Nav: << previous: 152.乘积最大子数组 | next: 154.寻找旋转排序数组中的最小值 II >>
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 = [0,1,2,4,5,6,7]</code> might become:</p>
<ul>
<li><code>[4,5,6,7,0,1,2]</code> if it was rotated <code>4</code> times.</li>
<li><code>[0,1,2,4,5,6,7]</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> of <strong>unique</strong> elements, return <em>the minimum element of this array</em>.</p>
<p>You must write an algorithm that runs in <code>O(log n) time</code>.</p>
<p> </p>
<p><strong class="example">Example 1:</strong></p>
<pre>
<strong>Input:</strong> nums = [3,4,5,1,2]
<strong>Output:</strong> 1
<strong>Explanation:</strong> The original array was [1,2,3,4,5] rotated 3 times.
</pre>
<p><strong class="example">Example 2:</strong></p>
<pre>
<strong>Input:</strong> nums = [4,5,6,7,0,1,2]
<strong>Output:</strong> 0
<strong>Explanation:</strong> The original array was [0,1,2,4,5,6,7] and it was rotated 4 times.
</pre>
<p><strong class="example">Example 3:</strong></p>
<pre>
<strong>Input:</strong> nums = [11,13,15,17]
<strong>Output:</strong> 11
<strong>Explanation:</strong> The original array was [11,13,15,17] and it was rotated 4 times.
</pre>
<p> </p>
<p><strong>Constraints:</strong></p>
<ul>
<li><code>n == nums.length</code></li>
<li><code>1 <= n <= 5000</code></li>
<li><code>-5000 <= nums[i] <= 5000</code></li>
<li>All the integers of <code>nums</code> are <strong>unique</strong>.</li>
<li><code>nums</code> is sorted and rotated between <code>1</code> and <code>n</code> times.</li>
</ul>
> [!tip]- Hint 1
>
> Array was originally in ascending order. Now that the array is rotated, there would be a point in the array where there is a small deflection from the increasing sequence. eg. The array would be something like [4, 5, 6, 7, 0, 1, 2].
> [!tip]- Hint 2
>
> You can divide the search space into two and see which direction to go.
Can you think of an algorithm which has O(logN) search complexity?
> [!tip]- Hint 3
>
> <ol>
<li>All the elements to the left of inflection point > first element of the array.</li>
<li>All the elements to the right of inflection point < first element of the array.</li>
<ol>
---
[submissions](https://leetcode.com/problems/find-minimum-in-rotated-sorted-array/submissions/) | [solutions](https://leetcode.com/problems/find-minimum-in-rotated-sorted-array/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 = [0,1,2,4,5,6,7]</code> 在变化后可能得到：
<ul>
<li>若旋转 <code>4</code> 次，则可以得到 <code>[4,5,6,7,0,1,2]</code></li>
<li>若旋转 <code>7</code> 次，则可以得到 <code>[0,1,2,4,5,6,7]</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>给你一个元素值 <strong>互不相同</strong> 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>你必须设计一个时间复杂度为 <code>O(log n)</code> 的算法解决此问题。</p>
<p> </p>
<p><strong>示例 1：</strong></p>
<pre>
<strong>输入：</strong>nums = [3,4,5,1,2]
<strong>输出：</strong>1
<strong>解释：</strong>原数组为 [1,2,3,4,5] ，旋转 3 次得到输入数组。
</pre>
<p><strong>示例 2：</strong></p>
<pre>
<strong>输入：</strong>nums = [4,5,6,7,0,1,2]
<strong>输出：</strong>0
<strong>解释：</strong>原数组为 [0,1,2,4,5,6,7] ，旋转 4 次得到输入数组。
</pre>
<p><strong>示例 3：</strong></p>
<pre>
<strong>输入：</strong>nums = [11,13,15,17]
<strong>输出：</strong>11
<strong>解释：</strong>原数组为 [11,13,15,17] ，旋转 4 次得到输入数组。
</pre>
<p> </p>
<p><strong>提示：</strong></p>
<ul>
<li><code>n == nums.length</code></li>
<li><code>1 <= n <= 5000</code></li>
<li><code>-5000 <= nums[i] <= 5000</code></li>
<li><code>nums</code> 中的所有整数 <strong>互不相同</strong></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>
> [!tip]- 提示 1
>
> Array was originally in ascending order. Now that the array is rotated, there would be a point in the array where there is a small deflection from the increasing sequence. eg. The array would be something like [4, 5, 6, 7, 0, 1, 2].
> [!tip]- 提示 2
>
> You can divide the search space into two and see which direction to go.
Can you think of an algorithm which has O(logN) search complexity?
> [!tip]- 提示 3
>
> <ol>
<li>All the elements to the left of inflection point > first element of the array.</li>
<li>All the elements to the right of inflection point < first element of the array.</li>
<ol>
---
[提交记录](https://leetcode.cn/problems/find-minimum-in-rotated-sorted-array/submissions/) | [题解](https://leetcode.cn/problems/find-minimum-in-rotated-sorted-array/solution/)
Solutions & Notes
properties:
note.updated:
displayName: Last Updated
note.relative_links:
displayName: Related Links
note.desc:
displayName: Description
note.grade:
displayName: Rating
note.program_language:
displayName: Language
note.time_complexity:
displayName: TC
note.space_complexity:
displayName: SC
views:
- type: table
name: Solutions & Notes
filters:
and:
- file.hasLink(this.file)
- file.tags.containsAny("leetcode/solution", "leetcode/note")
order:
- file.name
- desc
- program_language
- time_complexity
- space_complexity
- grade
- relative_links
- updated
sort:
- property: grade
direction: ASC
- property: time_complexity
direction: ASC
- property: program_language
direction: ASC
columnSize:
file.name: 104
note.space_complexity: 65
note.grade: 126
Similar Problems
properties:
note.lcTopics:
displayName: Topics
note.lcAcRate:
displayName: AC Rate
note.favorites:
displayName: Favorites
note.grade:
displayName: Rating
note.translatedTitle:
displayName: Title (CN)
note.lcDifficulty:
displayName: Difficulty
views:
- type: table
name: Similar Problems
filters:
and:
- file.hasLink(this.file)
- similarQuestions.contains(this.file)
order:
- file.name
- translatedTitle
- lcTopics
- lcDifficulty
- lcAcRate
- grade
- favorites
sort:
- property: file.name
direction: ASC
- property: lcTopics
direction: DESC
columnSize:
note.translatedTitle: 240
note.lcTopics: 347
note.lcAcRate: 75
note.grade: 122