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 alphabates 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++

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// 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

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Java














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// 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)); 


    } 


} 



















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Python3














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# 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 



















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C#














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// 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 



















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Output:


aaamz







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