79. 单词搜索

English Version

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 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

 

进阶：你可以使用搜索剪枝的技术来优化解决方案，使其在 board 更大的情况下可以更快解决问题？

解法

回溯（深度优先搜索 DFS ）实现。

Python3

class Solution:
    def exist(self, board: List[List[str]], word: str) -> bool:
        def dfs(i, j, cur):
            if cur == len(word):
                return True
            if i < 0 or i >= m or j < 0 or j >= n or board[i][j] == '0' or word[cur] != board[i][j]:
                return False
            t = board[i][j]
            board[i][j] = '0'
            for a, b in [[0, 1], [0, -1], [-1, 0], [1, 0]]:
                x, y = i + a, j + b
                if dfs(x, y, cur + 1):
                    return True
            board[i][j] = t
            return False

        m, n = len(board), len(board[0])
        return any(dfs(i, j, 0) for i in range(m) for j in range(n))

Java

class Solution {
    public boolean exist(char[][] board, String word) {
        int m = board.length;
        int n = board[0].length;
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                if (dfs(i, j, 0, m, n, board, word)) {
                    return true;
                }
            }
        }
        return false;
    }

    private boolean dfs(int i, int j, int cur, int m, int n, char[][] board, String word) {
        if (cur == word.length()) {
            return true;
        }
        if (i < 0 || i >= m || j < 0 || j >= n || board[i][j] != word.charAt(cur)) {
            return false;
        }
        board[i][j] += 256;
        int[] dirs = {-1, 0, 1, 0, -1};
        for (int k = 0; k < 4; ++k) {
            int x = i + dirs[k];
            int y = j + dirs[k + 1];
            if (dfs(x, y, cur + 1, m, n, board, word)) {
                return true;
            }
        }
        board[i][j] -= 256;
        return false;
    }
}

TypeScript

function exist(board: string[][], word: string): boolean {
    let m = board.length,
        n = board[0].length;
    let visited = Array.from({ length: m }, v => new Array(n).fill(false));
    for (let i = 0; i < m; ++i) {
        for (let j = 0; j < n; ++j) {
            if (dfs(board, word, i, j, 0, visited)) {
                return true;
            }
        }
    }
    return false;
}

function dfs(
    board: string[][],
    word: string,
    i: number,
    j: number,
    depth: number,
    visited: boolean[][],
): boolean {
    let m = board.length,
        n = board[0].length;
    if (i < 0 || i > m - 1 || j < 0 || j > n - 1 || visited[i][j]) {
        return false;
    }
    if (board[i][j] != word.charAt(depth)) {
        return false;
    }

    if (depth == word.length - 1) {
        return true;
    }

    visited[i][j] = true;
    ++depth;
    let res = false;
    for (let [dx, dy] of [
        [0, 1],
        [0, -1],
        [1, 0],
        [-1, 0],
    ]) {
        let x = i + dx,
            y = j + dy;
        res = res || dfs(board, word, x, y, depth, visited);
    }
    visited[i][j] = false;
    return res;
}

C++

class Solution {
public:
    bool exist(vector<vector<char>>& board, string word) {
        int m = board.size(), n = board[0].size();
        for (int i = 0; i < m; ++i)
            for (int j = 0; j < n; ++j)
                if (dfs(i, j, 0, m, n, board, word))
                    return true;
        return false;
    }

    bool dfs(int i, int j, int cur, int m, int n, vector<vector<char>>& board, string& word) {
        if (cur == word.size()) return true;
        if (i < 0 || i >= m || j < 0 || j >= n || board[i][j] != word[cur]) return false;
        char t = board[i][j];
        board[i][j] = '0';
        vector<int> dirs = {-1, 0, 1, 0, -1};
        for (int k = 0; k < 4; ++k)
        {
            int x = i + dirs[k], y = j + dirs[k + 1];
            if (dfs(x, y, cur + 1, m, n, board, word)) return true;
        }
        board[i][j] = t;
        return false;
    }
};

Go

func exist(board [][]byte, word string) bool {
	m, n := len(board), len(board[0])
	var dfs func(i, j, cur int) bool
	dfs = func(i, j, cur int) bool {
		if cur == len(word) {
			return true
		}
		if i < 0 || i >= m || j < 0 || j >= n || board[i][j] != word[cur] {
			return false
		}
		t := board[i][j]
		board[i][j] = '0'
		dirs := []int{-1, 0, 1, 0, -1}
		for k := 0; k < 4; k++ {
			x, y := i+dirs[k], j+dirs[k+1]
			if dfs(x, y, cur+1) {
				return true
			}
		}
		board[i][j] = t
		return false
	}
	for i := 0; i < m; i++ {
		for j := 0; j < n; j++ {
			if dfs(i, j, 0) {
				return true
			}
		}
	}
	return false
}

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