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题目：79. 单词搜索

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 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

提示：

• m == board.length
• n = board[i].length
• 1 <= m, n <= 6
• 1 <= word.length <= 15
• board 和 word 仅由大小写英文字母组成

一、模式识别

1.棋盘格：回溯法

棋盘格问题，回溯法典型应用，用回溯算法

层间：word内顺序访问

层内：board遍历或上一个字母上下左右

无需找到所有结果，找到第一个结果后返回

2.搜索方式

1.word首字母在board中二维遍历

2.word内（层间）顺序访问，剩余字母分别搜索上一个字母的上下左右

3.访问过的字母不可以重复访问

二.代码实现

1.基础实现

class Solution:def get_candidate(self, board, visited, i, j):candidate = []if i - 1 >= 0 and not visited[i - 1][j]:candidate.append((board[i - 1][j], i - 1, j))if j - 1 >= 0 and not visited[i][j - 1]:candidate.append((board[i][j - 1], i, j - 1))if i + 1 < len(board) and not visited[i + 1][j]:candidate.append((board[i + 1][j], i + 1, j))if j + 1 < len(board[0]) and not visited[i][j + 1]:candidate.append((board[i][j + 1], i, j + 1))return candidatedef backtracking(self, board, word, visited, start_idx, i, j):if start_idx == len(word):return Trueif start_idx == 0:for i in range(len(board)):for j in range(len(board[i])):if board[i][j] == word[0]:visited[i][j] = Trueif self.backtracking(board, word, visited, 1, i, j):return Truevisited[i][j] = Falseelse:for ch, a, b in self.get_candidate(board, visited, i, j):if ch == word[start_idx]:visited[a][b] = Trueif self.backtracking(board, word, visited, start_idx + 1, a, b):return Truevisited[a][b] = Falsereturn Falsedef exist(self, board: List[List[str]], word: str) -> bool:visited = [[False] * len(board[0]) for _ in range(len(board))]return self.backtracking(board, word, visited, 0, -1, -1)

start_idx记录访问顺序

visited用于标记访问过的字母

首字母二维遍历board

剩余字母层间顺序访问，层内访问上一个字母在board中的上下左右

耗时：2000ms-4000ms

2.启发式搜索

class Solution:def get_candidate(self, board, i, j):candidate = []if i - 1 >= 0 and board[i - 1][j]:candidate.append((board[i - 1][j], i - 1, j))if j - 1 >= 0 and board[i][j - 1]:candidate.append((board[i][j - 1], i, j - 1))if i + 1 < len(board) and board[i + 1][j]:candidate.append((board[i + 1][j], i + 1, j))if j + 1 < len(board[0]) and board[i][j + 1]:candidate.append((board[i][j + 1], i, j + 1))return candidatedef backtracking(self, board, word, start_idx, i, j):if start_idx == len(word):return Trueif start_idx == 0:for i in range(len(board)):for j in range(len(board[i])):if board[i][j] == word[0]:board[i][j] = Falseif self.backtracking(board, word, 1, i, j):return Trueboard[i][j] = word[0]else:for ch, a, b in self.get_candidate(board, i, j):if ch == word[start_idx]:board[a][b] = Falseif self.backtracking(board, word, start_idx + 1, a, b):return Trueboard[a][b] = word[start_idx]return Falsedef exist(self, board: List[List[str]], word: str) -> bool:# visited = [[False] * len(board[0]) for _ in range(len(board))]cnt=Counter(c for row in board for c in row)if not cnt>=Counter(word):return Falseif cnt[word[-1]]<cnt[word[0]]:word=word[::-1]return self.backtracking(board, word, 0, -1, -1)

在提交排行榜中看到的启发式搜索

思路：主要搜索开销都在第一步的board的遍历，于是从第一步开刀

实现逻辑：如果尾端字母在board出现频率低于首端则word反序

计算开销直接降到0ms-3ms