Check if The Number is Fascinating

Problem Description

You are given an integer n that consists of exactly 3 digits. We call the number n fascinating if, after the following modification, the resulting number contains all the digits from 1 to 9 exactly once and does not contain any 0's: Concatenate n with the numbers 2 * n and 3 * n. Return true if n is fascinating, or false otherwise.

Key Insights

• The input number n must be a 3-digit integer (100 <= n <= 999).
• To determine if n is fascinating, we need to concatenate n with 2 * n and 3 * n.
• After concatenation, we check if the resulting string contains all digits from 1 to 9 exactly once, without any 0's.
• We can use a set to track unique digits and ensure the count matches the required criteria.

Space and Time Complexity

Time Complexity: O(1) - The operations involve a constant number of digits (up to 9). Space Complexity: O(1) - We use a fixed-size set to track digit occurrences.

Solution

To solve the problem, we will:

1. Calculate the values of n, 2 * n, and 3 * n.
2. Concatenate these three values into a single string.
3. Use a set to track unique digits found in the concatenated string.
4. Finally, check if the set contains exactly the digits from '1' to '9'.

Code Solutions