题目
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
分析
为了判断给定的单词 word
是否存在于二维字符网格 board
中,可以使用深度优先搜索(DFS)算法。具体思路是遍历网格中的每个单元格,以每个单元格为起点进行深度优先搜索,看是否能找到与 word
匹配的路径。
DFS
时间复杂度:O(),
是单词的长度
空间复杂度:O()
class Solution {
private:int rows, cols;std::vector<std::pair<int, int>> directions = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}};// 深度优先搜索函数bool dfs(std::vector<std::vector<char>>& board, const std::string& word, int x, int y, int index) {// 如果越界、当前单元格字符不匹配或已访问过,返回 falseif (x < 0 || x >= rows || y < 0 || y >= cols || board[x][y] != word[index]) {return false;}// 如果已经匹配到单词的最后一个字符,返回 trueif (index == word.length() - 1) {return true;}// 标记当前单元格为已访问char originalChar = board[x][y];board[x][y] = '#';// 尝试四个方向for (const auto& dir : directions) {int newX = x + dir.first;int newY = y + dir.second;if (dfs(board, word, newX, newY, index + 1)) {return true;}}// 回溯,恢复当前单元格的原始字符board[x][y] = originalChar;return false;}
public:bool exist(std::vector<std::vector<char>>& board, std::string word) {rows = board.size();cols = board[0].size();// 遍历网格中的每个单元格for (int i = 0; i < rows; ++i) {for (int j = 0; j < cols; ++j) {if (dfs(board, word, i, j, 0)) {return true;}}}return false;}
};