Given an integer N, the task is to find the smallest positive integer, which when multiplied by N, has sum of digits equal to the sum of digits of N.
Examples:
Input: N = 4
Output: 28
Explanation:
- Sum of digits of N = 4
- 4 * 28 = 112
- Sum of digits = 1 + 1 + 2 = 4, which is equal to sum of digits of N.
Input: N = 3029
Output: 37
Explanation:
- Sum of digits of N = 3 + 0 + 2 + 9 = 14
- 3029 * 37 = 112073
- Sum of digits = 1 + 1 + 2 + 0 + 7 + 3 = 14, which is equal to sum of digits of N.
Approach: Follow the steps to solve the problem:
- Since N can be large, take the input of N as a string. Calculate the sum of digits of N and store it in a variable, say S.
- Since the answer needs to exceed 10, starting from number 11, multiply it with N and store it in a variable, say res.
- Calculate the sum of digits of res and check if the sum of digits of res is equal to the S or not. If found to be true, then print the integer.
Below is the implementation of the above approach:
C++
// C++ program for the above approach #include <iostream> using namespace std;
// Function to find the minimum // integer having sum of digits // of a number multiplied by n // equal to sum of digits of n void find_num(string n)
{ // Initialize answer
int ans = 0;
int sumOfDigitsN = 0;
// Find sum of digits of N
for ( int c = 0; c < n.length(); c++)
{
sumOfDigitsN += n - '0' ;
}
int x=11;
while ( true )
{
// Multiply N with x
int newNum = x * stoi(n);
int tempSumDigits = 0;
string temp = to_string(newNum);
// Sum of digits of the new number
for ( int c = 0; c < temp.length(); c++)
{
tempSumDigits += temp - '0' ;
}
// If condition satisfies
if (tempSumDigits == sumOfDigitsN)
{
ans = x;
break ;
}
//increase x
x++;
}
// Print answer
cout << ans << endl;
} // Driver Code int main()
{ string N = "3029" ;
// Function call
find_num(N);
return 0;
} // This code is contributed by Sunil Sakariya |
Java
// Java program for the above approach class GFG {
// Function to find the minimum
// integer having sum of digits
// of a number multiplied by n
// equal to sum of digits of n
static void find_num(String n)
{
// Initialize answer
int ans = 0 ;
// Convert string to
// character array
char [] digitsOfN
= n.toCharArray();
int sumOfDigitsN = 0 ;
// Find sum of digits of N
for ( char c : digitsOfN) {
sumOfDigitsN
+= Integer.parseInt(
Character.toString(c));
}
for ( int x = 11 ; x > 0 ; x++) {
// Multiply N with x
int newNum
= x * Integer.parseInt(n);
int tempSumDigits = 0 ;
char [] temp
= Integer.toString(
newNum)
.toCharArray();
// Sum of digits of the new number
for ( char c : temp) {
tempSumDigits
+= Integer.parseInt(
Character.toString(c));
}
// If condition satisfies
if (tempSumDigits == sumOfDigitsN) {
ans = x;
break ;
}
}
// Print answer
System.out.println(ans);
}
// Driver Code
public static void main(String[] args)
{
String N = "3029" ;
// Function call
find_num(N);
}
} |
Python3
# Python3 program for the above approach # Function to find the minimum # integer having sum of digits # of a number multiplied by n # equal to sum of digits of n def find_num(n):
# Initialize answer
ans = 0
# Convert string to
# character array
digitsOfN = str (n)
sumOfDigitsN = 0
# Find sum of digits of N
for c in digitsOfN:
sumOfDigitsN + = int (c)
for x in range ( 11 , 50 ):
# Multiply N with x
newNum = x * int (n)
tempSumDigits = 0
temp = str (newNum)
# Sum of digits of the new number
for c in temp:
tempSumDigits + = int (c)
#print(tempSumDigits,newNum)
# If condition satisfies
if (tempSumDigits = = sumOfDigitsN):
ans = x
break
# Print answer
print (ans)
# Driver Code if __name__ = = '__main__' :
N = "3029"
# Function call
find_num(N)
# This code is contributed by mohit kumar 29 |
C#
// C# program for the above approach using System;
using System.Globalization;
class GFG{
// Function to find the minimum // integer having sum of digits // of a number multiplied by n // equal to sum of digits of n static void find_num( string n)
{ // Initialize answer
int ans = 0;
// Convert string to
// character array
char [] digitsOfN = n.ToCharArray();
int sumOfDigitsN = 0;
// Find sum of digits of N
foreach ( char c in digitsOfN)
{
sumOfDigitsN += Int32.Parse(
Char.ToString(c));
}
for ( int x = 11; x > 0; x++)
{
// Multiply N with x
int newNum = x * Int32.Parse(n);
int tempSumDigits = 0;
string str = newNum.ToString();
char [] temp = str.ToCharArray();
// Sum of digits of the new number
foreach ( char c in temp)
{
tempSumDigits += Int32.Parse(
Char.ToString(c));
}
// If condition satisfies
if (tempSumDigits == sumOfDigitsN)
{
ans = x;
break ;
}
}
// Print answer
Console.WriteLine(ans);
} // Driver Code public static void Main()
{ string N = "3029" ;
// Function call
find_num(N);
} } // This code is contributed by susmitakundugoaldanga |
Javascript
<script> // Javascript program for the above approach // Function to find the minimum // integer having sum of digits // of a number multiplied by n // equal to sum of digits of n function find_num(n)
{ // Initialize answer
var ans = 0;
var sumOfDigitsN = 0;
// Find sum of digits of N
for ( var c = 0; c < n.length; c++)
{
sumOfDigitsN += n - '0' ;
}
var x=11;
while ( true )
{
// Multiply N with x
var newNum = x * parseInt(n);
var tempSumDigits = 0;
var temp = (newNum.toString());
// Sum of digits of the new number
for ( var c = 0; c < temp.length; c++)
{
tempSumDigits += temp - '0' ;
}
// If condition satisfies
if (tempSumDigits == sumOfDigitsN)
{
ans = x;
break ;
}
//increase x
x++;
}
// Print answer
document.write( ans );
} // Driver Code var N = "3029" ;
// Function call find_num(N); </script> |
Output:
37
Time Complexity: O(N)
Auxiliary Space: O(log N)