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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  0.076s

IHeap.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 = 1

tHeapSort

• 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)