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The iterative approach involves summing the digits of the number repeatedly until the sum becomes a single-digit number. This is a straightforward approach and uses basic loops to repeatedly process the digits of the number.
1function addDigits(num) {
2 while (num >= 10) {
3 let sum = 0;
4 while (num > 0) {
5 sum += num % 10;
6 num = Math.floor(num / 10);
7 }
8 num = sum;
9 }
10 return num;
11}
12
13console.log(addDigits(38));The JavaScript solution also relies on loops to process and sum the digits until a single digit is left.
The mathematical approach leverages a known number theory result related to digit root which can be deduced using modulo 9 arithmetic. The result for the repeated digit sum is equivalent to the number modulo 9, except that when the number is zero it should remain zero.
1#include <iostream>
2
int addDigits(int num) {
if (num == 0) return 0;
if (num % 9 == 0) return 9;
return num % 9;
}
int main() {
int num = 38;
std::cout << addDigits(num) << std::endl;
return 0;
}In C++, we use an identical approach to solve the problem in optimal time by checking conditions around the modulo operation.