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.
Vincoli
1 ≤ n ≤ 1,000,000. Subtracting zero is not a useful move and is excluded.
Esempi
Input:
n = 14
Output atteso:
expected = 3Input:
long long n = 14;
Output atteso:
long long expected = 3;Input:
long n = 14;
Output atteso:
long expected = 3;Spiegazione
14 → 10 → 9 → 0 uses three steps. Neither possible first subtraction can reach zero in only two steps.
Input:
n = 7
Output atteso:
expected = 1Input:
long long n = 7;
Output atteso:
long long expected = 1;Input:
long n = 7;
Output atteso:
long expected = 1;Spiegazione
Subtract the only digit, 7, to reach 0 immediately.
Come affrontarlo
Prova prima da solo, poi apri un suggerimento alla volta.
Suggerimento 1
Each number depends on the best answer for smaller numbers reachable by subtracting one digit.
Suggerimento 2
Dynamic programming over all values up to n avoids repeated work.
Suggerimento 3
Remember that the available digits change after every subtraction, and zero is never a valid choice.
Complessità attesa
O(n * d) time, O(n) extra space
Riferimenti
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