トライ木

• ハッシュテーブルで探索しようとした時の発想に似ている．
• 比較に基づいて位置を探索していくと最も効率よくて$O(\log n)$
• だが，値そのものが位置に直接関係しているように，要するに値と位置が一対一に対応していれば，$O(1)$で探索ができる
• この発想を「列」に対して適用したのがハッシュテーブルで，配列でもリストでも実装できてそれぞれハッシュ値の衝突時の解決策が異なってオープンアドレス法とチェイン法
• では，「値と位置が一対一に対応」を木に適用しようとしたらどうなるか...
• それがトライ木

• キーの値自体でどの枝を降りればいいかが決定するような木構造
  • 英語なら各ノードは最大で26個の子供を持つことになる
• トライ木を用いることで，$k$文字の英単語を検索すると，検索しようとする単語の個数によらず$O(k)$で探索できることになる
• ただし，記憶領域を無駄に使う
• ウェブサーバーのルーティングに使うとか応用ができそうだぞ

package main

import "log"

type Node struct {
    Children map[rune]*Node
    isEndOfWord bool
}

func NewNode() *Node {
    return &Node{Children:make(map[rune]*Node), isEndOfWord:false}
}

type Trie struct {
    Root *Node
}

func NewTrie() *Trie {
    return &Trie{Root: NewNode()}
}

func (t *Trie) Put(key string) {
    pCrawl := t.Root
    length := len(key)
    runes := []rune(key)
    for i := 0; i < length; i++ {
        if pCrawl.Children[runes[i]] == nil {
            pCrawl.Children[runes[i]] = NewNode()
        }
        pCrawl = pCrawl.Children[runes[i]]
    }
    pCrawl.isEndOfWord = true
}

func (t *Trie) Search(key string) bool {
    pCrawl := t.Root
    length := len(key)
    runes := []rune(key)
    for i := 0; i < length; i++ {
        if pCrawl.Children[runes[i]] == nil {
            return false
        }
        pCrawl = pCrawl.Children[runes[i]]
    }
    return pCrawl != nil && pCrawl.isEndOfWord
}

func main() {
    keys := []string{"the","a","there","anaswe","any","by","their"}
    t := NewTrie()
    for _, key := range keys {
        t.Put(key)
    }
    log.Printf("%#v\n", t)
    targets := []string{"the", "these", "their", "thaw", "a"}
    for _, target := range targets {
        if t.Search(target) {
            log.Println("Found!")
        } else {
            log.Println("Not Found!")
        }
    }
}

package main

import (
    "bufio"
    "errors"
    "log"
    "os"
)

type Trie struct {
    Value interface{}
    Children map[rune]*Trie
}

func (t *Trie) Search(key string) interface{} {
    node := t
    for _, r := range key {
        node = node.Children[r]
        if node == nil {
            return nil // no value are stored with the given key
        }
    }
    return node.Value
}

func (t *Trie) Put(key string, value interface{}) {
    node := t
    for _, r := range key {
        child, _ := node.Children[r]
        if child == nil {
            child = NewTrie()
            node.Children[r] = child
        }
        node = child
    }
    isNewValue := node.Value == nil
    if isNewValue {
        log.Printf("Put: new value <%#v> was put with key <%s>\n", value, key)
        node.Value = value
    } else {
        log.Printf("Update: <%#v> ==> <%#v> with key <%s>\n", node.Value, value, key)
        node.Value = value
    }
}

func (t *Trie) Delete(key string) error {
    path := make([]PathRecord, len(key))
    node := t
    for i, r := range key {
        path[i] = PathRecord{node: node, r:r}
        node = node.Children[r]
        if node == nil {
            return errors.New("no node for such key")
        }
    }
    deleted := node.Value
    node.Value = nil
    if node.isLeaf() {
        for i := len(key)-1; i >= 0; i-- {
            parent := path[i].node
            r := path[i].r
            delete(parent.Children, r)
            if parent.Value != nil || !parent.isLeaf() {
                break
            }
        }
    }
    log.Printf("Delete: <key: %s, value: %#v>\n", key, deleted)
    return nil
}

func (t *Trie) isLeaf() bool {
    return len(t.Children) == 0
}

func NewTrie() *Trie {
    return &Trie{Children:make(map[rune]*Trie)}
}

type PathRecord struct {
    node *Trie
    r rune
}

func prepare(fileName string) []string {
    ret := make([]string, 0)
    file, err := os.Open(fileName)
    if err != nil {
        log.Fatalln("Can not open file")
    }
    defer file.Close()
    scanner := bufio.NewScanner(file)
    for scanner.Scan() {
        ret = append(ret, scanner.Text())
    }
    if err = scanner.Err(); err != nil {
        log.Fatalln("Can not read file right")
    }
    return ret
}

func main() {
    t := NewTrie()
    keys := prepare("keys")
    values := prepare("values")
    for i := 0; i < 2000; i++ {
        t.Put(keys[i], values[i])
    }
    for i := 0; i < 2000; i++ {
        if t.Search(keys[i]) == nil {
            log.Printf("Not Found! <key: %s>\n", keys[i])
        } else {
            log.Printf("Found! <key: %s, value: %#v>\n", keys[i], t.Search(keys[i]))
        }
    }
    for i := 500; i < 1500; i++ {
        err := t.Delete(keys[i])
        if err != nil {
            log.Fatalf("Error: Fail to delete <key: %s>\n", keys[i])
        }
    }
    for i := 0; i < 2000; i++ {
        if t.Search(keys[i]) == nil {
            log.Printf("Not Found! <key: %s>\n", keys[i])
        } else {
            log.Printf("Found! <key: %s, value: %#v>\n", keys[i], t.Search(keys[i]))
        }
    }
}

