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最近阅读<<我的第一本算法书>>(【日】石田保辉；宫崎修一)
本系列笔记拟采用golang练习之
堆排序
堆排序的特点是利用了数据结构中的堆。
首先，在堆中存储所有的数据，并按降序来构建堆。
为了排序，需要再从堆中把数据一个个取出来。
堆排序一开始需要将n个数据存进堆里，所需时间为O(nlogn)。
每轮取出最大的数据并重构堆所需要的时间为O(logn)。
由于总共有n轮，所以重构后排序的时间也是O(nlog n)。
因此，整体来看堆排序的时间复杂度为O(nlog n)。
这样来看，堆排序的运行时间比之前讲到的冒泡排序、选择排序、插入排序的时间O(n^2)都要短。
摘自 <<我的第一本算法书>> 【日】石田保辉；宫崎修一目标
- 构造一个堆, 并测试堆排序的效率
设计
- IHeap: 定义堆的接口
tArrayHeap
- 基于数组的堆的实现.
- 堆是一种特殊的二叉完全树: 父节点总是小于任意的子节点
堆的父子节点的索引存在线性关系, 以0下标为例
- parent.index = (node.index - 1) / 2
- leftChild.index = node.index*2 + 1
- rightChild.index = leftChild.index + 1
ISorter:
- 定义排序接口
- 定义值比较函数以兼容任意值类型
- 通过调整比较函数可实现倒序输出
tHeapSort
- 利用tArrayHeap进行堆排序
- 先把整个数组push进heap
- 然后逐个pop出来, 即可
单元测试
heap_sort_test.go, 测试过程与之前的冒泡, 选择, 插入等类似, 但测试数组扩大到10万元素.
package sorting
import (
"fmt"
"learning/gooop/sorting"
"learning/gooop/sorting/heap_sort"
"math/rand"
"testing"
"time"
)
func Test_HeapSort(t *testing.T) {
fnAssertTrue := func(b bool, msg string) {
if !b {
t.Fatal(msg)
}
}
reversed := false
fnCompare := func(a interface{}, b interface{}) sorting.CompareResult {
i1 := a.(int)
i2 := b.(int)
if i1 < i2 {
if reversed {
return sorting.GREATER
} else {
return sorting.LESS
}
} else if i1 == i2 {
return sorting.EQUAL
} else {
if reversed {
return sorting.LESS
} else {
return sorting.GREATER
}
}
}
fnTestSorter := func(sorter sorting.ISorter) {
reversed = false
// test simple array
samples := []interface{} { 2,3,1,5,4,7,6 }
sorter.Sort(samples, fnCompare)
fnAssertTrue(fmt.Sprintf("%v", samples) == "[1 2 3 4 5 6 7]", "expecting 1,2,3,4,5,6,7")
t.Log("pass sorting [2 3 1 5 4 7 6] >> [1 2 3 4 5 6 7]")
// test 10000 items sorting
rnd := rand.New(rand.NewSource(time.Now().UnixNano()))
sampleCount := 100*1000
t.Logf("prepare large array with %v items", sampleCount)
samples = make([]interface{}, sampleCount)
for i := 0;i < sampleCount;i++ {
samples[i] = rnd.Intn(sampleCount*10)
}
t.Logf("sorting large array with %v items", sampleCount)
t0 := time.Now().UnixNano()
sorter.Sort(samples, fnCompare)
cost := time.Now().UnixNano() - t0
for i := 1;i < sampleCount;i++ {
fnAssertTrue(fnCompare(samples[i-1], samples[i]) != sorting.GREATER, "expecting <=")
}
t.Logf("end sorting large array, cost = %v ms", cost / 1000000)
// test 0-20
sampleCount = 20
t.Log("sorting 0-20")
samples = make([]interface{}, sampleCount)
for i := 0;i < sampleCount;i++ {
for {
p := rnd.Intn(sampleCount)
if samples[p] == nil {
samples[p] = i
break
}
}
}
t.Logf("unsort = %v", samples)
sorter.Sort(samples, fnCompare)
t.Logf("sorted = %v", samples)
fnAssertTrue(fmt.Sprintf("%v", samples) == "[0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19]", "expecting 0-20")
t.Log("pass sorting 0-20")
// test special
samples = []interface{} {}
sorter.Sort(samples, fnCompare)
t.Log("pass sorting []")
samples = []interface{} { 1 }
sorter.Sort(samples, fnCompare)
t.Log("pass sorting [1]")
samples = []interface{} { 3,1 }
sorter.Sort(samples, fnCompare)
fnAssertTrue(fmt.Sprintf("%v", samples) == "[1 3]", "expecting 1,3")
t.Log("pass sorting [1 3]")
reversed = true
samples = []interface{} { 2, 3,1 }
sorter.Sort(samples, fnCompare)
fnAssertTrue(fmt.Sprintf("%v", samples) == "[3 2 1]", "expecting 3,2,1")
t.Log("pass sorting [3 2 1]")
}
t.Log("\ntesting HeapSort")
fnTestSorter(heap_sort.HeapSort)
}测试输出
10万元素排序只需数十毫秒,
确实比冒泡, 选择, 插入等排序有指数级的提升.
代价是多占用了一个堆的空间.
