Package g0801_0900.s0837_new_21_game

Class Solution

  • All Implemented Interfaces:
    
public final class Solution

    837 - New 21 Game.

    Medium

    Alice plays the following game, loosely based on the card game "21".

    Alice starts with 0 points and draws numbers while she has less than k points. During each draw, she gains an integer number of points randomly from the range [1, maxPts], where maxPts is an integer. Each draw is independent and the outcomes have equal probabilities.

    Alice stops drawing numbers when she gets k or more points.

    Return the probability that Alice has n or fewer points.

    Answers within <code>10<sup>-5</sup></code> of the actual answer are considered accepted.

    Example 1:

    Input: n = 10, k = 1, maxPts = 10

    Output: 1.00000

    Explanation: Alice gets a single card, then stops.

    Example 2:

    Input: n = 6, k = 1, maxPts = 10

    Output: 0.60000

    Explanation: Alice gets a single card, then stops. In 6 out of 10 possibilities, she is at or below 6 points.

    Example 3:

    Input: n = 21, k = 17, maxPts = 10

    Output: 0.73278

    Constraints:

    • <code>0 <= k <= n <= 10<sup>4</sup></code>

    • <code>1 <= maxPts <= 10<sup>4</sup></code>

    • Nested Class Summary

      Nested Classes 
      Modifier and Type Class Description

    • Field Summary

      Fields 
      Modifier and Type Field Description

    • Constructor Summary

      Constructors 
      Constructor Description
      Solution()

    • Enum Constant Summary

      Enum Constants 
      Enum Constant Description

    • Method Summary

      Modifier and Type Method Description
      final Double new21Game(Integer n, Integer k, Integer maxPts)

      • Methods inherited from class java.lang.Object

        clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait