Find the smallest number whose sum of digits is N
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 = NInput: 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#
// 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
19
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 =
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#
// 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> |
Output
19
Time complexity: O(logN) since inbuilt pow function is being used
Auxiliary space: O(1), since no extra space has been taken.
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