diff --git a/QianHu/LeetCode/33-SearchInRotatedSortedArray/__init__.py b/QianHu/LeetCode/33-SearchInRotatedSortedArray/__init__.py new file mode 100644 index 0000000..7c68785 --- /dev/null +++ b/QianHu/LeetCode/33-SearchInRotatedSortedArray/__init__.py @@ -0,0 +1 @@ +# -*- coding: utf-8 -*- \ No newline at end of file diff --git a/QianHu/LeetCode/33-SearchInRotatedSortedArray/img_ex1.jpeg b/QianHu/LeetCode/33-SearchInRotatedSortedArray/img_ex1.jpeg new file mode 100644 index 0000000..90a9527 Binary files /dev/null and b/QianHu/LeetCode/33-SearchInRotatedSortedArray/img_ex1.jpeg differ diff --git a/QianHu/LeetCode/33-SearchInRotatedSortedArray/img_ex2.jpeg b/QianHu/LeetCode/33-SearchInRotatedSortedArray/img_ex2.jpeg new file mode 100644 index 0000000..cd153e3 Binary files /dev/null and b/QianHu/LeetCode/33-SearchInRotatedSortedArray/img_ex2.jpeg differ diff --git a/QianHu/LeetCode/33-SearchInRotatedSortedArray/img_ex3.jpeg b/QianHu/LeetCode/33-SearchInRotatedSortedArray/img_ex3.jpeg new file mode 100644 index 0000000..f67c511 Binary files /dev/null and b/QianHu/LeetCode/33-SearchInRotatedSortedArray/img_ex3.jpeg differ diff --git a/QianHu/LeetCode/33-SearchInRotatedSortedArray/main.py b/QianHu/LeetCode/33-SearchInRotatedSortedArray/main.py new file mode 100644 index 0000000..45f29a1 --- /dev/null +++ b/QianHu/LeetCode/33-SearchInRotatedSortedArray/main.py @@ -0,0 +1,39 @@ +# -*- coding: utf-8 -*- + + +class Solution(object): + def search(self, nums, target): + """ + :type nums: List[int] + :type target: int + :rtype: int + """ + low = 0 + high = len(nums) + while low < high: + mid = (low + high) // 2 + if target == nums[mid]: + return mid + if nums[mid] < nums[low]: + if target < nums[mid] or target >= nums[low]: + high = mid + else: + low = mid + 1 + elif nums[mid] > nums[high - 1]: + if target > nums[mid] or target < nums[low]: + low = mid + 1 + else: + high = mid + else: + if target > nums[mid]: + low = mid + 1 + else: + high = mid + return -1 + + +if __name__ == '__main__': + solution = Solution() + nums = [8, 1, 2, 3, 4, 5, 6, 7] + target = 6 + assert solution.search(nums, target) == 6 diff --git a/QianHu/LeetCode/33-SearchInRotatedSortedArray/readme.md b/QianHu/LeetCode/33-SearchInRotatedSortedArray/readme.md new file mode 100644 index 0000000..24da487 --- /dev/null +++ b/QianHu/LeetCode/33-SearchInRotatedSortedArray/readme.md @@ -0,0 +1,147 @@ +# LeetCode - 33. Search in Rotated Sorted Array + +link: [https://leetcode.com/problems/search-in-rotated-sorted-array/](https://leetcode.com/problems/search-in-rotated-sorted-array/) + +## 题目 + +Suppose an array sorted in ascending order is rotated at some pivot unknown to you beforehand. + +(i.e., [0,1,2,4,5,6,7] might become [4,5,6,7,0,1,2]). + +You are given a target value to search. If found in the array return its index, otherwise return -1. + +You may assume no duplicate exists in the array. + +Your algorithm's runtime complexity must be in the order of O(log n). + +Example 1: +``` +Input: nums = [4,5,6,7,0,1,2], target = 0 +Output: 4 +Example 2: +``` + +``` +Input: nums = [4,5,6,7,0,1,2], target = 3 +Output: -1 +``` +Accepted 