LeetCode——79. 单词搜索

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.

https://leetcode-cn.com/problems/word-search/

深度优先遍历 DFS

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}};
    private int m; // 盘面上有多少行
    private int n; // 盘面上有多少列
    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

改进

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;
    }
};