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heap_sort.go
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/**
* Copyright © https://github.com./jarry All rights reserved.
* @author: [email protected]
* @version: 1.0
*/
package main
import (
"fmt"
"time"
)
/* 根据完全二叉树结构性质，父子节点与数组下标的关系，通过数组下标i得到节点位置 */
// 获取父节点
func getParent(i int) int {
return int((i - 1) / 2)
}
// 获取左节点
func getLeft(i int) int {
return 2*i + 1
}
// 获取右节点
func getRight(i int) int {
return 2*i + 2
}
// 始终保持大顶堆特性, 构建大顶堆的递归写法
func maxHeapify(arr []int, idx int, size int) {
var max = idx
var left = getLeft(idx)
var right = getRight(idx)
// 获取最大数的位置
if left < size && arr[left] > arr[max] {
max = left
}
if right < size && arr[right] > arr[max] {
max = right
}
fmt.Println("idx=", idx, "left=", left, "right=", right, "max=", max, "size:", size)
if max != idx {
// 保持最大顶堆，如果当前父节点小于子节点，则进行交换
arr[idx], arr[max] = arr[max], arr[idx]
// 继续递归执行，直到整棵树符合最大堆特性
maxHeapify(arr, max, size)
}
}
// 堆排序算法
func heapSort(arr []int) []int {
var arrLen = len(arr)
// 最底层的父节点
var parent = getParent(arrLen) - 1
// 最底层的子节点
var child = arrLen - 1
// 从最后的父节点开始遍历，把最大的那个父节点冒出到堆顶
for ; parent >= 0; parent-- {
maxHeapify(arr, parent, arrLen)
fmt.Println("parent sort:", parent, arr)
}
fmt.Println("child start:", "parent=", parent, " child=", child)
// 从子节点往上开始交换和保持大顶堆
for child > 0 {
// 将顶端的父节点与当前子节点互换
arr[0], arr[child] = arr[child], arr[0]
// 自最底层往上遍历排序
maxHeapify(arr, 0, child)
fmt.Println("child sort:", child, arr)
child--
}
return arr
}
// test
func main() {
fmt.Println("heap sort1:")
time1 := time.Now()
data1 := []int{7, 11, 9, 10, 12, 13, 8}
fmt.Println(heapSort(data1[:]))
fmt.Println("data1 end. cost:", time.Since(time1))
}
/*
oringal array: [7, 11, 9, 10, 12, 13, 8]
heap:
7(0)
/ \
11(1) 9(2)
/ \ / \
10(3) 12(4) 13(5) 8(6)
父节点步骤，构建大顶堆，父节点要大于左右子节点
1. maxHeapify: idx= 2 left= 5 right= 6 max= 5 size= 7
7(0)
/ \
11(1) 13(2)
/ \ / \
10(3) 12(4) 9(5) 8(6)
2. maxHeapify: idx= 1 left= 3 right= 4 max= 4 size= 7
7(0)
/ \
12(1) 13(2)
/ \ / \
10(3) 11(4) 9(5) 8(6)
3. maxHeapify: idx= 0 left= 1 right= 2 max= 2 size= 7
13(0)
/ \
12(1) 7(2)
/ \ / \
10(3) 11(4) 9(5) 8(6)
3.1 maxHeapify recursion: idx= 2 left= 5 right= 6 max= 5 size= 7
13(0)
/ \
12(1) 9(2)
/ \ / \
10(3) 11(4) 7(5) 8(6)
子节点堆排序:
1. swap, child = 6:
8(0)
/ \
12(1) 9(2)
/ \ / \
10(3) 11(4) 7(5) 13(6)
1.1 maxHeapify: idx= 0 left= 1 right= 2 max= 1 size= 6
12(0)
/ \
8(1) 9(2)
/ \ / \
10(3) 11(4) 7(5) 13(6)
1.2 maxHeapify recursion: idx= 1 left= 3 right= 4 max= 4 size= 6
12(0)
/ \
