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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.
1def add_digits(num):
2 while num >= 10:
3 sum = 0
4 while num > 0:
5 sum += num % 10
6 num //= 10
7 num = sum
8 return num
9
10print(add_digits(38))Python's implementation uses loops to compute the sum of the digits repeatedly until a single-digit number is obtained.
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.
1def
Python leverages the modulo operation directly, taking advantage of the digit root principle for fast computation.