Construct Smallest Number From DI String

lcpy gen -n 2375   # by problem number
lcpy gen -s construct_smallest_number_from_di_string   # by problem name

Input: pattern = "IIIDIDDD"
Output: "123549876"
Explanation:
At indices 0, 1, 2, and 4 we must have that num[i] < num[i+1].
At indices 3, 5, 6, and 7 we must have that num[i] > num[i+1].
Some possible values of num are "245639871", "135749862", and "123849765".
It can be proven that "123549876" is the smallest possible num that meets the conditions.

Input: pattern = "DDD"
Output: "4321"
Explanation:
Some possible values of num are "9876", "7321", and "8742".
It can be proven that "4321" is the smallest possible num that meets the conditions.

class Solution:
    # Time: O(n)
    # Space: O(n)
    def smallest_number(self, pattern: str) -> str:
        result: list[str] = []
        stack: list[str] = []
        for i in range(len(pattern) + 1):
            stack.append(str(i + 1))
            if i == len(pattern) or pattern[i] == "I":
                while stack:
                    result.append(stack.pop())
        return "".join(result)