トライ木

# 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**

![](https://upload.wikimedia.org/wikipedia/commons/thumb/b/be/Trie_example.svg/250px-Trie_example.svg.png)

- 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

```go
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!")
		}
	}
}
```

```go
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
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```

```
// values
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kaw37i2tCEkpVSjjAyVG
spLN48sjeify8jw_5B96
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Vi5iPtmV5SKb9AJ5fycb
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EVQFDBScGkGSuj2pW3aU
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4GYtcnYupJW7ZtyMUsDz
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sifjdHaaNgR7mJDXn7ez
FuuyFsQdJuJ-mCfa3ktd
aH29mrz5-VDz3F-LWUzk
WdVCsPJGXMAfQdUaVJcr
JDhuuaY8b_gSVeppCm3Y
gU25rBU7czTTkmpkxF_e
eTW5UWwdGMrEm39zHwN4
9r5aTY_6ySCn4ki86DwF
-7BFYa5ZzpCatJKfhr3G
kcu4EKZaTzH4sK6rrVVt
DsYBuki9gb5hCS_JBUC-
rtxC5Q_sYGAPTehReu4W
sSULrHb3RhSecj4SNUz3
wzU2u5NT_rP3rKMnaPrE
QwMegJPa_-nAKLbUYEYB
fuXbZ8c9s7xJsFuAhaXW
QZdcNempkFayZf5MB6Ns
5dfd8EKRjwzx5_dC7nd7
TyFzjGLNecxxhMyEsbwu
xSn7rcndRws9p4tpLANg
NRrwgCYBmFtLeH2cnxZ3
BmKHAm4hiWSze3DQuC_W
NMEJsMQ8_AWdw5JVMHxA
FPJnXaxJgySCr5RLmG2V
mTCVSiWSxy22dPaBuCKC
Yek_xcf2iLarheijWnun
Ym8y9_j7ph3Wj_-TA_Ug
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