From 2b3cdfbc3fd5393f51a5deee6ec9b5002f63c6be Mon Sep 17 00:00:00 2001 From: "haiji.yang" Date: Wed, 30 Dec 2020 20:38:48 +0800 Subject: [PATCH] add heapSort :new: :book: --- note/datastructureAlgorithm/README.md | 2 + .../book/algorithm/tree/HeapSort.md | 155 ++++++++++++++++++ .../book/algorithm/tree/img/HeapSort01.jpg | Bin 0 -> 38259 bytes .../book/algorithm/tree/img/HeapSort02.jpg | Bin 0 -> 22497 bytes .../book/algorithm/tree/img/HeapSort03.jpg | Bin 0 -> 41672 bytes .../book/algorithm/tree/img/HeapSort04.jpg | Bin 0 -> 87349 bytes .../book/algorithm/tree/img/HeapSort05.jpg | Bin 0 -> 84857 bytes .../book/algorithm/tree/img/HeapSort06.jpg | Bin 0 -> 86704 bytes .../book/algorithm/tree/img/HeapSort07.jpg | Bin 0 -> 81150 bytes .../book/algorithm/tree/img/HeapSort08.jpg | Bin 0 -> 87819 bytes .../book/algorithm/tree/img/HeapSort09.jpg | Bin 0 -> 81561 bytes .../book/algorithm/tree/img/HeapSort10.jpg | Bin 0 -> 41884 bytes .../advanced/algorithm/sort/HeapSort.java | 82 +++++++++ 13 files changed, 239 insertions(+) create mode 100644 note/datastructureAlgorithm/book/algorithm/tree/HeapSort.md create mode 100644 note/datastructureAlgorithm/book/algorithm/tree/img/HeapSort01.jpg create mode 100644 note/datastructureAlgorithm/book/algorithm/tree/img/HeapSort02.jpg create mode 100644 note/datastructureAlgorithm/book/algorithm/tree/img/HeapSort03.jpg create mode 100644 note/datastructureAlgorithm/book/algorithm/tree/img/HeapSort04.jpg create mode 100644 note/datastructureAlgorithm/book/algorithm/tree/img/HeapSort05.jpg create mode 100644 note/datastructureAlgorithm/book/algorithm/tree/img/HeapSort06.jpg create mode 100644 note/datastructureAlgorithm/book/algorithm/tree/img/HeapSort07.jpg create mode 100644 note/datastructureAlgorithm/book/algorithm/tree/img/HeapSort08.jpg create mode 100644 note/datastructureAlgorithm/book/algorithm/tree/img/HeapSort09.jpg create mode 100644 note/datastructureAlgorithm/book/algorithm/tree/img/HeapSort10.jpg create mode 100644 source-code/src/main/java/com/javayh/advanced/algorithm/sort/HeapSort.java diff --git a/note/datastructureAlgorithm/README.md b/note/datastructureAlgorithm/README.md index 65c9a5f..fda5286 100644 --- a/note/datastructureAlgorithm/README.md +++ b/note/datastructureAlgorithm/README.md @@ -23,5 +23,7 @@ - [🔖 