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.