1227. Airplane Seat Assignment Probability ¶

Problem

n passengers board an airplane with exactly n seats. The first passenger has lost the ticket and picks a seat randomly. But after that, the rest of the passengers will:

Take their own seat if it is still available, and
Pick other seats randomly when they find their seat occupied

Return the probability that the n^th person gets his own seat.

Example 1:

Input: n = 1
Output: 1.00000
Explanation: The first person can only get the first seat.

Example 2:

Input: n = 2
Output: 0.50000
Explanation: The second person has a probability of 0.5 to get the second seat (when first person gets the first seat).

Constraints:

1 <= n <= 10⁵