1227. Airplane Seat Assignment Probability

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 passengers will:

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

What is the probability that the n-th person can get 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 <= 10^5

Subproblem O(N)
- f(n) will always be 0.5 when n >= 2

public double nthPersonGetsNthSeat(int n) {
    if(n == 1) return 1.0;
    return 1.0 / n + (double)(n-2) / n * nthPersonGetsNthSeat(n-1);
}