From 38d572915f7134212b2c483c568b283eb2088bc8 Mon Sep 17 00:00:00 2001 From: CyC2018 Date: Fri, 30 Oct 2026 20:18:35 +0800 Subject: [PATCH] =?UTF-8?q?Update=20Leetcode=20=E9=A2=98=E8=A7=A3=20-=20?= =?UTF-8?q?=E6=8E=92=E5=BA=8F.md?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit 补充快速选择的切分推导及示例配图,补充字符频率排序与颜色排序的解题思路说明,调整部分复杂度表述并补充参考资料。 --- notes/Leetcode 题解 - 排序.md | 30 +++++++++++++++++++++-------- notes/pics/lc-sort-quickselect.png | Bin 0 -> 155614 bytes 2 files changed, 22 insertions(+), 8 deletions(-) create mode 100644 notes/pics/lc-sort-quickselect.png diff --git a/notes/Leetcode 题解 - 排序.md b/notes/Leetcode 题解 - 排序.md index edf80633..c574574c 100644 --- a/notes/Leetcode 题解 - 排序.md +++ b/notes/Leetcode 题解 - 排序.md @@ -9,24 +9,23 @@ * [2. 按照字符出现次数对字符串排序](#2-按照字符出现次数对字符串排序) * [荷兰国旗问题](#荷兰国旗问题) * [1. 按颜色进行排序](#1-按颜色进行排序) + * [参考资料](#参考资料) ## 快速选择 -用于求解 **Kth Element** 问题,也就是第 K 个元素的问题。 +用于求解 Kth Element 问题,也就是第 K 个元素的问题。 可以使用快速排序的 partition() 进行实现。需要先打乱数组,否则最坏情况下时间复杂度为 O(N2)。 ## 堆 -用于求解 **TopK Elements** 问题,也就是 K 个最大元素的问题。使用大小为 K 的小顶堆来实现:不断地往小顶堆中插入新元素,当堆中元素的数量大于 K 时,移除堆顶元素,也就是当前堆中最小的元素,剩下的元素都为当前添加过的元素中最大的 K 个元素。插入和移除堆顶元素的时间复杂度都为 log2K。 +用于求解 TopK Elements 问题,也就是 K 个最大元素的问题。使用大小为 K 的小顶堆来实现:不断地往小顶堆中插入新元素,当堆中元素的数量大于 K 时,移除堆顶元素,也就是当前堆中最小的元素,剩下的元素都为当前添加过的元素中最大的 K 个元素。插入和移除堆顶元素的时间复杂度都为 O(logK)。 堆也可以用于求解 Kth Element 问题,得到了大小为 K 的小顶堆之后,堆顶元素就是第 K 大的元素。同理,求 K 个最小元素或者第 K 小的元素时使用大顶堆。 -快速选择也可以求解 TopK Elements 问题,因为找到 Kth Element 之后,再遍历一次数组,所有大于等于 Kth Element 的元素都是 TopK Elements。 - -可以看到,快速选择和堆排序都可以求解 Kth Element 和 TopK Elements 问题。 +快速选择也可以求解 TopK Elements 问题:快速选择结束时,第 K 大的元素已经位于下标 N - K,它右边的都不小于它,取数组最后 K 个元素即可,这 K 个元素之间不保证有序。不能简单地取出所有大于等于第 K 大元素的数,有重复值时会多于 K 个。 ### 1. Kth Element @@ -41,7 +40,7 @@ Output: 5 题目描述:找到数组中第 k 大的元素。 -**排序** :时间复杂度 O(NlogN),空间复杂度 O(1) +排序:时间复杂度 O(NlogN),空间复杂度 O(logN)(JDK 对基本类型的排序在部分输入下还会分配额外的数组)。 ```java public int findKthLargest(int[] nums, int k) { @@ -50,7 +49,7 @@ public int findKthLargest(int[] nums, int k) { } ``` -**堆** :时间复杂度 O(NlogK),空间复杂度 O(K)。 +堆:时间复杂度 O(NlogK),空间复杂度 O(K)。 ```java public int findKthLargest(int[] nums, int k) { @@ -64,7 +63,13 @@ public int findKthLargest(int[] nums, int k) { } ``` -**快速选择** :平均时间复杂度 O(N),空间复杂度 O(1) +快速选择:平均时间复杂度 O(N),空间复杂度 O(1)。 + +第 k 大的元素就是升序排序后下标为 N - k 的元素。partition() 与快速排序的[切分](算法%20-%20排序.md#2-切分)相同,返回切分元素的最终位置 j,它左边的元素都不大于它,右边的都不小于它。j 等于目标下标时直接得到答案;j 小于目标下标时只需要在右半边继续切分,否则在左半边,每次只处理一边,平均下来总的比较次数是 N + N / 2 + N / 4 + ... ≈ 2N。 + +以 [3, 2, 1, 5, 6, 4]、k = 2 为例(为便于对照没有打乱),两轮切分就找到了答案: + +

```java public int findKthLargest(int[] nums, int k) { @@ -179,6 +184,8 @@ Explanation: So 'e' must appear before both 'r' and 't'. Therefore "eetr" is also a valid answer. ``` +把每个字符按出现次数放进桶中,从出现次数最多的桶开始,把每个字符重复它的出现次数拼接起来。 + ```java public String frequencySort(String s) { Map frequencyForNum = new HashMap<>(); @@ -230,6 +237,8 @@ Output: [0,0,1,1,2,2] 题目描述:只有 0/1/2 三种颜色。 +三个指针把数组分成四段:[0, zero] 全是 0,[zero + 1, one - 1] 全是 1,[one, two - 1] 还没处理,[two, n - 1] 全是 2。one 指向的数为 0 时,与 zero + 1 交换,交换过来的数一定是 1(或者就是它自己),因此 one 可以前进;为 2 时与 two - 1 交换,换过来的数还没看过,one 不能前进。 + ```java public void sortColors(int[] nums) { int zero = -1, one = 0, two = nums.length; @@ -250,3 +259,8 @@ private void swap(int[] nums, int i, int j) { nums[j] = t; } ``` + +## 参考资料 + +- [LeetCode 题库](https://leetcode.com/problemset/) +- Sedgewick R, Wayne K. 算法(第 4 版)[M]. 人民邮电出版社, 2012. diff --git a/notes/pics/lc-sort-quickselect.png b/notes/pics/lc-sort-quickselect.png new file mode 100644 index 0000000000000000000000000000000000000000..827728b7274d05256981b4a3411a46b9cec13223 GIT binary patch literal 155614 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