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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

快速排序(Quick Sort)

快速排序算法首先会在序列中随机选择一个基准值（pivot），
然后将除了基准值以外的数, 
分为“比基准值小的数”和“比基准值大的数”这两个类别，
再将其排列成以下形式:
[ 比基准值小的数 ] 基准值 [ 比基准值大的数 ]

接着，对两个“[]”中的数据进行排序之后，
整体的排序便完成了。

对“[]”里面的数据进行排序时同样也会使用快速排序。

快速排序是一种“分治法”。
它将原本的问题分成两个子问题（比基准值小的数和比基准值大的数），
然后再分别解决这两个问题(递归地)。

平均运行时间为O(nlogn)

摘自 <<我的第一本算法书>> 【日】石田保辉；宫崎修一

流程(非递归, 原地快速排序)

1. 给定待排序数组data[N]
2. 定义待排序栈stack, 其中元素是一个(left, right)整型坐标, 表示待排序子序列的范围
3. 初始时, 将(0, N-1)压入stack, 表示需要将整个序列进行排序
4. 当stack不为空时, 循环执行:
   1. 待排序子序列出栈: left, right = stack.pop()
   2. 取基准值v = data[left], 然后data[left]置为nil, 腾出一个格子备用
   3. 取左指针l = left, 右指针r = right, 当前指针标识(左/右)rside = true
   4. 如果rside == true, 将右指针r向左移动, 直到: data[r] < v, 或r=l
   5. 如果找到data[r] < v, 则把data[r]置入data[l]指向的空位, data[r]设nil, 腾出一个格子
   6. 如果rside == false, 将左指针l向右移动, 直到: data[l] > v, 或l=r
   7. 如果找到data[l] > v, 则把data[l]置入data[r]指向的空位, data[l]设nil, 腾出一个格子
   8. 如果l == r, 左右序列切分完成, 将基准值v置入data[l], 返回
   9. 循环执行步骤4-8
5. stack为空, 排序完成

为什么要非递归

• 极端情况下(比如特别大的数组, 刚好已经是倒序排列, 而每次取基准值是取left位置), 递归算法可能导致栈嵌套过深, 一个是占用大量内存, 二个是可能导致栈溢出错误.
• 快速排序需要左右子序列的中间结果, 再进行合并, 因此无法通过尾递归优化消除栈嵌套

目标

• 实现并验证快速排序
• 使用辅助的子序列坐标栈, 实现非递归执行
• 原地排序, 不占用额外空间

设计

• ISorter: 定义排序器接口. 定义值比较函数以兼容任意数值类型, 通过调整比较函数实现倒序排序
• tQStack: 实现一个堆栈, 辅助快速排序时, 记录待排序的子序列坐标
• tQuickSort: 非递归的原地快速排序器, 实现ISorter接口, 使用辅助栈消除递归

单元测试

quick_sort_test.go, 测试过程与堆排序, 归并排序类似, 样本规模为10万元素

package sorting

import (
    "fmt"
    "learning/gooop/sorting"
    "learning/gooop/sorting/quick_sort"
    "math/rand"
    "testing"
    "time"
)

func Test_QuickSort(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 }
        samples = 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()))
        for plus := 0;plus < 5;plus++ {
            sampleCount := 100 * 1000 + plus
            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()
            samples = 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)

        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{} {}
        samples = sorter.Sort(samples, fnCompare)
        t.Log("pass sorting []")

        samples = []interface{} { 1 }
        samples = sorter.Sort(samples, fnCompare)
        t.Log("pass sorting [1]")

        samples = []interface{} { 3,1 }
        samples = 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 }
        samples = 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 QuickSorter")
    fnTestSorter(quick_sort.QuickSorter)
}

测试输出

• 快速排序真的很快, 与堆排序,归并排序是一个数量级, 10万随机元素排序耗时仅数十毫秒
• 对随机数据的排序比归并排序还稍快一些, 这可能是因为原地排序不需要预分配缓冲区

