Design Add and Search Words Data Structure

Design a data structure that supports adding new words and finding if a string matches any previously added string.

Implement the WordDictionary class:

• WordDictionary() Initializes the object.
• void addWord(word) Adds word to the data structure, it can be matched later.
• bool search(word) Returns true if there is any string in the data structure that matches word or false otherwise. word may contain dots '.' where dots can be matched with any letter.

Examples

Example:

Input
["WordDictionary","addWord","addWord","addWord","search","search","search","search"]
[[],["bad"],["dad"],["mad"],["pad"],["bad"],[".ad"],["b.."]]
Output
[null,null,null,null,false,true,true,true]

Explanation
WordDictionary wordDictionary = new WordDictionary();
wordDictionary.addWord("bad");
wordDictionary.addWord("dad");
wordDictionary.addWord("mad");
wordDictionary.search("pad"); // return False
wordDictionary.search("bad"); // return True
wordDictionary.search(".ad"); // return True
wordDictionary.search("b.."); // return True

Constraints:

• 1 <= word.length <= 25
• word in addWord consists of lowercase English letters.
• word in search consist of '.' or lowercase English letters.
• There will be at most 3 dots in word for search queries.
• At most 10^4 calls will be made to addWord and search.

解析

題目要設計一個資料結構 WordDictionary，內部需要實作以下方法

1. Constructor: 用來建構 WordDictionary
2. addWord(word string): 用來新增 word 到 WordDictionary
3. search(word string): 用來搜尋 word 是否已經存在 WordDictionary

要注意的是當 字元使用 '.' 代表任意字元

舉例來說: 'b..' 代表所有以 b 為首 長度為 3 的字串

如果不考慮 '.' 的狀況，使用 Trie 及可以處理

但考慮到 '.' 需要對字串搜尋做特殊處理

參考下圖:

針對搜尋的 word 字串拆已每個字元 char 做搜尋

當字元搜訊 index 與字串長度相等則回傳 true

當遇到字元是 '.'

則把當下結點的所有 children 做 loop , 以下個字元index 開始做字元比對

當字元不是 '.'

則檢查是否有這個字元的 edge, 如果沒有則回傳 false

如果有，則以這個字元的 edge 所指向的結點作為root 往下一個字元index 繼續做比對

程式碼

package sol

type Node struct {
	Children  map[byte]*Node
	EndOfWord bool
}
type WordDictionary struct {
	root *Node
}

func Constructor() WordDictionary {
	return WordDictionary{
		root: &Node{
			Children:  make(map[byte]*Node),
			EndOfWord: false,
		},
	}
}

func (this *WordDictionary) AddWord(word string) {
	cur := this.root
	wLen := len(word)
	for idx := 0; idx < wLen; idx++ {
		r := word[idx]
		if _, exists := cur.Children[r]; !exists {
			cur.Children[r] = &Node{
				Children:  make(map[byte]*Node),
				EndOfWord: false,
			}
		}
		cur = cur.Children[r]
	}
	cur.EndOfWord = true
}

func (this *WordDictionary) Search(word string) bool {
	return DFS(0, this.root, &word)
}

func DFS(i int, root *Node, word *string) bool {
	cur := root
	wLen := len(*word)
	if wLen == i {
		return cur.EndOfWord
	}
	c := (*word)[i]
	if c == '.' {
		for _, child := range cur.Children {
			if DFS(i+1, child, word) { // check next char
				return true
			}
		}
		return false
	} else {
		if _, exists := cur.Children[c]; !exists {
			return false
		}
		return DFS(i+1, cur.Children[c], word)
	}
}

困難點

1. 在處理 "." 需要透過 DFS 的方式把所有可能值搜尋過一遍

Solve Point

• [x] Understand what problem need to solve
• [x] Analysis Complexity