Project Notes

Find Minimum in Rotated Sorted Array II

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Description

tab: English
 
<p>Suppose an array of length <code>n</code> sorted in ascending order is <strong>rotated</strong> between <code>1</code> and <code>n</code> times. For example, the array <code>nums = [0,1,4,4,5,6,7]</code> might become:</p>
 
<ul>
	<li><code>[4,5,6,7,0,1,4]</code> if it was rotated <code>4</code> times.</li>
	<li><code>[0,1,4,4,5,6,7]</code> if it was rotated <code>7</code> times.</li>
</ul>
 
<p>Notice that <strong>rotating</strong> an array <code>[a[0], a[1], a[2], ..., a[n-1]]</code> 1 time results in the array <code>[a[n-1], a[0], a[1], a[2], ..., a[n-2]]</code>.</p>
 
<p>Given the sorted rotated array <code>nums</code> that may contain <strong>duplicates</strong>, return <em>the minimum element of this array</em>.</p>
 
<p>You must decrease the overall operation steps as much as possible.</p>
 
<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<pre><strong>Input:</strong> nums = [1,3,5]
<strong>Output:</strong> 1
</pre><p><strong class="example">Example 2:</strong></p>
<pre><strong>Input:</strong> nums = [2,2,2,0,1]
<strong>Output:</strong> 0
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>
 
<ul>
	<li><code>n == nums.length</code></li>
	<li><code>1 &lt;= n &lt;= 5000</code></li>
	<li><code>-5000 &lt;= nums[i] &lt;= 5000</code></li>
	<li><code>nums</code> is sorted and rotated between <code>1</code> and <code>n</code> times.</li>
</ul>
 
<p>&nbsp;</p>
<p><strong>Follow up:</strong> This problem is similar to&nbsp;<a href="https://leetcode.com/problems/find-minimum-in-rotated-sorted-array/description/" target="_blank">Find Minimum in Rotated Sorted Array</a>, but&nbsp;<code>nums</code> may contain <strong>duplicates</strong>. Would this affect the runtime complexity? How and why?</p>
 
<p>&nbsp;</p>
 
 
 
---
 
[submissions](https://leetcode.com/problems/find-minimum-in-rotated-sorted-array-ii/submissions/) | [solutions](https://leetcode.com/problems/find-minimum-in-rotated-sorted-array-ii/solutions/)
 
 
tab: 中文
 
已知一个长度为 <code>n</code> 的数组，预先按照升序排列，经由 <code>1</code> 到 <code>n</code> 次 <strong>旋转</strong> 后，得到输入数组。例如，原数组 <code>nums = [0,1,4,4,5,6,7]</code> 在变化后可能得到：
<ul>
	<li>若旋转 <code>4</code> 次，则可以得到 <code>[4,5,6,7,0,1,4]</code></li>
	<li>若旋转 <code>7</code> 次，则可以得到 <code>[0,1,4,4,5,6,7]</code></li>
</ul>
 
<p>注意，数组 <code>[a[0], a[1], a[2], ..., a[n-1]]</code> <strong>旋转一次</strong> 的结果为数组 <code>[a[n-1], a[0], a[1], a[2], ..., a[n-2]]</code> 。</p>
 
<p>给你一个可能存在 <strong>重复</strong> 元素值的数组 <code>nums</code> ，它原来是一个升序排列的数组，并按上述情形进行了多次旋转。请你找出并返回数组中的 <strong>最小元素</strong> 。</p>
 
<p>你必须尽可能减少整个过程的操作步骤。</p>
 
<p>&nbsp;</p>
 
<p><strong>示例 1：</strong></p>
 
<pre>
<strong>输入：</strong>nums = [1,3,5]
<strong>输出：</strong>1
</pre>
 
<p><strong>示例 2：</strong></p>
 
<pre>
<strong>输入：</strong>nums = [2,2,2,0,1]
<strong>输出：</strong>0
</pre>
 
<p>&nbsp;</p>
 
<p><strong>提示：</strong></p>
 
<ul>
	<li><code>n == nums.length</code></li>
	<li><code>1 &lt;= n &lt;= 5000</code></li>
	<li><code>-5000 &lt;= nums[i] &lt;= 5000</code></li>
	<li><code>nums</code> 原来是一个升序排序的数组，并进行了 <code>1</code> 至 <code>n</code> 次旋转</li>
</ul>
 
<p>&nbsp;</p>
 
<p><strong>进阶：</strong>这道题与 <a href="https://leetcode-cn.com/problems/find-minimum-in-rotated-sorted-array/description/">寻找旋转排序数组中的最小值</a> 类似，但 <code>nums</code> 可能包含重复元素。允许重复会影响算法的时间复杂度吗？会如何影响，为什么？</p>
 
 
 
---
 
[提交记录](https://leetcode.cn/problems/find-minimum-in-rotated-sorted-array-ii/submissions/) | [题解](https://leetcode.cn/problems/find-minimum-in-rotated-sorted-array-ii/solution/)

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