Lexicographically smallest string of length N and sum K

Given two integers N and K. The task is to print the lexicographically smallest string of length N consisting of lower-case English alphabets such that the sum of the characters of the string equals to K where ‘a’ = 1, ‘b’ = 2, ‘c’ = 3, ….. and ‘z’ = 26.
Examples: 

Input: N = 5, K = 42 
Output: aaamz 
“aaany”, “babmx”, “aablz” etc. are also valid strings 
but “aaamz” is the lexicographically smallest.
Input: N = 3, K = 25 
Output: aaw 

Approach:

• Initialize char array of size N and fill all the element by ‘a’.
• Start traversing from the end of the array and replace the elements of the array by ‘z’ if K ≥ 26 or replace it by the character having ASCII value (K + 97 – 1).
• At the same time decrease the value of K by replaced element value i.e. for a = 1, b = 2, c = 3, …, z = 26.
• Also, note that we are subtracting previous element value i.e. (total ‘a’) before current element and adding the same before the end of for loop.
• Check for K < 0 condition and break the for loop.
• Return the new string formed by the elements of the char array as the answer.

Below is the implementation of the above approach: 

C++

// C++ implementation of the approach
#include<bits/stdc++.h>
using namespace std;

// Function to return the lexicographically
// smallest string of length n that
// satisfies the given condition
string lexo_small(int n, int k)
{
    string arr = "";

    for(int i = 0; i < n; i++)
        arr += 'a';

    // Iteration from the last position
    // in the array
    for (int i = n - 1; i >= 0; i--)
    {
        k -= i;

        // If k is a positive integer
        if (k >= 0)
        {

            // 'z' needs to be inserted
            if (k >= 26)
            {
                arr[i] = 'z';
                k -= 26;
            }

            // Add the required character
            else
            {
                char c= (char)(k + 97 - 1);
                arr[i] = c;
                k -= arr[i] - 'a' + 1;
            }
        }

        else
            break;

        k += i;
    }
    return arr;
}

// Driver code
int main()
{
    int n = 5, k = 42;

    string arr = lexo_small(n, k);

    cout << arr;
}

// This code is contributed by Mohit Kumar

Java

// Java implementation of the approach
import java.util.Arrays;

public class Main {

    // Function to return the lexicographically
    // smallest string of length n that
    // satisfies the given condition
    public static char[] lexo_small(int n, int k)
    {
        char arr[] = new char[n];

        Arrays.fill(arr, 'a');

        // Iteration from the last position
        // in the array
        for (int i = n - 1; i >= 0; i--) {

            k -= i;

            // If k is a positive integer
            if (k >= 0) {

                // 'z' needs to be inserted
                if (k >= 26) {
                    arr[i] = 'z';
                    k -= 26;
                }

                // Add the required character
                else {
                    arr[i] = (char)(k + 97 - 1);
                    k -= arr[i] - 'a' + 1;
                }
            }

            else
                break;

            k += i;
        }

        return arr;
    }

    // Driver code
    public static void main(String[] args)
    {
        int n = 5, k = 42;

        char arr[] = lexo_small(n, k);

        System.out.print(new String(arr));
    }
}

Python3

# Python implementation of the approach

# Function to return the lexicographically
# smallest string of length n that
# satisfies the given condition
def lexo_small(n, k):

    arr = "";

    for i in range(n):
        arr += 'a';

    # Iteration from the last position
    # in the array
    for i in range(n-1,-1,-1):
        k -= i;

        # If k is a positive integer
        if (k >= 0):

            # 'z' needs to be inserted
            if (k >= 26):
                arr = arr[:i] + 'z' + arr[i+1:];
                k -= 26;

            # Add the required character
            else:
                c= (k + 97 - 1);
                arr = arr[:i] + chr(c) + arr[i+1:];
                k -= ord(arr[i]) - ord('a') + 1;

        else:
            break;

        k += i;
    return arr;

# Driver code
if __name__ == '__main__':
    n = 5; k = 42;

    arr = lexo_small(n, k);

    print(arr);

# This code contributed by PrinciRaj1992

C#

// C# implementation of the approach
using System;

class GFG
{

    // Function to return the lexicographically
    // smallest string of length n that
    // satisfies the given condition
    public static char[] lexo_small(int n, int k)
    {
        char []arr = new char[n];
        int i;

        for(i = 0; i < n; i++)
            arr[i] = 'a' ;

        // Iteration from the last position
        // in the array
        for (i = n - 1; i >= 0; i--)
        {
            k -= i;

            // If k is a positive integer
            if (k >= 0)
            {

                // 'z' needs to be inserted
                if (k >= 26)
                {
                    arr[i] = 'z';
                    k -= 26;
                }

                // Add the required character
                else
                {
                    arr[i] = (char)(k + 97 - 1);
                    k -= arr[i] - 'a' + 1;
                }
            }

            else
                break;

            k += i;
        }
        return arr;
    }

    // Driver code
    public static void Main()
    {
        int n = 5, k = 42;

        char []arr = lexo_small(n, k);

        Console.WriteLine(new string(arr));
    }
}

// This code is contributed by AnkitRai01

Javascript

<script>

// javascript implementation of the approach


// Function to return the lexicographically
// smallest string of length n that
// satisfies the given condition
function lexo_small(n , k)
{
    var arr = Array.from({length: n}, (_, i) => 'a');

    // Iteration from the last position
    // in the array
    for (var i = n - 1; i >= 0; i--) {

        k -= i;

        // If k is a positive integer
        if (k >= 0) {

            // 'z' needs to be inserted
            if (k >= 26) {
                arr[i] = 'z';
                k -= 26;
            }

            // Add the required character
            else {
                arr[i] = String.fromCharCode(k + 97 - 1);
                k -= arr[i] - 'a' + 1;
            }
        }

        else
            break;

        k += i;
    }

    return arr;
}

// Driver code
var n = 5, k = 42;

var arr = lexo_small(n, k);

document.write(arr.join(''));

// This code contributed by shikhasingrajput
</script>

Output:

aaamz