手撸golang 基本数据结构与算法 哈希表

缘起

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

哈希表

哈希表存储的是由键（key）和值（value）组成的数据。
在哈希表中，我们可以利用哈希函数快速访问到数组中的目标数据。

如果发生哈希冲突(哈希函数对不同的键, 返回了相同的哈希值)，
就使用链表进行存储(因此, 哈希表一般至少是数组+链表的二维结构)。

如果数组的空间太小，
使用哈希表的时候就容易发生冲突，
线性查找的使用频率也会更高；
反过来，如果数组的空间太大，
就会出现很多空箱子，造成内存的浪费。

摘自 <<我的第一本算法书>>(【日】石田保辉；宫崎修一)

目标

• 实现一个哈希表, 提供对键值对数据的增删改查, 且性能不能太差

• 物理结构

  • 采用分区 + 数组 + 链表的三维结构
  • 分区是一个双向链表, 由小到大呈2次幂增长
  • 当前分区总是指向最新也是最大的那个分区
  • 查找某个键时, 需要遍历所有分区

• 哈希函数

  • 合适的哈希函数对性能影响非常巨大
  • 对哈希函数的要求一般是足够快, 足够"散", 对不同键值最好能随机均匀分布
  • 本示例采用hash/crc64, 多项式为ECMA
  • 如果哈希函数的计算比较耗时, 则应当尽可能重复利用计算结果

• 扩容与缩容

  • 扩容

    • 填充因子为3/4, 即当前分区的元素数>容量的3/4时, 创建2倍大的新分区
    • 扩容不做任何拷贝和rehash.
    • 扩容后, 非当前分区变成只读和只删.
  • 缩容: 当某个分区未持有任何元素, 且不为当前分区时, 删除此分区

设计

• IHasher: 哈希支持接口, 定义哈希计算函数, 和键值相等比较函数
• IMap: 哈希表接口
• IMapIterator: 哈希表迭代器接口

• tCrc64Hasher:

  • 基于hash/crc64, 实现IHasher接口.
  • 支持多种键类型
  • 对于整型的键, 返回自身;
  • 其他类型的键, 转为%v字符串再计算crc64的哈希值.
• tHashMap: 哈希表的实现, 使用分区(双链)+数组+链表(单链)三维结构
• tPartition: 哈希表分区. 其大小呈2次幂
• tBucket: 哈希桶, 每个桶内的任何元素, 哈希值是一致的
• tHashMapIterator: 哈希表迭代器的实现

单元测试

hashmap_test.go, 除基本功能测试, 还测试了百万键值插入+遍历的性能

package data_structure

import (
    "fmt"
    "learning/gooop/data_structure/hashmap"
    "strconv"
    "testing"
    "time"
)

func Test_HashMap(t *testing.T) {
    fnAssertTrue := func(b bool, msg string) {
        if !b {
            t.Fatal(msg)
        }
    }

    fnEquals := func(a interface{}, b interface{}) bool {
        i1,b1 := a.(int)
        if b1 {
            i2,b2 := b.(int)
            if b2 {
                return i1 == i2
            }
        }

        s1,b1 := a.(string)
        if b1 {
            s2,b2 := b.(string)
            if b2 {
                return s1 == s2
            }
        }

        return a == b
    }

    hasher := hashmap.NewCrc64Hashful(fnEquals)
    hm := hashmap.NewHashMap(hasher, 2)

    hm.Put(1, "10")
    t.Log(hm)
    fnAssertTrue(hm.Size() == 1, "expecting size == 1")
    fnAssertTrue(hm.IsNotEmpty(), "expecting not empty")

    ok,v := hm.Get(1)
    fnAssertTrue(ok, "expecting ok")
    fnAssertTrue(v == "10", "expecting 10")

    hm.Put(2, "20")
    hm.Put(3, "30")
    hm.Put(4, "40")
    hm.Put(5, "50")
    t.Log(hm)
    fnAssertTrue(hm.Size() == 5, "expecting size == 5")
    ok,v = hm.Get(2)
    fnAssertTrue(ok == true && v == "20", "expecting true and 20")

    hm.Clear()
    t.Log(hm)
    fnAssertTrue(hm.Size() == 0, "expecting size == 0")
    fnAssertTrue(hm.IsEmpty(), "expecting empty")

    iter := hm.Iterator()
    fnAssertTrue(!iter.More(), "expecting no more")

