leetcode-problemset/leetcode/problem/new-21-game.html

<p>Alice plays the following game, loosely based on the card game <strong>&quot;21&quot;</strong>.</p>

<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>

<p>Alice stops drawing numbers when she gets <code>k</code> <strong>or more points</strong>.</p>

<p>Return the probability that Alice has <code>n</code> or fewer points.</p>

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

<p>&nbsp;</p>
<p><strong>Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 10, k = 1, maxPts = 10
<strong>Output:</strong> 1.00000
<strong>Explanation:</strong> Alice gets a single card, then stops.
</pre>

<p><strong>Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 6, k = 1, maxPts = 10
<strong>Output:</strong> 0.60000
<strong>Explanation:</strong> Alice gets a single card, then stops.
In 6 out of 10 possibilities, she is at or below 6 points.
</pre>

<p><strong>Example 3:</strong></p>

<pre>
<strong>Input:</strong> n = 21, k = 17, maxPts = 10
<strong>Output:</strong> 0.73278
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>0 &lt;= k &lt;= n &lt;= 10<sup>4</sup></code></li>
	<li><code>1 &lt;= maxPts &lt;= 10<sup>4</sup></code></li>
</ul>