// keys
a
ability
able
about
above
accept
according
account
across
act
action
activity
actually
add
address
administration
admit
adult
affect
after
again
against
age
agency
agent
ago
agree
agreement
ahead
air
all
allow
almost
alone
along
already
also
although
always
American
among
amount
analysis
and
animal
another
answer
any
anyone
anything
appear
apply
approach
area
argue
arm
around
arrive
art
article
artist
as
ask
assume
at
attack
attention
attorney
audience
author
authority
available
avoid
away
baby
back
bad
bag
ball
bank
bar
base
be
beat
beautiful
because
become
bed
before
begin
behavior
behind
believe
benefit
best
better
between
beyond
big
bill
billion
bit
black
blood
blue
board
body
book
born
both
box
boy
break
bring
brother
budget
build
building
business
but
buy
by
call
camera
campaign
can
cancer
candidate
capital
car
card
care
career
carry
case
catch
cause
cell
center
central
century
certain
certainly
chair
challenge
chance
change
character
charge
check
child
choice
choose
church
citizen
city
civil
claim
class
clear
clearly
close
coach
cold
collection
college
color
come
commercial
common
community
company
compare
computer
concern
condition
conference
Congress
consider
consumer
contain
continue
control
cost
could
country
couple
course
court
cover
create
crime
cultural
culture
cup
current
customer
cut
dark
data
daughter
day
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debate
decade
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degree
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democratic
describe
design
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detail
determine
develop
development
die
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different
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direction
director
discover
discuss
discussion
disease
do
doctor
dog
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down
draw
dream
drive
drop
drug
during
each
early
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eat
economic
economy
edge
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eight
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election
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employee
end
energy
enjoy
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entire
environment
environmental
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establish
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exist
expect
experience
expert
explain
eye
face
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fail
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fear
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fight
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fill
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finish
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fly
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hang
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health
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heart
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share
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should
shoulder
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single
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teach
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technology
television
tell
ten
tend
term
test
than
thank
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them
themselves
then
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thing
think
third
this
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though
thought
thousand
threat
three
through
throughout
throw
thus
time
to
today
together
tonight
too
top
total
tough
toward
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training
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woman
wonder
word
work
worker
world
worry
would
write
writer
wrong
yard
yeah
year
yes
yet
you
young
your
yourself

// values
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kaw37i2tCEkpVSjjAyVG
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TDpkrMrF-TXX_8-TnkmM
K5Kf7BcQfyyn_JW_RjeN
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h4JWUJHYNPSEdCN-zGWF
gMwPEGU4axgHhuZ62rNR
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LxAa5jXJNhCTZnAVSAyD
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_zVCnDD-2DsawbeNgV6N
hQ8Jjr3JcTX7y_aziWVw
siFcXG8xeGRkE8khcQwi
ukUWkSw78QVb38bCHCQ2
p5-yWxjLUJQ_bg_C_C9S
5tnEtZnAmWHHy4dei226
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fn9saBpnwPBPzyf6rE4d
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GnLEHF-TFmzFt7zhx2d8
Kt3ZXkucSfemmi8i--fu
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A2StXpdfa22E6DGZH2gx
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xRBiWJ-jAzyxR2L_Nz8c
E7bg7-Gfj8aKWTTmaBhz
GUt3VJMERJEnfun4CkeJ
DTrPpMUEW_JUYC2y2nx4
9CjJPYjpwQWDUy3Vhw84
udrWBnCj-zAFapY4X4gs
2kmNGHuNXHVBU-wz7s8n
ttcrjw2ehrC2MwK3fnUR
69-WGHfk9Q7KjuPcriwf
LHz-DCP_hY2WXVcXxH_x
uJxdZkiYQT7j3WyBngEz
ZLFVpHcPaPaGG36U3Kb2
7TR3GMBhPaakDARSsFCe
n2RADwyiywe8dBjGjtrb
LKcgR855RmY8Sa6F6jZX
2p-Nc6SumgCUjChkUVmF
eDg_jDbt7n_bMGK_jnhX
LUhyzX-TPzT_p6ihRr_N
gKjCrGWiP8y8kcaVAaNs
JaxpLGsWQRLQ4PDSFBCa
9GxYCeYjGWnpRgED8hEF
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VgQ7L2QSYQYfQjuaXr4r
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fwPxFYzgT2KT3PGFUUww
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Yek_xcf2iLarheijWnun
Ym8y9_j7ph3Wj_-TA_Ug
XgN4xwkamrY6G7NBACEC
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4L5xR2uJfEKk7www-r3t
zKRaCUFdhWdTmHpTW4Bi
DG-mf_pFjLpMeaV2t-Wz
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