给定一个二维网格和一个单词，找出该单词是否存在于网格中。
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:
board =
[
['A','B','C','E'],
['S','F','C','S'],
['A','D','E','E']
]
给定 word = "ABCCED", 返回 true.
给定 word = "SEE", 返回 true.
给定 word = "ABCB", 返回 false.解法一：
这道题是典型的深度优先遍历 DFS 的应用，原二维数组就像是一个迷宫，可以上下左右四个方向行走，我们以二维数组中每一个数都作为起点和给定字符串做匹配，我们还需要一个和原数组等大小的 visited 数组，是 bool 型的，用来记录当前位置是否已经被访问过，因为题目要求一个 cell 只能被访问一次。如果二维数组 board 的当前字符和目标字符串 word 对应的字符相等，则对其上下左右四个邻字符分别调用 DFS 的递归函数，只要有一个返回 true，那么就表示可以找到对应的字符串，否则就不能找到，具体看代码实现如下：
c++
class Solution {
public:
bool exist(vector<vector<char>>& board, string word) {
if (board.empty() || board[0].empty()) return false;
int m = board.size(), n = board[0].size();
vector<vector<bool>> visited(m, vector<bool>(n));
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
if (search(board, word, 0, i, j, visited)) return true;
}
}
return false;
}
bool search(vector<vector<char>>& board, string word, int idx, int i, int j, vector<vector<bool>>& visited) {
if (idx == word.size()) return true;
int m = board.size(), n = board[0].size();
if (i < 0 || j < 0 || i >= m || j >= n || visited[i][j] || board[i][j] != word[idx]) return false;
visited[i][j] = true;
bool res = search(board, word, idx + 1, i - 1, j, visited)
|| search(board, word, idx + 1, i + 1, j, visited)
|| search(board, word, idx + 1, i, j - 1, visited)
|| search(board, word, idx + 1, i, j + 1, visited);
visited[i][j] = false;
return res;
}
};java
public class Solution {
private boolean[][] marked;
// x-1,y
// x,y-1 x,y x,y+1
// x+1,y
private int[][] direction = {{-1, 0}, {0, -1}, {0, 1}, {1, 0}};
// 盘面上有多少行
private int m;
// 盘面上有多少列
private int n;
private String word;
private char[][] board;
public boolean exist(char[][] board, String word) {
m = board.length;
if (m == 0) {
return false;
}
n = board[0].length;
marked = new boolean[m][n];
this.word = word;
this.board = board;
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
if (dfs(i, j, 0)) {
return true;
}
}
}
return false;
}
private boolean inArea(int x, int y) {
return x >= 0 && x < m && y >= 0 && y < n;
}
private boolean dfs(int i, int j, int start) {
if (start == word.length() - 1) {
return board[i][j] == word.charAt(start);
}
if (board[i][j] == word.charAt(start)) {
marked[i][j] = true;
for (int k = 0; k < 4; k++) {
int newX = i + direction[k][0];
int newY = j + direction[k][1];
if (inArea(newX, newY) && !marked[newX][newY]) {
if (dfs(newX, newY, start + 1)) {
return true;
}
}
}
marked[i][j] = false;
}
return false;
}
}python
from typing import List
class Solution:
# (x-1,y)
# (x,y-1) (x,y) (x,y+1)
# (x+1,y)
directions = [(0, -1), (-1, 0), (0, 1), (1, 0)]
def exist(self, board: List[List[str]], word: str) -> bool:
m = len(board)
if m == 0:
return False
n = len(board[0])
marked = [[False for _ in range(n)] for _ in range(m)]
for i in range(m):
for j in range(n):
# 对每一个格子都从头开始搜索
if self.__search_word(board, word, 0, i, j, marked, m, n):
return True
return False
def __search_word(self, board, word, index,
start_x, start_y, marked, m, n):
# 先写递归终止条件
if index == len(word) - 1:
return board[start_x][start_y] == word[index]
# 中间匹配了，再继续搜索
if board[start_x][start_y] == word[index]:
# 先占住这个位置，搜索不成功的话，要释放掉
marked[start_x][start_y] = True
for direction in self.directions:
new_x = start_x + direction[0]
new_y = start_y + direction[1]
# 注意：如果这一次 search word 成功的话，就返回
if 0 <= new_x < m and 0 <= new_y < n and \
not marked[new_x][new_y] and \
self.__search_word(board, word,
index + 1,
new_x, new_y,
marked, m, n):
return True
marked[start_x][start_y] = False
return False解法二：
我们还可以不用 visited 数组，直接对 board 数组进行修改，将其遍历过的位置改为井号，记得递归调用完后需要恢复之前的状态，参见代码如下：
c++
class Solution {
public:
bool exist(vector<vector<char>>& board, string word) {
if (board.empty() || board[0].empty()) return false;
int m = board.size(), n = board[0].size();
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
if (search(board, word, 0, i, j)) return true;
}
}
return false;
}
bool search(vector<vector<char>>& board, string word, int idx, int i, int j) {
if (idx == word.size()) return true;
int m = board.size(), n = board[0].size();
if (i < 0 || j < 0 || i >= m || j >= n || board[i][j] != word[idx]) return false;
char c = board[i][j];
board[i][j] = '#';
bool res = search(board, word, idx + 1, i - 1, j)
|| search(board, word, idx + 1, i + 1, j)
|| search(board, word, idx + 1, i, j - 1)
|| search(board, word, idx + 1, i, j + 1);
board[i][j] = c;
return res;
}
};