    hm.Put(1, "10")
    hm.Put(2, "20")
    hm.Put(3, "30")
    t.Log(hm)
    fnAssertTrue(hm.Has(1) && hm.Has(2) && hm.Has(3) && !hm.Has(4), "expecting has 1,2,3")

    hm.Put(4, "40")
    hm.Put(5, "50")
    hm.Put(6, "60")
    t.Log(hm)
    iter = hm.Iterator()
    fnAssertTrue(iter.More(), "expecting more")
    e,k,v := iter.Next()
    t.Logf("%v>%s", k, v)
    fnAssertTrue(e == nil, "e == nil")
    e,k,v = iter.Next()
    t.Logf("%v>%s", k, v)
    fnAssertTrue(e == nil, "e == nil")
    e,k,v = iter.Next()
    t.Logf("%v>%s", k, v)
    fnAssertTrue(e == nil, "e == nil")
    e,k,v = iter.Next()
    t.Logf("%v>%s", k, v)
    fnAssertTrue(e == nil, "e == nil")
    e,k,v = iter.Next()
    t.Logf("%v>%s", k, v)
    fnAssertTrue(e == nil, "e == nil")
    e,k,v = iter.Next()
    t.Logf("%v>%s", k, v)
    fnAssertTrue(e == nil, "e == nil")
    e,k,v = iter.Next()
    fnAssertTrue(e != nil, "expecting e != nil")

    ok,v = hm.Remove(3)
    t.Log(hm)
    fnAssertTrue(ok && v == "30" && hm.Size() == 5, "expecting remove 30")

    ok,v = hm.Remove(2)
    t.Log(hm)
    fnAssertTrue(ok && v == "20" && hm.Size() == 4, "expecting remove 20")

    t0 := time.Now().UnixNano()
    hm.Clear()
    size := 1000 * 1000
    for i := 0; i < size;i++ {
        hm.Put(strconv.Itoa(i), i)
    }
    millis := (time.Now().UnixNano() - t0) / 1000000
    t.Logf("putting %v string>int = %v ms", size, millis)
    fnAssertTrue(hm.Size() == size, fmt.Sprintf("expecting %v", size))

    for i := 0;i < size;i++ {
        ok, v = hm.Get(strconv.Itoa(i))
        fnAssertTrue(ok == true && v == i, "expecting i")
    }
}

测试输出

$ go test -v hashmap_test.go 
=== RUN   Test_HashMap
    hashmap_test.go:42: s=1,v=1 p[1:b[1 1]]
    hashmap_test.go:54: s=5,v=5 p[4:b[1 4],5:b[1 5]] p[1:b[1 1],2:b[1 2],3:b[1 3]]
    hashmap_test.go:60: s=0,v=6 p[]
    hashmap_test.go:70: s=3,v=9 p[1:b[1 1],2:b[1 2],3:b[1 3]]
    hashmap_test.go:76: s=6,v=12 p[1:b[1 1],2:b[1 2],3:b[1 3],4:b[1 4],5:b[1 5],6:b[1 6]]
    hashmap_test.go:80: 1>10
    hashmap_test.go:83: 2>20
    hashmap_test.go:86: 3>30
    hashmap_test.go:89: 4>40
    hashmap_test.go:92: 5>50
    hashmap_test.go:95: 6>60
    hashmap_test.go:101: s=5,v=13 p[1:b[1 1],2:b[1 2],4:b[1 4],5:b[1 5],6:b[1 6]]
    hashmap_test.go:105: s=4,v=14 p[1:b[1 1],4:b[1 4],5:b[1 5],6:b[1 6]]
    hashmap_test.go:115: putting 1000000 string>int = 1590 ms
--- PASS: Test_HashMap (2.17s)
PASS
ok      command-line-arguments  2.181s

IHasher.go

哈希支持接口, 定义哈希计算函数, 和键值相等比较函数

package hashmap

type IHasher interface {
    Hash(key interface{}) uint64
    Equals(a interface{}, b interface{}) bool
}

IMap.go

哈希表接口

package hashmap

type IMap interface {
    Size() int
    IsEmpty() bool
    IsNotEmpty() bool

    Put(key interface{}, value interface{})
    Get(key interface{}) (bool,interface{})
    Has(key interface{}) bool
    Remove(key interface{}) (bool, interface{})
    Clear()

    Iterator() IMapIterator
    String() string
}

IMapIterator.go

哈希表迭代器接口

package hashmap

type IMapIterator interface {
    More() bool
    Next() (err error, key interface{}, value interface{})
}

tCrc64Hasher.go

• 基于hash/crc64, 实现IHasher接口.
• 支持多种键类型
• 对于整型的键, 返回自身;
• 其他类型的键, 转为%v字符串再计算crc64的哈希值.

