1227_airplane_seat_assignment_probability.md

1227 - Airplane Seat Assignment Probability

leetcode link

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).

Solution 1: Don't think, recurse! - O(n)

// 14/09/2020
double nthPersonGetsNthSeat(int n) {
    if(n == 1) return 1;
    return 1.0/(double)n + nthPersonGetsNthSeat(n-1) * (double)(n-2)/(double)n;
}

Solution 2: Think, don't code! - O(1)

// 14/09/2020
double nthPersonGetsNthSeat(int n) {
    return (n == 1)?1.0:0.5;
}