1227. Airplane Seat Assignment Probability

Medium

30 Points

Math

Dynamic Programming

Brainteaser

Probability and Statistics

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: Return the probability that the nth person gets his own seat.

Examples

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