leetcode-problemset/leetcode-cn/problem (English)/分割圆的最少切割次数(English) [minimum-cuts-to-divide-a-circle].html

<p>A <strong>valid cut</strong> in a circle can be:</p>

<ul>
	<li>A cut that is represented by a straight line that touches two points on the edge of the circle and passes through its center, or</li>
	<li>A cut that is represented by a straight line that touches one point on the edge of the circle and its center.</li>
</ul>

<p>Some valid and invalid cuts are shown in the figures below.</p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/10/29/alldrawio.png" style="width: 450px; height: 174px;" />
<p>Given the integer <code>n</code>, return <em>the <strong>minimum</strong> number of cuts needed to divide a circle into </em><code>n</code><em> equal slices</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/10/24/11drawio.png" style="width: 200px; height: 200px;" />
<pre>
<strong>Input:</strong> n = 4
<strong>Output:</strong> 2
<strong>Explanation:</strong> 
The above figure shows how cutting the circle twice through the middle divides it into 4 equal slices.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/10/24/22drawio.png" style="width: 200px; height: 201px;" />
<pre>
<strong>Input:</strong> n = 3
<strong>Output:</strong> 3
<strong>Explanation:</strong>
At least 3 cuts are needed to divide the circle into 3 equal slices. 
It can be shown that less than 3 cuts cannot result in 3 slices of equal size and shape.
Also note that the first cut will not divide the circle into distinct parts.
</pre>

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

<ul>
	<li><code>1 &lt;= n &lt;= 100</code></li>
</ul>