Problem
At each step, choose a nonzero decimal digit currently present in the number and subtract that digit. Digits are taken from the new value after every step. Find the minimum number of steps needed to reach zero.
Implement removing_digits(n).
Input
n: The positive starting number.
Output
Return the fewest subtraction steps.
Constraints
1 ≤ n ≤ 1,000,000. Subtracting zero is not a useful move and is excluded.
Examples
Input:
n = 14
Expected output:
expected = 3Input:
long long n = 14;
Expected output:
long long expected = 3;Input:
long n = 14;
Expected output:
long expected = 3;Explanation
14 → 10 → 9 → 0 uses three steps. Neither possible first subtraction can reach zero in only two steps.
Input:
n = 7
Expected output:
expected = 1Input:
long long n = 7;
Expected output:
long long expected = 1;Input:
long n = 7;
Expected output:
long expected = 1;Explanation
Subtract the only digit, 7, to reach 0 immediately.
How to approach it
Try on your own first, then open one hint at a time.
Hint 1
Each number depends on the best answer for smaller numbers reachable by subtracting one digit.
Hint 2
Dynamic programming over all values up to n avoids repeated work.
Hint 3
Remember that the available digits change after every subtraction, and zero is never a valid choice.
Expected complexity
O(n * d) time, O(n) extra space
References
This challenge is adapted for CodeUtility. Follow the statement and constraints above.