package hashmap

import (
    "fmt"
    "hash/crc64"
)

var gCrc64Table = crc64.MakeTable(crc64.ECMA)

type FnEquals func(a interface{}, b interface{}) bool

type tCrc64Hasher struct {
    fnEquals FnEquals
}

const INT_MAX = int(^uint(0) >> 1)
const INT_MIN = ^INT_MAX
const INT32_MAX = int32(^uint32(0) >> 1)
const INT32_MIN = ^INT32_MAX
const INT64_MAX = int64(^uint64(0) >> 1)
const INT64_MIN = ^INT64_MAX

func (me *tCrc64Hasher) Hash(it interface{}) uint64 {
    if it == nil {
        return 0
    }

    if v,ok := it.(int);ok {
        return uint64(v - INT_MIN)

    } else if v,ok := it.(int64);ok {
        return uint64(v - INT64_MIN)

    } else if v,ok := it.(int32);ok {
        return uint64(v - INT32_MIN)

    } else if v,ok := it.(uint32);ok {
        return uint64(v)

    }  else if v,ok := it.(uint64);ok {
        return v

    } else if v,ok := it.(string);ok {
        return crc64.Checksum([]byte(v), gCrc64Table)

    } else {
        data := []byte(fmt.Sprintf("%v", it))
        return crc64.Checksum(data, gCrc64Table)
    }
}


func (me *tCrc64Hasher) Equals(a interface{}, b interface{}) bool {
    if a == nil && b == nil {
        return true
    }
    if a == nil || b == nil {
        return false
    }

    fn := me.fnEquals
    if fn == nil {
        return a == b
    } else {
        return fn(a, b)
    }
}

func NewCrc64Hashful(fn FnEquals) IHasher {
    return &tCrc64Hasher{
        fnEquals: fn,
    }
}

tHashMap.go

哈希表的实现, 使用分区(双链)+数组+链表(单链)三维结构

package hashmap

import (
    "fmt"
    "strings"
)

type tHashMap struct {
    hasher     IHasher
    partitions *tPartition
    size int
    version int
}


func NewHashMap(hasher IHasher, capacity int) IMap {
    if capacity < 4 {
        capacity = 4
    }

    part := newPartition(hasher, capacity)
    return &tHashMap{
        hasher: hasher,
        partitions: part,
        size: 0,
        version: 0,
    }
}

func (me *tHashMap) Size() int {
    return me.size
}

func (me *tHashMap) IsEmpty() bool {
    return me.Size() <= 0
}

func (me *tHashMap) IsNotEmpty() bool {
    return !me.IsEmpty()
}

func (me *tHashMap) Put(key interface{}, value interface{}) {
    hash := me.hasher.Hash(key)
    ok, _, bucket, node, _ := me.findByKeyAndHash(key, hash)
    if ok {
        bucket.putAt(node, key, value)

    } else {
        if me.partitions.nearlyFull() {
            // create new partition
            part := newPartition(me.hasher, int(me.partitions.bucketCount * 2))
            part.next = me.partitions
            me.partitions.prev = part
            me.partitions = part
            part.appendByKeyAndHash(key, value, hash)
        } else {
            me.partitions.appendByKeyAndHash(key, value, hash)
        }

        me.size++
    }

    me.version++
}


func (me *tHashMap) findByKey(key interface{}) (ok bool, part *tPartition, bucket *tBucket, node *tLinkedNode, prev *tLinkedNode) {
    hash := me.hasher.Hash(key)
    return me.findByKeyAndHash(key, hash)
}

func (me *tHashMap) findByKeyAndHash(key interface{}, hash uint64) (ok bool, part *tPartition, bucket *tBucket, node *tLinkedNode, prev *tLinkedNode) {
    for part = me.partitions; part != nil; part = part.next {
        ok, bucket, node, prev = part.findByKeyAndHash(key, hash)
        if ok {
            return ok, part, bucket, node, prev
        }
    }

    return false, nil, nil, nil, nil
}

func (me *tHashMap) Get(key interface{}) (bool,interface{}) {
    ok, _, _, node, _ := me.findByKey(key)
    if ok {
        return true, node.value
    } else {
        return false, nil
    }
}

func (me *tHashMap) Has(key interface{}) bool {
    ok, _, _, _, _ := me.findByKey(key)
    return ok
}

func (me *tHashMap) Remove(key interface{}) (ok bool, value interface{}) {
    ok, part, bucket, node, prev := me.findByKey(key)
    if ok {
        value = node.value
        bucket.removeAt(node, prev)