线性查找](book/algorithm/search/SeqSearch.md) - [🔖 二分查找](book/algorithm/search/BinarySearch.md) - [🔖 斐波那契(黄金分割法)查找算法](book/algorithm/search/GoldenSection.md) +##### [树结构](README.md) +- [🔖 堆排序](book/algorithm/tree/HeapSort.md) \ No newline at end of file diff --git a/note/datastructureAlgorithm/book/algorithm/tree/HeapSort.md b/note/datastructureAlgorithm/book/algorithm/tree/HeapSort.md new file mode 100644 index 0000000..6f6eba6 --- /dev/null +++ b/note/datastructureAlgorithm/book/algorithm/tree/HeapSort.md @@ -0,0 +1,155 @@ +## 堆排序 + +### 介绍 +1) 堆排序是利用堆这种数据结构而设计的一种排序算法,堆排序是一种选择排序,它的最坏,最好,平均时间复杂度均为 O(nlogn),它也是不稳定排序。 +2) 堆是具有以下性质的完全二叉树:每个结点的值都大于或等于其左右孩子结点的值,称为大顶堆, 注意 : 没有要求结点的左孩子的值和右孩子的值的大小关系。 +3) 每个结点的值都小于或等于其左右孩子结点的值,称为小顶堆 +4) 大顶堆举例说明 + +![大顶堆举例说明](img/HeapSort01.jpg) + +5) 小顶堆举例说明 + +![小顶堆举例说明](img/HeapSort02.jpg) + +6) 一般升序采用大顶堆,降序采用小顶堆 + +### 堆排序基本思想 +堆排序的基本思想是: +1) 将待排序序列构造成一个大顶堆 +2) 此时,整个序列的最大值就是堆顶的根节点。 +3) 将其与末尾元素进行交换,此时末尾就为最大值。 +4) 然后将剩余 n-1 个元素重新构造成一个堆,这样会得到 n 个元素的次小值。如此反复执行,便能得到一个有序序列了。 + +可以看到在构建大顶堆的过程中,元素的个数逐渐减少,最后就得到一个有序序列了. + +### 堆排序步骤图解说明 +要求:给你一个数组 {4,6,8,5,9} , 要求使用堆排序法,将数组升序排序。 + +- 步骤一 +构造初始堆。将给定无序序列构造成一个大顶堆(一般升序采用大顶堆,降序采用小顶堆)。原始的数组 [4, 6, 8, 5, 9] +1) .假设给定无序序列结构如下 + +![小顶堆举例说明](img/HeapSort03.jpg) + +2) .此时我们从最后一个非叶子结点开始(叶结点自然不用调整,第一个非叶子结点arr.length/2-1=5/2-1=1,也就是下面的 6 结点),从左至右,从下至上进行调整。 + +![小顶堆举例说明](img/HeapSort04.jpg) + +3) .找到第二个非叶节点 4,由于[4,9,8]中 9 元素最大,4 和 9 交换。 + +![小顶堆举例说明](img/HeapSort05.jpg) + +4) 这时,交换导致了子根[4,5,6]结构混乱,继续调整,[4,5,6]中 6 最大,交换 4 和 6。 + +![小顶堆举例说明](img/HeapSort06.jpg) + +此时,我们就将一个无序序列构造成了一个大顶堆。 + +- 步骤二 + 将堆顶元素与末尾元素进行交换,使末尾元素最大。然后继续调整堆,再将堆顶元素与末尾元素交换, +得到第二大元素。如此反复进行交换、重建、交换。 + +1) .将堆顶元素 9 和末尾元素 4 进行交换 + +![小顶堆举例说明](img/HeapSort07.jpg) + +2) .重新调整结构,使其继续满足堆定义 + +![小顶堆举例说明](img/HeapSort08.jpg) + +3) .再将堆顶元素 8 与末尾元素 5 进行交换,得到第二大元素 8. + +![小顶堆举例说明](img/HeapSort09.jpg) + +4) 后续过程,继续进行调整,交换,如此反复进行,最终使得整个序列有序 + +![小顶堆举例说明](img/HeapSort10.jpg) + +再简单总结下堆排序的基本思路: +1). 将无序序列构建成一个堆,根据升序降序需求选择大顶堆或小顶堆; +2). 将堆顶元素与末尾元素交换,将最大元素"沉"到数组末端; +3). 重新调整结构,使其满足堆定义,然后继续交换堆顶元素与当前末尾元素,反复执行调整+交换步骤, 直到整个序列有序。 + +### 堆排序代码实现 + +要求:给你一个数组 {4,6,8,5,9} , 要求使用堆排序法,将数组升序排序。代码实现:看老师演示: +说明: +1) 堆排序不是很好理解,老师通过 Debug 帮助大家理解堆排序 +2) 堆排序的速度非常快,在我的机器上 8 百万数据 3 秒左右。