386. Lexicographical Numbers

public class Solution
{
    public IList<int> LexicalOrder(int n)
    {
        // Initialize a List to store the lexicographically ordered numbers
        List<int> result = new List<int>();
        // Start with the smallest lexicographically number 1
        int current = 1;

        for (int i = 0; i < n; ++i)
        {
            // Add the current number to the result list
            result.Add(current);

            // Check if the next lexicographical step is to multiply by 10
            if (current * 10 <= n)
                current *= 10; // If so, go down one level of the lexical tree
            else
            {
                // If reached the end of this lexical level (e.g., n is 13 and current is 9),
                // or the increment leads past n, go up one level and increment
                while (current % 10 == 9 || current + 1 > n)
                    current /= 10;
                current++; // Increment to the next number in lexical order
            }
        }

        // Return the list containing the lexicographically ordered numbers
        return result;
    }
}