Numbers At Most N Given Digit Set — LeetCode 902 Python Solution

The problem

Given an array of digits which is sorted in non-decreasing order. You can write numbers using each digits[i] as many times as we want.

Example

Input

digits = ["1","3","5","7"], n = 100

Output

20

Explanation

The 20 numbers that can be written are:

Python solution

class Solution:
    def atMostNGivenDigitSet(self, digits: List[str], n: int) -> int:
        @cache
        def dfs(i: int, lead: int, limit: bool) -> int:
            if i >= len(s):
                return lead ^ 1

            up = int(s[i]) if limit else 9
            ans = 0
            for j in range(up + 1):
                if j == 0 and lead:
                    ans += dfs(i + 1, 1, limit and j == up)
                elif j in nums:
                    ans += dfs(i + 1, 0, limit and j == up)
            return ans

        s = str(n)
        nums = {int(x) for x in digits}
        return dfs(0, 1, True)

Complexity

Pattern: Monotonic Stack

Answer "what is the next greater element" for every position in one pass. LeetCode 902. Numbers At Most N Given Digit Set is filed here because the reference solution below belongs to the algorithm family this hub collects, even though its LeetCode tags point elsewhere.

The monotonic stack guide has the Python template for the pattern and the 225 LeetCode problems that use it.

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