Find the smallest number whose sum of digits is N

Last Updated : 22 Sep, 2022

Given a positive integers N, the task is to find the smallest number whose sum of digits is N.
Example:

Input: N = 10
Output: 19
Explanation: 1 + 9 = 10 = N

Input: N = 18
Output: 99
Explanation: 9 + 9 = 18 = N

Naive Approach:

A Naive approach is to run a loop of i starting from 0 and find Sum of digits of i and check if it's equal to N or not.

Below is the implementation of the above approach.

C++

// C++ program to find the smallest
// number whose sum of digits is also N
#include <iostream>
#include <math.h>
using namespace std;

// Function to get sum of digits
int getSum(int n)
{
    int sum = 0;
    while (n != 0) {
        sum = sum + n % 10;
        n = n / 10;
    }
    return sum;
}

// Function to find the smallest
// number whose sum of digits is also N
void smallestNumber(int N)
{
    int i = 1;
    while (1) {
        // Checking if number has
        // sum of digits = N
        if (getSum(i) == N) {
            cout << i;
            break;
        }
        i++;
    }
}

// Driver code
int main()
{
    int N = 10;
    smallestNumber(N);

    return 0;
}

Java

// Java program to find the smallest
// number whose sum of digits is also N
class GFG{

// Function to get sum of digits
static int getSum(int n)
{
    int sum = 0;
    while (n != 0) 
    {
        sum = sum + n % 10;
        n = n / 10;
    }
    return sum;
}

// Function to find the smallest
// number whose sum of digits is also N
static void smallestNumber(int N)
{
    int i = 1;
    while (1 != 0) 
    {
        // Checking if number has
        // sum of digits = N
        if (getSum(i) == N) 
        {
            System.out.print(i);
            break;
        }
        i++;
    }
}

// Driver code
public static void main(String[] args)
{
    int N = 10;
    smallestNumber(N);
}
}

// This code is contributed 
// by shivanisinghss2110

Python3

# Python3 program to find the smallest
# number whose sum of digits is also N

# Function to get sum of digits
def getSum(n):

    sum1 = 0;
    while (n != 0):
        sum1 = sum1 + n % 10;
        n = n // 10;
    
    return sum1;

# Function to find the smallest
# number whose sum of digits is also N
def smallestNumber(N):

    i = 1;
    while (1):
        # Checking if number has
        # sum of digits = N
        if (getSum(i) == N):
            print(i);
            break;
        
        i += 1;
    
# Driver code
N = 10;
smallestNumber(N);

# This code is contributed by Code_Mech

// C# program to find the smallest
// number whose sum of digits is also N
using System;

class GFG{

// Function to get sum of digits
static int getSum(int n)
{
    int sum = 0;
    while (n != 0) 
    {
        sum = sum + n % 10;
        n = n / 10;
    }
    return sum;
}

// Function to find the smallest
// number whose sum of digits is also N
static void smallestNumber(int N)
{
    int i = 1;
    while (1 != 0) 
    {
        
        // Checking if number has
        // sum of digits = N
        if (getSum(i) == N) 
        {
            Console.Write(i);
            break;
        }
        i++;
    }
}

// Driver code
public static void Main(String[] args)
{
    int N = 10;
    
    smallestNumber(N);
}
}

// This code is contributed by Amit Katiyar

JavaScript

<script>

//Javascript program to find /the smallest
// number whose sum of digits is also N
 
// Function to get sum of digits
function getSum(n)
{
    let sum = 0;
    while (n != 0) {
        sum = sum + n % 10;
        n = Math.floor(n / 10);
    }
    return sum;
}
 
// Function to find the smallest
// number whose sum of digits is also N
function smallestNumber(N)
{
    let i = 1;
    while (1) {
        // Checking if number has
        // sum of digits = N
        if (getSum(i) == N) {
            document.write(i);
            break;
        }
        i++;
    }
}
 
// Driver code

    let N = 10;
    smallestNumber(N);
 
    
// This code is contributed by Mayank Tyagi

</script>

Output

Time Complexity: O(N).
Auxiliary space: O(1)

Efficient Approach:

An efficient approach to this problem is an observation. Let's see some examples.
- If N = 10, then ans = 19
- If N = 20, then ans = 299
- If N = 30, then ans = 3999
So, it is clear that the answer will have all digits as 9 except the first one so that we get the smallest number.
So, the Nth term will be =

(N \bmod 9 + 1) * 10^\frac{N}{9} - 1

Below is the implementation of the above approach

C++

// C++ program to find the smallest
// number whose sum of digits is also N
#include <iostream>
#include <math.h>
using namespace std;

// Function to find the smallest
// number whose sum of digits is also N
void smallestNumber(int N)
{
    cout << (N % 9 + 1)
                    * pow(10, (N / 9))
                - 1;
}

// Driver code
int main()
{
    int N = 10;
    smallestNumber(N);

    return 0;
}

Java

// Java program to find the smallest
// number whose sum of digits is also N
class GFG{
 
// Function to find the smallest
// number whose sum of digits is also N
static void smallestNumber(int N)
{
    System.out.print((N % 9 + 1) * 
            Math.pow(10, (N / 9)) - 1);
}
 
// Driver code
public static void main(String[] args)
{
    int N = 10;
    smallestNumber(N);
}
}

// This code is contributed by sapnasingh4991

Python3

# Python3 program to find the smallest
# number whose sum of digits is also N

# Function to find the smallest
# number whose sum of digits is also N
def smallestNumber(N):

    print((N % 9 + 1) * pow(10, (N // 9)) - 1)

# Driver code
N = 10
smallestNumber(N)

# This code is contributed by Code_Mech

// C# program to find the smallest
// number whose sum of digits is also N
using System;
class GFG{

// Function to find the smallest
// number whose sum of digits is also N
static void smallestNumber(int N)
{
    Console.WriteLine((N % 9 + 1) * 
             Math.Pow(10, (N / 9)) - 1);
}

// Driver code
public static void Main()
{
    int N = 10;
    
    smallestNumber(N);
}
}

// This code is contributed by Ritik Bansal

JavaScript

<script>

    // Javascript program to find the smallest
    // number whose sum of digits is also N
    
    // Function to find the smallest
    // number whose sum of digits is also N
    function smallestNumber(N)
    {
        document.write( (N % 9 + 1) * Math.pow(10, parseInt(N / 9, 10)) - 1 );
    }
    
    let N = 10;
    smallestNumber(N);
    
</script>