        // 缩容
        if part.size <= 0 && part != me.partitions {
            me.removePartition(part)
        }

        me.size--
        me.version++
        return ok, value

    } else {
        return false, nil
    }
}

func (me *tHashMap) removePartition(part *tPartition) {
    prev := part.prev
    next := part.next

    if prev != nil {
        prev.next = next
    }

    if next != nil {
        next.prev = prev
    }

    if me.partitions == part {
        me.partitions = next
    }
}

func (me *tHashMap) Clear() {
    if me.IsEmpty() {
        return
    }

    part := newPartition(me.hasher, len(me.partitions.buckets))
    me.partitions = part
    me.size = 0

    me.version++
}


func (me *tHashMap) Iterator() IMapIterator {
    return newHashMapIterator(me)
}

func (me *tHashMap) String() string {
    itemStrings := make([]string, 0)
    for p := me.partitions;p != nil;p = p.next {
        itemStrings = append(itemStrings, p.String())
    }
    return fmt.Sprintf("s=%v,v=%v %s", me.size, me.version, strings.Join(itemStrings, " "))
}

tPartition.go

哈希表分区. 其大小呈2次幂

package hashmap

import (
    "fmt"
    "strings"
)

type tPartition struct {
    hasher IHasher
    buckets []*tBucket
    bucketCount uint64
    prev *tPartition
    next *tPartition
    size int
    threshhold int
}

func newPartition(hasher IHasher, bucketCount int) *tPartition {
    it := &tPartition{
        hasher: hasher,
        buckets: make([]*tBucket, bucketCount),
        bucketCount: uint64(bucketCount),
        prev: nil,
        next: nil,
        size: 0,
        threshhold: bucketCount * 3 / 4,
    }
    for i,_ := range it.buckets {
        it.buckets[i] = newBucket(hasher)
    }
    return it
}

func (me *tPartition) putByKey(key interface{}, value interface{}) bool {
    hash := me.hasher.Hash(key)
    return me.putByKeyAndHash(key, value, hash)
}

func (me *tPartition) putByKeyAndHash(key interface{}, value interface{}, hash uint64) bool {
    if me.getBucketByHash(hash).put(key, value) {
        me.size++
        return true
    }
    return false
}

func (me *tPartition) appendByKeyAndHash(key interface{}, value interface{}, hash uint64) {
    me.getBucketByHash(hash).append(key, value)
    me.size++
}

func (me *tPartition) getBucketByKey(key interface{}) *tBucket {
    hash := me.hasher.Hash(key)
    return me.getBucketByHash(hash)
}

func (me *tPartition) getBucketByHash(hash uint64) *tBucket {
    return me.buckets[int(hash % me.bucketCount)]
}

func (me *tPartition) get(key interface{}) (bool,interface{}) {
    return me.getBucketByKey(key).get(key)
}

func (me *tPartition) findByKey(key interface{}) (ok bool,bucket *tBucket,node *tLinkedNode, prev *tLinkedNode) {
    bucket = me.getBucketByKey(key)
    ok,node,prev = bucket.find(key)
    return ok,bucket,node, prev
}

func (me *tPartition) findByKeyAndHash(key interface{}, hash uint64) (ok bool,bucket *tBucket,node *tLinkedNode, prev *tLinkedNode) {
    bucket = me.getBucketByHash(hash)
    ok,node,prev = bucket.find(key)
    return ok,bucket,node, prev
}

func (me *tPartition) remove(key interface{}) (bool, value interface{}) {
    ok,node := me.getBucketByKey(key).remove(key)
    if ok {
        me.size--
        return true, node.value

    } else {
        return false, nil
    }
}

func (me *tPartition) nearlyFull() bool {
    return me.size >= me.threshhold
}

func (me *tPartition) String() string {
    itemStrings := make([]string, 0)
    for i,b := range me.buckets {
        if b.size > 0 {
            itemStrings = append(itemStrings, fmt.Sprintf("%v:%s", i, b.String()))
        }
    }
    return fmt.Sprintf("p[%s]", strings.Join(itemStrings, ","))
}

tBucket.go

哈希桶, 每个桶内的任何元素, 哈希值是一致的

package hashmap

import (
    "fmt"
    "strings"
)

type tBucket struct {
    hasher IHasher
    nodes  *tLinkedNode
    size int
}

type tLinkedNode struct {
    key interface{}
    value interface{}
    next *tLinkedNode
}

