[NeetCode 150] Search for Word II

Given a 2-D grid of characters board and a list of strings words, return all words that are present in the grid.

For a word to be present it must be possible to form the word with a path in the board with horizontally or vertically neighboring cells. The same cell may not be used more than once in a word.

Example 1:

复制代码
Input:
board = [
  ["a","b","c","d"],
  ["s","a","a","t"],
  ["a","c","k","e"],
  ["a","c","d","n"]
],
words = ["bat","cat","back","backend","stack"]

Output: ["cat","back","backend"]

Example 2:

复制代码
Input:
board = [
  ["x","o"],
  ["x","o"]
],
words = ["xoxo"]

Output: []

Constraints:

复制代码
1 <= board.length, board[i].length <= 10
board[i] consists only of lowercase English letter.
1 <= words.length <= 100
1 <= words[i].length <= 10

words[i] consists only of lowercase English letters.

All strings within words are distinct.

Solution

Compared with basic Search for Word, this problem involves multiple queries. For one query, we have to go through the whole matrix and apply DFS, which consume O ( n × m × Len ( w o r d ) ) O(n\times m\times \text{Len}(word)) O(n×m×Len(word)) time complexity. If we simply repeat this process on every query, the time complexity is O ( n × m × ∑ w ∈ w o r d s Len ( w ) ) O(n\times m\times \sum_{w\in words}\text{Len}(w)) O(n×m×∑w∈wordsLen(w)), which is too time-consuming.

In fact, we can go through the whole matrix and apply DFS at each position only once, because in just one going through, we can meet all possible words that can be produced by the matrix. There is no need to repeat it.

One possible solution is to record all strings while we go through the matrix, using a set or hash algorithm, but the number of all possible strings might be large and we only need few among them. The overall time and space complexity will be O ( n 2 m 2 ) O(n^2m^2) O(n2m2).

Actually, the DFS can be much more efficient if we search according to the given word list. To achieve this, we can build a Trie tree on all the words we want to find in the matrix. Then, we simultaneously move on both the matrix and Trie tree. Under the guidance of Trie tree, we only search the position that can compose a prefix of target words. Although in the worst case, the time complexity will still be O ( n 2 m 2 ) O(n^2m^2) O(n2m2), but in general cases, the time complexity will be about O ( ∑ w ∈ w o r d s Len ( w ) ) O( \sum_{w\in words}\text{Len}(w)) O(∑w∈wordsLen(w)) and the space complexity will be constantly O ( n × m + ∑ w ∈ w o r d s Len ( w ) ) O(n\times m+ \sum_{w\in words}\text{Len}(w)) O(n×m+∑w∈wordsLen(w)).

Code

py 复制代码
class Trie:
    def __init__(self):
        self.is_word = [False]
        self.tree = [{}]
        self.id_cnt = 0
        self.word_cnt = [0]
    
    def insert(self, word):
        node = 0
        self.word_cnt[0] += 1
        for c in word:
            if c not in self.tree[node]:
                self.id_cnt += 1
                self.tree[node][c] = self.id_cnt
                self.is_word.append(False)
                self.tree.append({})
                self.word_cnt.append(0)
            node = self.tree[node][c]
            self.word_cnt[node] += 1
        self.is_word[node] = True

    def remove(self, word):
        node = 0
        self.word_cnt[0] -= 1
        for c in word:
            if c not in self.tree[node]:
                return
            node = self.tree[node][c]
            if self.word_cnt[node] <= 0:
                return
            self.word_cnt[node] -= 1
        self.is_word[node] = False



class Solution:
    def findWords(self, board: List[List[str]], words: List[str]) -> List[str]:
        trie = Trie()
        for word in words:
            trie.insert(word)
        ans = []
        vis = set()
        X = [ 1,-1, 0, 0]
        Y = [ 0, 0, 1,-1]
        def dfs(x, y, node, string):
            print(x, y, node, string)
            if trie.word_cnt[node] <= 0:
                return
            if trie.is_word[node]:
                ans.append(string)
                trie.remove(string)
            vis.add((x, y))
            for i in range(4):
                nxt_x = x + X[i]
                nxt_y = y + Y[i]
                if 0 <= nxt_x < len(board) and 0 <= nxt_y < len(board[0]) and (nxt_x, nxt_y) not in vis:
                    nxt_char = board[nxt_x][nxt_y]
                    if nxt_char in trie.tree[node]:
                        dfs(nxt_x, nxt_y, trie.tree[node][nxt_char], string+nxt_char)
            vis.remove((x,y))
            return False

        for i in range(len(board)):
            for j in range(len(board[0])):
                if board[i][j] in trie.tree[0]:
                    dfs(i, j, trie.tree[0][board[i][j]], board[i][j])
        return ans
        
相关推荐
CoovallyAIHub15 小时前
中科大DSAI Lab团队多篇论文入选ICCV 2025,推动三维视觉与泛化感知技术突破
深度学习·算法·计算机视觉
NAGNIP16 小时前
Serverless 架构下的大模型框架落地实践
算法·架构
moonlifesudo16 小时前
半开区间和开区间的两个二分模版
算法
moonlifesudo16 小时前
300:最长递增子序列
算法
CoovallyAIHub21 小时前
港大&字节重磅发布DanceGRPO:突破视觉生成RLHF瓶颈,多项任务性能提升超180%!
深度学习·算法·计算机视觉
CoovallyAIHub1 天前
英伟达ViPE重磅发布!解决3D感知难题,SLAM+深度学习完美融合(附带数据集下载地址)
深度学习·算法·计算机视觉
聚客AI2 天前
🙋‍♀️Transformer训练与推理全流程:从输入处理到输出生成
人工智能·算法·llm
大怪v2 天前
前端:人工智能?我也会啊!来个花活,😎😎😎“自动驾驶”整起!
前端·javascript·算法
惯导马工2 天前
【论文导读】ORB-SLAM3:An Accurate Open-Source Library for Visual, Visual-Inertial and
深度学习·算法
骑自行车的码农2 天前
【React用到的一些算法】游标和栈
算法·react.js