0837-new-21-game.rb

# frozen_string_literal: true

# 837. New 21 Game
# https://leetcode.com/problems/new-21-game
# Medium

=begin
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 10**-5 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:
0 <= k <= n <= 104
1 <= maxPts <= 104
=end

# @param {Integer} n
# @param {Integer} k
# @param {Integer} max_pts
# @return {Float}
defnew21_game(n,k,max_pts)
return1ifk - 1 + max_pts <= n

result=Array.new(k + max_pts,0.0)

k.upto(n)do |i|
result[i]=1
end

sum=result[k...(k + max_pts)].sum

(k - 1).downto(0)do |i|
result[i]=sum / max_pts
sum += result[i] - result[i + max_pts]
end

result[0].round(5)
end

# ********************#
# TEST #
# ********************#

require"test/unit"
classTest_new21_game < Test::Unit::TestCase
deftest_
assert_equal1.00000,new21_game(10,1,10)
assert_equal0.60000,new21_game(6,1,10)
assert_equal0.73278,new21_game(21,17,10)
end
end