$ go test -v quick_sort_test.go 
=== RUN   Test_QuickSort
    quick_sort_test.go:111: 
        testing QuickSorter
    quick_sort_test.go:48: pass sorting [2 3 1 5 4 7 6] >> [1 2 3 4 5 6 7]
    quick_sort_test.go:54: prepare large array with 100000 items
    quick_sort_test.go:60: sorting large array with 100000 items
    quick_sort_test.go:67: end sorting large array, cost = 27 ms
    quick_sort_test.go:54: prepare large array with 100001 items
    quick_sort_test.go:60: sorting large array with 100001 items
    quick_sort_test.go:67: end sorting large array, cost = 28 ms
    quick_sort_test.go:54: prepare large array with 100002 items
    quick_sort_test.go:60: sorting large array with 100002 items
    quick_sort_test.go:67: end sorting large array, cost = 33 ms
    quick_sort_test.go:54: prepare large array with 100003 items
    quick_sort_test.go:60: sorting large array with 100003 items
    quick_sort_test.go:67: end sorting large array, cost = 32 ms
    quick_sort_test.go:54: prepare large array with 100004 items
    quick_sort_test.go:60: sorting large array with 100004 items
    quick_sort_test.go:67: end sorting large array, cost = 27 ms
    quick_sort_test.go:72: sorting 0-20
    quick_sort_test.go:83: unsort = [11 3 4 2 9 19 18 7 12 6 13 5 10 0 15 14 17 1 8 16]
    quick_sort_test.go:86: sorted = [0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19]
    quick_sort_test.go:88: pass sorting 0-20
    quick_sort_test.go:93: pass sorting []
    quick_sort_test.go:97: pass sorting [1]
    quick_sort_test.go:102: pass sorting [1 3]
    quick_sort_test.go:108: pass sorting [3 2 1]
--- PASS: Test_QuickSort (0.18s)
PASS
ok      command-line-arguments  0.184s

ISorter.go

定义排序器接口. 定义值比较函数以兼容任意数值类型, 通过调整比较函数实现倒序排序

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

tQStack.go

实现一个堆栈, 辅助快速排序时, 记录待排序的子序列坐标

package quick_sort

type tQStack struct {
    stack []tIntPair
    capacity int
    size int
}

type tIntPair [2]int
var gEmptyPair = [2]int{ -1, -1 }

func newQStack() *tQStack {
    return &tQStack{
        stack: make([]tIntPair, 0),
        capacity: 0,
        size: 0,
    }
}

func (me *tQStack) push(left,right int) {
    node := tIntPair([2]int{left,right})
    if me.size < me.capacity {
        me.stack[me.size] = node
    } else {
        me.stack = append(me.stack, node)
        me.capacity++
    }
    me.size++
}

func (me *tQStack) pop() (left, right int) {
    me.size--
    it := me.stack[me.size]
    me.stack[me.size] = gEmptyPair
    return it[0], it[1]
}

func (me *tQStack) isEmpty() bool {
    return me.size <= 0
}

func (me *tQStack) isNotEmpty() bool {
    return me.size > 0
}

tQuickSort.go

非递归的原地快速排序器, 实现ISorter接口, 使用辅助栈消除递归

package quick_sort

import (
    "learning/gooop/sorting"
)

type tQuickSort struct {
}

func newQuickSort() sorting.ISorter {
    return &tQuickSort{}
}

func (me *tQuickSort) Sort(data []interface{}, comparator sorting.CompareFunction) []interface{} {
    if data == nil {
        return nil
    }

    size := len(data)
    if size <= 1 {
        return data
    }

    if size == 2 {
        if comparator(data[0], data[1]) == sorting.GREATER {
            data[0],data[1] = data[1], data[0]
            return data
        }
    }

    stack := newQStack()
    stack.push(0, size - 1)
    me.qsort(data, comparator, stack)
    return data
}

func (me *tQuickSort) qsort(data []interface{}, comparator sorting.CompareFunction, stack *tQStack) {
    for ;stack.isNotEmpty(); {
        left, right := stack.pop()
        lfrom, lto, rfrom, rto := me.split(data, comparator, left, right)

        if lfrom < lto {
            stack.push(lfrom, lto)
        }
        if rfrom < rto  {
            stack.push(rfrom, rto)
        }
    }
}

func (me *tQuickSort) split(data []interface{}, comparator sorting.CompareFunction, left int, right int) (lfrom, lto, rfrom, rto int) {
    if left >= right {
        return
    }

    v := data[left]
    l := left
    r := right
    rside := true

    for {
        hit := false
        if rside {
            for ; r > l; r-- {
                if comparator(data[r], v) == sorting.LESS {
                    hit = true
                    break
                }
            }

            if hit {
                data[l], data[r] = data[r], nil
                l++
                rside = false
            }
        } else {
            for ; l < r;l++ {
                if comparator(data[l], v) == sorting.GREATER {
                    hit = true
                    break
                }
            }

            if hit {
                data[r], data[l] = data[l], nil
                r--
                rside = true
            }
        }

        if l == r {
            data[l] = v
            break
        }
    }

    return left, l - 1, r + 1, right
}

var QuickSorter = newQuickSort()

(end)

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