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Count Digits - Walkthrough - Recursion | Python | Repovive

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Count Digits - Walkthrough

Step-by-step solution

This problem follows the same structure as sum of digits, but you count instead of adding.

Base case: When $n < 10$ , you have a single digit. A single-digit number has exactly $1$ digit.

def count_digits(n):
    if n < 10:
        return 1
    return 1 + count_digits(n // 10)

Tracing count_digits(123):

count_digits(123) = 1 + count_digits(12)
  count_digits(12) = 1 + count_digits(1)
    count_digits(1) = 1  <- Base case

Working back: $1 + 1 + 1 = 3$ . Each division by $10$ removes one digit and adds $1$ to the count.