문제
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.
제약 조건
1 ≤ n ≤ 1,000,000. Subtracting zero is not a useful move and is excluded.
예시
입력:
n = 14
예상 출력:
expected = 3입력:
long long n = 14;
예상 출력:
long long expected = 3;입력:
long n = 14;
예상 출력:
long expected = 3;설명
14 → 10 → 9 → 0 uses three steps. Neither possible first subtraction can reach zero in only two steps.
입력:
n = 7
예상 출력:
expected = 1입력:
long long n = 7;
예상 출력:
long long expected = 1;입력:
long n = 7;
예상 출력:
long expected = 1;설명
Subtract the only digit, 7, to reach 0 immediately.
접근 방법
먼저 스스로 풀어 본 뒤 힌트를 하나씩 열어 보세요.
힌트 1
Each number depends on the best answer for smaller numbers reachable by subtracting one digit.
힌트 2
Dynamic programming over all values up to n avoids repeated work.
힌트 3
Remember that the available digits change after every subtraction, and zero is never a valid choice.
예상 복잡도
O(n * d) time, O(n) extra space
참고 자료
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