O(nlogn) +3) 代码实现 +```java +{ + public static void main(String[] args) { + //要求将数组进行升序排序 + int arr[] = {4, 6, 8, 5, 9}; + heapSort(arr); + System.out.println("堆排序后:"+ Arrays.toString(arr)); + } + + public static void heapSort(int arr[]) { + int temp = 0; + System.out.println("堆排序!!"); + // //分步完成 + //adjustHeap(arr, 1, arr.length); + //System.out.println("第一次" + Arrays.toString(arr)); // 4, 9, 8, 5, 6 + + //adjustHeap(arr, 0, arr.length); + //System.out.println("第 2 次" + Arrays.toString(arr)); // 9,6,8,5,4 + //完成我们最终代码 + //将无序序列构建成一个堆,根据升序降序需求选择大顶堆或小顶堆 + for (int i = arr.length / 2 - 1; i >= 0; i--) { + adjustHeap(arr, i, arr.length); + } + + /* + * 2).将堆顶元素与末尾元素交换,将最大元素"沉"到数组末端; + 3).重新调整结构,使其满足堆定义,然后继续交换堆顶元素与当前末尾元素,反复执行调整+交换步骤,直到整个序列有序。 + */ + for (int j = arr.length - 1; j > 0; j--) { + //交换 + temp = arr[j]; + arr[j] = arr[0]; + arr[0] = temp; + adjustHeap(arr, 0, j); + } + + } + //将一个数组(二叉树), 调整成一个大顶堆 + + /** + * 功能: 完成 将 以 i 对应的非叶子结点的树调整成大顶堆 + * 举例 int arr[] = {4, 6, 8, 5, 9}; => i = 1 => adjustHeap => 得 到 {4, 9, 8, 5, 6} + * 如果我们再次调用 adjustHeap 传入的是 i = 0 => 得到 {4, 9, 8, 5, 6} => {9,6,8,5, 4} + * + * @param arr 待调整的数组 + * @param i 表示非叶子结点在数组中索引 + * @param length 表示对多少个元素继续调整, length 是在逐渐的减少 + */ + private static void adjustHeap(int[] arr, int i, int length) { + int temp = arr[i];//先取出当前元素的值,保存在临时变量 + //开始调整 + //说明 + //1. k = i * 2 + 1 k 是 i 结点的左子结点 + for (int k = i * 2 + 1; k < length; k = k * 2 + 1) { + if (k + 1 < length && arr[k] < arr[k + 1]) { //说明左子结点的值小于右子结点的值 + k++; // k 指向右子结点 + } + if (arr[k] > temp) { + //如果子结点大于父结点 + arr[i] = arr[k]; //把较大的值赋给当前结点 + i = k; //!!! i 指向 k,继续循环比较 + } else { + break;//! + } + } + //当 for 循环结束后,我们已经将以 i 为父结点的树的最大值,放在了 最顶(局部) + arr[i] = temp;//将 temp 值放到调整后的位置 + } + +} +``` + + + + diff --git a/note/datastructureAlgorithm/book/algorithm/tree/img/HeapSort01.jpg b/note/datastructureAlgorithm/book/algorithm/tree/img/HeapSort01.jpg new file mode 100644 index 0000000000000000000000000000000000000000..b35ba3e3229501556107881f4c5181ccb7fb8786 GIT binary patch literal 38259 zcmb@u2Ut^Ev@RNZK}EWPfFecuma5e4RzN{OdNV{pK!^~L79fyqK?FoL0$~Fiq9C1s zlqA$dDWXI~S^^0qCJ0IiB-DfyZan9nbI*6abKgDpy|>8x60%k%V`R=T=NSM0FLow& zz5$Ng+g`H;?Ao;pa7*+9*r5O}1NQ9R{p%q*_KF_+4({8xckjN#2M+8%c;xVrBVvce z#Eu@5Jbv_;#4$0kX}^@q?E@;2(gqK+UmraCN8@`L*I|~bVZeh& zhYriioj574rmk^LQ_INM#Pq^Nv&&a(Z0)XIvv+g%@bvQb@eRBa6dZClG%PAQCN>Tl zpYZre%G1a`O=Re-{*%mc1#jsI024X=-jkW3a7l?cF`SeINQiei|4V9UCW- 