Problema
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.
Restricciones
1 ≤ n ≤ 1,000,000. Subtracting zero is not a useful move and is excluded.
Ejemplos
Entrada:
n = 14
Salida esperada:
expected = 3Entrada:
long long n = 14;
Salida esperada:
long long expected = 3;Entrada:
long n = 14;
Salida esperada:
long expected = 3;Explicación
14 → 10 → 9 → 0 uses three steps. Neither possible first subtraction can reach zero in only two steps.
Entrada:
n = 7
Salida esperada:
expected = 1Entrada:
long long n = 7;
Salida esperada:
long long expected = 1;Entrada:
long n = 7;
Salida esperada:
long expected = 1;Explicación
Subtract the only digit, 7, to reach 0 immediately.
Cómo abordarlo
Inténtalo primero por tu cuenta y luego abre las pistas una a una.
Pista 1
Each number depends on the best answer for smaller numbers reachable by subtracting one digit.
Pista 2
Dynamic programming over all values up to n avoids repeated work.
Pista 3
Remember that the available digits change after every subtraction, and zero is never a valid choice.
Complejidad esperada
O(n * d) time, O(n) extra space
Referencias
Este reto está adaptado para CodeUtility. Sigue el enunciado y las restricciones indicadas arriba.