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interview/16-LeetCode Hot 100/单词搜索.md
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单词搜索 (Word Search)

题目描述

给定一个 m x n 二维字符网格 board 和一个字符串单词 word。如果 word 存在于网格中,返回 true;否则,返回 false

单词必须按照字母顺序,通过相邻的单元格内的字母构成,其中"相邻"单元格是那些水平相邻或垂直相邻的单元格。同一个单元格内的字母不允许被重复使用。

示例

示例 1

输入board = [["A","B","C","E"],["S","F","C","S"],["A","D","E","E"]], word = "ABCCED"
输出true

示例 2

输入board = [["A","B","C","E"],["S","F","C","S"],["A","D","E","E"]], word = "SEE"
输出true

示例 3

输入board = [["A","B","C","E"],["S","F","C","S"],["A","D","E","E"]], word = "ABCB"
输出false

解题思路

方法一DFS + 回溯(推荐)

**核心思想:**对每个位置进行 DFS搜索是否存在匹配的单词路径。

算法步骤:

  1. 遍历网格的每个位置
  2. 如果当前位置字符匹配单词首字符,开始 DFS
  3. DFS 过程中:
    • 标记当前已访问
    • 向四个方向递归搜索
    • 如果找到完整单词,返回 true
    • 回溯时撤销访问标记

代码实现

Go 实现

package main

func exist(board [][]byte, word string) bool {
	m, n := len(board), len(board[0])
	visited := make([][]bool, m)
	for i := range visited {
		visited[i] = make([]bool, n)
	}

	var dfs func(i, j, k int) bool
	dfs = func(i, j, k int) bool {
		// 找到完整单词
		if k == len(word) {
			return true
		}

		// 边界检查或不匹配
		if i < 0 || i >= m || j < 0 || j >= n ||
			visited[i][j] || board[i][j] != word[k] {
			return false
		}

		// 标记访问
		visited[i][j] = true

		// 向四个方向搜索
		found := dfs(i+1, j, k+1) ||
			dfs(i-1, j, k+1) ||
			dfs(i, j+1, k+1) ||
			dfs(i, j-1, k+1)

		// 回溯:取消标记
		visited[i][j] = false

		return found
	}

	for i := 0; i < m; i++ {
		for j := 0; j < n; j++ {
			if board[i][j] == word[0] && dfs(i, j, 0) {
				return true
			}
		}
	}

	return false
}

Java 实现

复杂度分析

  • 时间复杂度: O(m × n × 4^L)

    • m × n 是网格大小
    • L 是单词长度
    • 最坏情况每个位置都要搜索 4 个方向
  • 空间复杂度: O(L)

    • 递归栈深度最大为 L
    • visited 数组 O(m × n)

P7 加分项

变形题目:单词搜索 II

LeetCode 212: 给定一个 m x n 二维字符网格 board 和一个单词列表 words返回所有在二维网格和字典中出现的单词。

func findWords(board [][]byte, words []string) []string {
	// 构建 Trie 树
	trie := buildTrie(words)
	result := []string{}

	for i := 0; i < len(board); i++ {
		for j := 0; j < len(board[0]); j++ {
			dfsBoard(board, i, j, trie, &result)
		}
	}

	return result
}