given N and K
        int N = 5, K = 3;
        String_palindrome(N, K);
    }
}

// This code is contributed by AnkThon

Javascript

<script>

// JavaScript program for above approach

    // Function to generate a String of
    // length N having longest palindromic
    // subString of length K
    function String_palindrome(N, K)
    {

        // Fill first K characters with 'a'
        for (let i = 0; i < K; i++)
            document.write("a");

        // Stores a non-palindromic sequence
        // to be repeated for N - k slots
        let s = "bcd";

        // Print N - k remaining characters
        for (let i = 0; i < N - K; i++)
            document.write(s[i % 3]);
    }


// Driver Code

     // Given N and K
        let N = 5, K = 3;
        String_palindrome(N, K);

</script>

Output:

aaabc

Time complexity: O(N)
Auxiliary space: O(1)