2549. Count Distinct Numbers on Board

Problem

You are given a positive integer n, that is initially placed on a board. Every day, for 109 days, you perform the following procedure:

• For each number x present on the board, find all numbers 1 <= i <= n such that x % i == 1.

• Then, place those numbers on the board.

Return** the number of distinct integers present on the board after** 109 days have elapsed.

Note:

• Once a number is placed on the board, it will remain on it until the end.

• % stands for the modulo operation. For example, 14 % 3 is 2.

  Example 1:

Input: n = 5
Output: 4
Explanation: Initially, 5 is present on the board. 
The next day, 2 and 4 will be added since 5 % 2 == 1 and 5 % 4 == 1. 
After that day, 3 will be added to the board because 4 % 3 == 1. 
At the end of a billion days, the distinct numbers on the board will be 2, 3, 4, and 5. 

Example 2:

Input: n = 3
Output: 2
Explanation: 
Since 3 % 2 == 1, 2 will be added to the board. 
After a billion days, the only two distinct numbers on the board are 2 and 3. 

  Constraints:

• 1 <= n <= 100

Solution (Java)

class Solution {
    public int distinctIntegers(int n) {
        return n == 1 ? 1 : n-1;
    }
}

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(n).