$ go test -v heap_sort_test.go
=== RUN Test_HeapSort
heap_sort_test.go:109:
testing HeapSort
heap_sort_test.go:48: pass sorting [2 3 1 5 4 7 6] >> [1 2 3 4 5 6 7]
heap_sort_test.go:53: prepare large array with 100000 items
heap_sort_test.go:59: sorting large array with 100000 items
heap_sort_test.go:66: end sorting large array, cost = 67 ms
heap_sort_test.go:70: sorting 0-20
heap_sort_test.go:81: unsort = [4 15 1 13 19 14 11 12 9 8 3 7 16 18 2 10 17 6 0 5]
heap_sort_test.go:84: sorted = [0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19]
heap_sort_test.go:86: pass sorting 0-20
heap_sort_test.go:91: pass sorting []
heap_sort_test.go:95: pass sorting [1]
heap_sort_test.go:100: pass sorting [1 3]
heap_sort_test.go:106: pass sorting [3 2 1]
--- PASS: Test_HeapSort (0.07s)
PASS
ok command-line-arguments 0.076sIHeap.go
定义堆的接口
package heap_sort
type IHeap interface {
Size() int
IsEmpty() bool
IsNotEmpty() bool
Push(value interface{})
Pop() (error, interface{})
}tArrayHeap
- 基于数组的堆的实现.
- 堆是一种特殊的二叉完全树: 父节点总是小于任意的子节点
堆的父子节点的索引存在线性关系, 以0下标为例
- parent.index = (node.index - 1) / 2
- leftChild.index = node.index*2 + 1
- rightChild.index = leftChild.index + 1
package heap_sort
import (
"errors"
"learning/gooop/sorting"
)
type tArrayHeap struct {
comparator sorting.CompareFunction
items []interface{}
size int
version int64
}
func newArrayHeap(comparator sorting.CompareFunction) IHeap {
return &tArrayHeap{
comparator: comparator,
items: make([]interface{}, 0),
size: 0,
version: 0,
}
}
func (me *tArrayHeap) Size() int {
return me.size
}
func (me *tArrayHeap) IsEmpty() bool {
return me.size <= 0
}
func (me *tArrayHeap) IsNotEmpty() bool {
return !me.IsEmpty()
}
func (me *tArrayHeap) Push(value interface{}) {
me.version++
me.ensureSize(me.size + 1)
me.items[me.size] = value
me.size++
me.shiftUp(me.size - 1)
me.version++
}
func (me *tArrayHeap) ensureSize(size int) {
for ;len(me.items) < size; {
me.items = append(me.items, nil)
}
}
func (me *tArrayHeap) parentOf(i int) int {
return (i - 1) / 2
}
func (me *tArrayHeap) leftChildOf(i int) int {
return i*2 + 1
}
func (me *tArrayHeap) rightChildOf(i int) int {
return me.leftChildOf(i) + 1
}
func (me *tArrayHeap) last() (i int, v interface{}) {
if me.IsEmpty() {
return -1, nil
}
i = me.size - 1
v = me.items[i]
return i,v
}
func (me *tArrayHeap) shiftUp(i int) {
if i <= 0 {
return
}
v := me.items[i]
pi := me.parentOf(i)
pv := me.items[pi]
if me.comparator(v, pv) == sorting.LESS {
me.items[pi], me.items[i] = v, pv
me.shiftUp(pi)
}
}
func (me *tArrayHeap) Pop() (error, interface{}) {
if me.IsEmpty() {
return gNoMoreElementsError, nil
}
me.version++
top := me.items[0]
li, lv := me.last()
me.items[0] = nil
me.size--
if me.IsEmpty() {
return nil, top
}
me.items[0] = lv
me.items[li] = nil
me.shiftDown(0)
me.version++
return nil, top
}
func (me *tArrayHeap) shiftDown(i int) {
pv := me.items[i]
ok, ci, cv := me.minChildOf(i)
if ok && me.comparator(cv, pv) == sorting.LESS {
me.items[i], me.items[ci] = cv, pv
me.shiftDown(ci)
}
}
func (me *tArrayHeap) minChildOf(p int) (ok bool, i int, v interface{}) {
li := me.leftChildOf(p)
if li >= me.size {
return false, 0, nil
}
lv := me.items[li]
ri := me.rightChildOf(p)
if ri >= me.size {
return true, li, lv
}
rv := me.items[ri]
if me.comparator(lv, rv) == sorting.LESS {
return true, li, lv
} else {
return true, ri, rv
}
}
var gNoMoreElementsError = errors.New("no more elements")ISorter
- 定义排序接口
- 定义值比较函数以兼容任意值类型
- 通过调整比较函数可实现倒序输出
package sorting
type ISorter interface {
Sort(data []interface{}, comparator CompareFunction) []interface{}
}
type CompareFunction func(a interface{}, b interface{}) CompareResult
type CompareResult int
const LESS CompareResult = -1
const EQUAL CompareResult = 0
const GREATER CompareResult = 1tHeapSort
- 堆排序器, 实现ISorter接口
- 利用tArrayHeap进行堆排序
- 先把整个数组push进heap
- 然后逐个pop出来, 即可
package heap_sort
import "learning/gooop/sorting"
type tHeapSort struct {
}
func newHeapSort() sorting.ISorter {
return &tHeapSort{}
}
func (me *tHeapSort) Sort(data []interface{}, comparator sorting.CompareFunction) []interface{} {
heap := newArrayHeap(comparator)
for _,it := range data {
heap.Push(it)
}
for i,_ := range data {
e,v := heap.Pop()
if e == nil {
data[i] = v
} else {
panic(e)
}
}
return data
}
var HeapSort = newHeapSort()(end)
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