समस्या
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.
सीमाएँ
1 ≤ n ≤ 1,000,000. Subtracting zero is not a useful move and is excluded.
उदाहरण
इनपुट:
n = 14
अपेक्षित आउटपुट:
expected = 3इनपुट:
long long n = 14;
अपेक्षित आउटपुट:
long long expected = 3;इनपुट:
long n = 14;
अपेक्षित आउटपुट:
long expected = 3;व्याख्या
14 → 10 → 9 → 0 uses three steps. Neither possible first subtraction can reach zero in only two steps.
इनपुट:
n = 7
अपेक्षित आउटपुट:
expected = 1इनपुट:
long long n = 7;
अपेक्षित आउटपुट:
long long expected = 1;इनपुट:
long n = 7;
अपेक्षित आउटपुट:
long expected = 1;व्याख्या
Subtract the only digit, 7, to reach 0 immediately.
कैसे हल करें
पहले खुद कोशिश करें, फिर एक-एक करके संकेत खोलें।
संकेत 1
Each number depends on the best answer for smaller numbers reachable by subtracting one digit.
संकेत 2
Dynamic programming over all values up to n avoids repeated work.
संकेत 3
Remember that the available digits change after every subtraction, and zero is never a valid choice.
अपेक्षित जटिलता
O(n * d) time, O(n) extra space
संदर्भ
यह चुनौती CodeUtility के लिए अनुकूलित की गई है। ऊपर दिए गए स्टेटमेंट और सीमाओं का पालन करें।