func newBucket(hasher IHasher) *tBucket {
    return &tBucket{
        hasher: hasher,
        nodes: nil,
        size: 0,
    }
}

func newLinkedNode(key interface{}, value interface{}) *tLinkedNode {
    return &tLinkedNode{
        key: key,
        value: value,
        next: nil,
    }
}

func (me *tBucket) put(key interface{}, value interface{}) bool {
    existed, node, _ := me.find(key)
    me.putAt(node, key, value)
    return !existed
}

func (me *tBucket) append(key interface{}, value interface{}) {
    me.putAt(nil, key, value)
}

func (me *tBucket) putAt(node *tLinkedNode, key interface{}, value interface{}) {
    if node != nil {
        node.value = value
        return
    }

    it := newLinkedNode(key, value)
    if me.nodes == nil {
        me.nodes = it

    } else {
        it.next = me.nodes
        me.nodes = it
    }

    me.size++
}

func (me *tBucket) get(key interface{}) (bool, interface{}) {
    ok, node, _ := me.find(key)
    if ok {
        return true, node.value
    }
    return false, nil
}

func (me *tBucket) find(key interface{}) (ok bool, node *tLinkedNode, prev *tLinkedNode) {
    prev = nil
    for it:=me.nodes;it != nil;it = it.next {
        if me.hasher.Equals(it.key, key) {
            return true, it, prev
        }
        prev = it
    }
    return false, nil, nil
}


func (me *tBucket) remove(key interface{}) (bool, *tLinkedNode) {
    ok,node, prev := me.find(key)
    if !ok {
        return false, nil
    }

    me.removeAt(node, prev)
    return true, node
}


func (me *tBucket) removeAt(node *tLinkedNode, prev *tLinkedNode) {
    if prev == nil {
        me.nodes = node.next
    } else {
        prev.next = node.next
    }
    me.size--
}

func (me *tBucket) String() string {
    itemStrings := make([]string, me.size)
    i := 0
    for it := me.nodes;it != nil;it = it.next {
        itemStrings[i] = fmt.Sprintf("%v", it.key)
        i++
    }
    return fmt.Sprintf("b[%v %s]", me.size, strings.Join(itemStrings, ","))
}

tHashMapIterator.go

哈希表迭代器的实现

package hashmap

import "errors"

type tHashMapIterator struct {
    hashMap *tHashMap
    pindex *tPartition
    bindex int
    nindex *tLinkedNode
    version int
    visited int
}


func newHashMapIterator(hashMap *tHashMap) IMapIterator {
    return &tHashMapIterator{
        hashMap: hashMap,
        pindex: hashMap.partitions,
        bindex: -1,
        nindex: nil,
        version: hashMap.version,
        visited: 0,
    }
}


func (me *tHashMapIterator) nextNode() *tLinkedNode {
    node := me.nindex
    for {
        if node == nil {
            bkt := me.nextBucket()
            if bkt == nil {
                return nil
            } else {
                me.nindex = bkt.nodes
                return me.nindex
            }

        } else {
            node = node.next
            if node != nil {
                me.nindex = node
                return node
            }
        }
    }
}

func (me *tHashMapIterator) nextBucket() *tBucket {
    part := me.pindex
    bi := me.bindex + 1

    for {
        if bi >= len(part.buckets) {
            part = me.nextPartition()
            if part == nil {
                return nil
            }

            bi = 0
        }

        bkt := part.buckets[bi]
        if bkt.nodes != nil {
            me.bindex = bi
            return bkt
        }

        bi++
    }
}


func (me *tHashMapIterator) nextPartition() *tPartition {
    if me.pindex == nil {
        return nil
    }
    me.pindex = me.pindex.next
    return me.pindex
}

func (me *tHashMapIterator) More() bool {
    if me.version != me.hashMap.version {
        return false
    }
    return me.visited < me.hashMap.size
}

func (me *tHashMapIterator) Next() (err error, key interface{}, value interface{}) {
    if me.version != me.hashMap.version {
        return gConcurrentModificationError, nil, nil
    }

    if !me.More() {
        return gNoMoreElementsError, nil, nil
    }

    node := me.nextNode()
    if node == nil {
        return gNoMoreElementsError, nil, nil

    } else {
        me.visited++
        return nil, node.key, node.value
    }
}

var gConcurrentModificationError = errors.New("concurrent modification error")
var gNoMoreElementsError = errors.New("no more elements")

(end)

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