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| 1 | +<h2><a href="https://leetcode.com/problems/new-21-game">New 21 Game</a></h2> <img src='https://img.shields.io/badge/Difficulty-Medium-orange' alt='Difficulty: Medium' /><hr><p>Alice plays the following game, loosely based on the card game <strong>"21"</strong>.</p> |
| 2 | + |
| 3 | +<p>Alice starts with <code>0</code> points and draws numbers while she has less than <code>k</code> points. During each draw, she gains an integer number of points randomly from the range <code>[1, maxPts]</code>, where <code>maxPts</code> is an integer. Each draw is independent and the outcomes have equal probabilities.</p> |
| 4 | + |
| 5 | +<p>Alice stops drawing numbers when she gets <code>k</code> <strong>or more points</strong>.</p> |
| 6 | + |
| 7 | +<p>Return the probability that Alice has <code>n</code> or fewer points.</p> |
| 8 | + |
| 9 | +<p>Answers within <code>10<sup>-5</sup></code> of the actual answer are considered accepted.</p> |
| 10 | + |
| 11 | +<p> </p> |
| 12 | +<p><strong class="example">Example 1:</strong></p> |
| 13 | + |
| 14 | +<pre> |
| 15 | +<strong>Input:</strong> n = 10, k = 1, maxPts = 10 |
| 16 | +<strong>Output:</strong> 1.00000 |
| 17 | +<strong>Explanation:</strong> Alice gets a single card, then stops. |
| 18 | +</pre> |
| 19 | + |
| 20 | +<p><strong class="example">Example 2:</strong></p> |
| 21 | + |
| 22 | +<pre> |
| 23 | +<strong>Input:</strong> n = 6, k = 1, maxPts = 10 |
| 24 | +<strong>Output:</strong> 0.60000 |
| 25 | +<strong>Explanation:</strong> Alice gets a single card, then stops. |
| 26 | +In 6 out of 10 possibilities, she is at or below 6 points. |
| 27 | +</pre> |
| 28 | + |
| 29 | +<p><strong class="example">Example 3:</strong></p> |
| 30 | + |
| 31 | +<pre> |
| 32 | +<strong>Input:</strong> n = 21, k = 17, maxPts = 10 |
| 33 | +<strong>Output:</strong> 0.73278 |
| 34 | +</pre> |
| 35 | + |
| 36 | +<p> </p> |
| 37 | +<p><strong>Constraints:</strong></p> |
| 38 | + |
| 39 | +<ul> |
| 40 | + <li><code>0 <= k <= n <= 10<sup>4</sup></code></li> |
| 41 | + <li><code>1 <= maxPts <= 10<sup>4</sup></code></li> |
| 42 | +</ul> |
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