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a/source-code/src/main/java/com/javayh/advanced/algorithm/sort/HeapSort.java b/source-code/src/main/java/com/javayh/advanced/algorithm/sort/HeapSort.java new file mode 100644 index 0000000..3fc937a --- /dev/null +++ b/source-code/src/main/java/com/javayh/advanced/algorithm/sort/HeapSort.java @@ -0,0 +1,82 @@ +package com.javayh.advanced.algorithm.sort; + +import java.util.Arrays; + +/** + *

+ * 堆排序 + *

+ * + * @author Dylan + * @version 1.0.0 + * @since 2020-12-30 8:28 PM + */ +public class HeapSort { + public static void main(String[] args) { + //要求将数组进行升序排序 + int arr[] = {4, 6, 8, 5, 9}; + heapSort(arr); + System.out.println("堆排序后:"+ Arrays.toString(arr)); + } + + public static void heapSort(int arr[]) { + int temp = 0; + System.out.println("堆排序!!"); + // //分步完成 + //adjustHeap(arr, 1, arr.length); + //System.out.println("第一次" + Arrays.toString(arr)); // 4, 9, 8, 5, 6 + + //adjustHeap(arr, 0, arr.length); + //System.out.println("第 2 次" + Arrays.toString(arr)); // 9,6,8,5,4 + //完成我们最终代码 + //将无序序列构建成一个堆,根据升序降序需求选择大顶堆或小顶堆 + for (int i = arr.length / 2 - 1; i >= 0; i--) { + adjustHeap(arr, i, arr.length); + } + + /* + * 2).将堆顶元素与末尾元素交换,将最大元素"沉"到数组末端; + 3).重新调整结构,使其满足堆定义,然后继续交换堆顶元素与当前末尾元素,反复执行调整+交换步骤,直到整个序列有序。 + */ + for (int j = arr.length - 1; j > 0; j--) { + //交换 + temp = arr[j]; + arr[j] = arr[0]; + arr[0] = temp; + adjustHeap(arr, 0, j); + } + + } + //将一个数组(二叉树), 调整成一个大顶堆 + + /** + * 功能: 完成 将 以 i 对应的非叶子结点的树调整成大顶堆 + * 举例 int arr[] = {4, 6, 8, 5, 9}; => i = 1 => adjustHeap => 得 到 {4, 9, 8, 5, 6} + * 如果我们再次调用 adjustHeap 传入的是 i = 0 => 得到 {4, 9, 8, 5, 6} => {9,6,8,5, 4} + * + * @param arr 待调整的数组 + * @param i 表示非叶子结点在数组中索引 + * @param length 表示对多少个元素继续调整, length 是在逐渐的减少 + */ + private static void adjustHeap(int[] arr, int i, int length) { + int temp = arr[i];//先取出当前元素的值,保存在临时变量 + //开始调整 + //说明 + //1. k = i * 2 + 1 k 是 i 结点的左子结点 + for (int k = i * 2 + 1; k < length; k = k * 2 + 1) { + if (k + 1 < length && arr[k] < arr[k + 1]) { //说明左子结点的值小于右子结点的值 + k++; // k 指向右子结点 + } + if (arr[k] > temp) { + //如果子结点大于父结点 + arr[i] = arr[k]; //把较大的值赋给当前结点 + i = k; //!!! i 指向 k,继续循环比较 + } else { + break;//! + } + } + //当 for 循环结束后,我们已经将以 i 为父结点的树的最大值,放在了 最顶(局部) + arr[i] = temp;//将 temp 值放到调整后的位置 + } + +} \ No newline at end of file

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