11(1) 9(2)
/ \ / \
10(3) 8(4) 7(5) 13(6)
2. swap, child = 5:
7(0)
/ \
11(1) 9(2)
/ \ / \
10(3) 8(4) 12(5) 13(6)
2.1 maxHeapify: idx= 0 left= 1 right= 2 max= 1 size= 5
11(0)
/ \
7(1) 9(2)
/ \ / \
10(3) 8(4) 12(5) 13(6)
2.2 maxHeapify recursion: idx= 1 left= 3 right= 4 max= 3 size= 5
11(0)
/ \
10(1) 9(2)
/ \ / \
7(3) 8(4) 12(5) 13(6)
3. swap, child = 4:
8(0)
/ \
10(1) 9(2)
/ \ / \
7(3) 11(4) 12(5) 13(6)
3.1 maxHeapify: idx= 0 left= 1 right= 2 max= 1 size= 4
10(0)
/ \
8(1) 9(2)
/ \ / \
7(3) 11(4) 12(5) 13(6)
3.2 maxHeapify recursion: idx= 1 left= 3 right= 4 max= 1 size= 4
4. swap, child = 3:
7(0)
/ \
8(1) 9(2)
/ \ / \
10(3) 11(4) 12(5) 13(6)
4.1 maxHeapify: idx= 0 left= 1 right= 2 max= 2 size= 3
9(0)
/ \
8(1) 7(2)
/ \ / \
10(3) 11(4) 12(5) 13(6)
4.2 maxHeapify recursion: idx= 2 left= 5 right= 6 max= 2 size= 3
5. swap, child = 2:
7(0)
/ \
8(1) 9(2)
/ \ / \
10(3) 11(4) 12(5) 13(6)
5.1 maxHeapify: idx= 0 left= 1 right= 2 max= 1 size= 2
8(0)
/ \
7(1) 9(2)
/ \ / \
10(3) 11(4) 12(5) 13(6)
5.2 maxHeapify recursion: idx= 1 left= 3 right= 4 max= 1 size= 2
6. swap, child = 1:
7(0)
/ \
8(1) 9(2)
/ \ / \
10(3) 11(4) 12(5) 13(6)
6.1 maxHeapify: idx= 0 left= 1 right= 2 max= 0 size= 1
*/
/*
jarry@jarrys-MacBook-Pro heapsort % go version
go version go1.19.5 darwin/amd64
jarry@jarrys-MacBook-Pro heapsort % go run heap_sort.go
heap sort1:
idx= 2 left= 5 right= 6 max= 5 size: 7
idx= 5 left= 11 right= 12 max= 5 size: 7
parent sort: 2 [7 11 13 10 12 9 8]
idx= 1 left= 3 right= 4 max= 4 size: 7
idx= 4 left= 9 right= 10 max= 4 size: 7
parent sort: 1 [7 12 13 10 11 9 8]
idx= 0 left= 1 right= 2 max= 2 size: 7
idx= 2 left= 5 right= 6 max= 5 size: 7
idx= 5 left= 11 right= 12 max= 5 size: 7
parent sort: 0 [13 12 9 10 11 7 8]
child start: parent= -1 child= 6
idx= 0 left= 1 right= 2 max= 1 size: 6
idx= 1 left= 3 right= 4 max= 4 size: 6
idx= 4 left= 9 right= 10 max= 4 size: 6
child sort: 6 [12 11 9 10 8 7 13]
idx= 0 left= 1 right= 2 max= 1 size: 5
idx= 1 left= 3 right= 4 max= 3 size: 5
idx= 3 left= 7 right= 8 max= 3 size: 5
child sort: 5 [11 10 9 7 8 12 13]
idx= 0 left= 1 right= 2 max= 1 size: 4
idx= 1 left= 3 right= 4 max= 1 size: 4
child sort: 4 [10 8 9 7 11 12 13]
idx= 0 left= 1 right= 2 max= 2 size: 3
idx= 2 left= 5 right= 6 max= 2 size: 3
child sort: 3 [9 8 7 10 11 12 13]
idx= 0 left= 1 right= 2 max= 1 size: 2
idx= 1 left= 3 right= 4 max= 1 size: 2
child sort: 2 [8 7 9 10 11 12 13]
idx= 0 left= 1 right= 2 max= 0 size: 1
child sort: 1 [7 8 9 10 11 12 13]
[7 8 9 10 11 12 13]
data1 end. cost: 213.241µs
*/