LeetCode in Kotlin

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 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

Solution

class Solution {
    fun new21Game(n: Int, k: Int, maxPts: Int): Double {
        if (k == 0) return 1.00
        if (k == 1 && maxPts <= n) return 1.00
        val dp = DoubleArray(n + 1)
        dp[0] = 1.00
        var prev = 0.00
        for (i in 1..n) {
            if (i - maxPts - 1 >= 0) {
                prev -= dp[i - 1 - maxPts]
            }
            if (i - 1 < k) {
                prev += dp[i - 1]
            }
            dp[i] = prev / maxPts
        }
        var res = 0.00
        for (i in k..n) {
            res += dp[i]
        }
        return res
    }
}

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