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g1201_1300.s1227_airplane_seat_assignment_probability.Solution Maven / Gradle / Ivy

package g1201_1300.s1227_airplane_seat_assignment_probability;

// #Medium #Dynamic_Programming #Math #Brainteaser #Probability_and_Statistics
// #2022_03_12_Time_1_ms_(15.63%)_Space_41.7_MB_(12.95%)

/**
 * 1227 - Airplane Seat Assignment Probability\.
 *
 * Medium
 *
 * `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_ nth _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
**/
public class Solution {
    public double nthPersonGetsNthSeat(int n) {
        if (n == 1) {
            return 1.0D;
        }
        return 0.5D;
    }
}