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算法题/find-the-winner-of-the-circular-game.html

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+<p>There are <code>n</code> friends that are playing a game. The friends are sitting in a circle and are numbered from <code>1</code> to <code>n</code> in <strong>clockwise order</strong>. More formally, moving clockwise from the <code>i<sup>th</sup></code> friend brings you to the <code>(i+1)<sup>th</sup></code> friend for <code>1 &lt;= i &lt; n</code>, and moving clockwise from the <code>n<sup>th</sup></code> friend brings you to the <code>1<sup>st</sup></code> friend.</p>
+
+
+
+<p>The rules of the game are as follows:</p>
+
+
+
+<ol>
+
+	<li><strong>Start</strong> at the <code>1<sup>st</sup></code> friend.</li>
+
+	<li>Count the next <code>k</code> friends in the clockwise direction <strong>including</strong> the friend you started at. The counting wraps around the circle and may count some friends more than once.</li>
+
+	<li>The last friend you counted leaves the circle and loses the game.</li>
+
+	<li>If there is still more than one friend in the circle, go back to step <code>2</code> <strong>starting</strong> from the friend <strong>immediately clockwise</strong> of the friend who just lost and repeat.</li>
+
+	<li>Else, the last friend in the circle wins the game.</li>
+
+</ol>
+
+
+
+<p>Given the number of friends, <code>n</code>, and an integer <code>k</code>, return <em>the winner of the game</em>.</p>
+
+
+
+<p>&nbsp;</p>
+
+<p><strong>Example 1:</strong></p>
+
+<img alt="" src="https://assets.leetcode.com/uploads/2021/03/25/ic234-q2-ex11.png" style="width: 500px; height: 345px;" />
+
+<pre>
+
+<strong>Input:</strong> n = 5, k = 2
+
+<strong>Output:</strong> 3
+
+<strong>Explanation:</strong> Here are the steps of the game:
+
+1) Start at friend 1.
+
+2) Count 2 friends clockwise, which are friends 1 and 2.