334,119 Submissions 1,033,865 + + + +## 题目来源与背景故事 + +LeetCode上一道Medium题目，2018年1月面试Face++ Python后端开发时遇到过一样的题目，当时回答的不好，一直在纠结C点的位置关系；在参加2018年清华大学研究生入学考试，计算机基础知识综合912中，也遇到了类似的题目，那道题目和此题略有区别，将下图中的BC交换了，实际是一个类似y = 1 - |x|形状，即AC段单调递增，CB段单调递减，这题比较简单，所以回答的还可以 + + + + +## 问题描述 + +给定一个有序数组，将其中前面部分，放至后面，在这样的数组中查找特定值，要求复杂度O(log N) + +![ex1](img_ex1.jpeg) + +## 题目分析 +此题目实际是是一个二分查找的应用，需要对原先二分查找的基础上修改条件判断 + +我们将low设置为A处，high设置在B处（右侧），mid的位置就很关键了，mid可能会落在AC之间，也可能在CB之间，接下来分情况考虑，更定输入nums，查找目标target + + + +### 1. mid恰好就是target所在位置 + +这是最理想的情况，也是循环结束的条件之一 + + + +### 2. mid落在[A, C)之间 + +![ex2](img_ex2.jpeg) + +此时，mid的特点是，nums[C] < nums[B] < nums[low] <= nums[mid] <= nums[C] + +#### 2.1 target位于[low, mid)之间 + +此时如果target位于[low, mid)，那么target的特点是，nums[low] <= nums[target] < nums[mid]，此时target位于完全有序的[low, mid)区间，退化成了一个标准的二分查找 + +#### 2.2 target位于(mid, high)之间 + +此时如果target位于位于(mid, high)之间，此时退化成一个规模更小的旋转数组查找，此时target有两种情况 + +- 位于(mid, C)之间，此时target的特点是nums[mid] < target && nums[low] < target +- 位于[C, B)之间，此时target特点是nums[mid] > target && nums[low] > target + + + +### 3. mid落在[C, B)之间 + +![ex3](img_ex3.jpeg) + +此时，mid的特点是，nums[C] <= nums[low] <= nums[B] < nums[mid] < nums[C] + +#### 2.1 target位于[low, mid)之间 + +此时如果target位于[low, mid)，那么target的特点是， nums[target] < nums[low] < nums[mid]，此时退化成一个规模更小的旋转数组查找，此时target有两种情况 + +- 位于[low, C)之间，此时target的特点是nums[mid] < target && target >= nums[low] +- 位于[C, mid)之间，此时target特点是nums[mid] > target && nums[low] > target + +#### 2.2 target位于(mid, high)之间 + +此时如果target位于(mid, high)，那么target的特点是，nums[mid] < nums[target] < nums[high]，此时target位于完全有序的(mid, high)区间，退化成了一个标准的二分查找 + + + +## 代码实现 + +```python +# -*- coding: utf-8 -*- + + +class Solution(object): + def search(self, nums, target): + """ + :type nums: List[int] + :type target: int + :rtype: int + """ + low = 0 + high = len(nums) + while low < high: + mid = (low + high) // 2 + if target == nums[mid]: + return mid + if nums[mid] < nums[low]: + if target < nums[mid] or target >= nums[low]: + high = mid + else: + low = mid + 1 + elif nums[mid] > nums[high - 1]: + if target > nums[mid] or target < nums[low]: + low = mid + 1 + else: + high = mid + else: + if target > nums[mid]: + low = mid + 1 + else: + high = mid + return -1 + + +if __name__ == '__main__': + solution = Solution() + nums = [8, 1, 2, 3, 4, 5, 6, 7] + target = 6 + assert solution.search(nums, target) == 6 + +``` + + + +## 运行结果 + +| Time Submitted | Status | Runtime | Language | +| -------------- | ---------------------------------------- | ------- | -------- | +| a day ago | [Accepted](https://leetcode.com/submissions/detail/193848779/) | 24 ms | python | \ No newline at end of file diff --git a/QianHu/LeetCode/__init__.py b/QianHu/LeetCode/__init__.py new file mode 100644 index 0000000..7c68785 --- /dev/null +++ b/QianHu/LeetCode/__init__.py @@ -0,0 +1 @@ +# -*- coding: utf-8 -*- \ No newline at end of file diff --git a/QianHu/readme.md b/QianHu/readme.md index f596e64..e1bab37 100644 --- a/QianHu/readme.md +++ b/QianHu/readme.md @@ -1,4 +1,7 @@ # QianHu贡献内容 -1.真二叉树重构 +## Tsinghua DS MOOC +### 1.真二叉树重构（ProperRebuild） +## LeetCode +### 33.Search in Rotated Sorted Array