Minesweeper问题及解法

问题描述：

Let's play the minesweeper game (Wikipedia, online game)!

You are given a 2D char matrix representing the game board. 'M' represents an unrevealed mine, 'E' represents an unrevealed empty square, 'B' represents a revealed blank square that has no adjacent (above, below, left, right, and all 4 diagonals) mines, digit ('1' to '8') represents how many mines are adjacent to this revealed square, and finally 'X' represents a revealed mine.

Now given the next click position (row and column indices) among all the unrevealed squares ('M' or 'E'), return the board after revealing this position according to the following rules:

1. If a mine ('M') is revealed, then the game is over - change it to 'X'.
2. If an empty square ('E') with no adjacent mines is revealed, then change it to revealed blank ('B') and all of its adjacent unrevealed squares should be revealed recursively.
3. If an empty square ('E') with at least one adjacent mine is revealed, then change it to a digit ('1' to '8') representing the number of adjacent mines.
4. Return the board when no more squares will be revealed.

示例:

Input: 

[['E', 'E', 'E', 'E', 'E'],
 ['E', 'E', 'M', 'E', 'E'],
 ['E', 'E', 'E', 'E', 'E'],
 ['E', 'E', 'E', 'E', 'E']]

Click : [3,0]

Output: 

[['B', '1', 'E', '1', 'B'],
 ['B', '1', 'M', '1', 'B'],
 ['B', '1', '1', '1', 'B'],
 ['B', 'B', 'B', 'B', 'B']]

Explanation:

Input: 

[['B', '1', 'E', '1', 'B'],
 ['B', '1', 'M', '1', 'B'],
 ['B', '1', '1', '1', 'B'],
 ['B', 'B', 'B', 'B', 'B']]

Click : [1,2]

Output: 

[['B', '1', 'E', '1', 'B'],
 ['B', '1', 'X', '1', 'B'],
 ['B', '1', '1', '1', 'B'],
 ['B', 'B', 'B', 'B', 'B']]

Explanation:

Note:

1. The range of the input matrix's height and width is [1,50].
2. The click position will only be an unrevealed square ('M' or 'E'), which also means the input board contains at least one clickable square.
3. The input board won't be a stage when game is over (some mines have been revealed).
4. For simplicity, not mentioned rules should be ignored in this problem. For example, you don't need to reveal all the unrevealed mines when the game is over, consider any cases that you will win the game or flag any squares.

问题分析：

此类题可简化为深度优先搜索的问题，遍历到的点根据游戏规则更改其值。

过程详见代码：

class Solution {
public:
    vector> updateBoard(vector>& board, vector& click) {
		int m = board.size();
		if (!m) return board;
		int n = board[0].size();
		bl(board, click[0], click[1], m, n);
		return board;
	}

	void bl(vector>& board, int i, int j, int m, int n)
	{
		if (board[i][j] == 'M')
		{
			board[i][j] = 'X';
			return;
		}
		if (board[i][j] == 'E')
		{
			int count = num(board,i,j,m,n);
			if (!count) board[i][j] = 'B';
			else
			{
				board[i][j] = '0' + count;
				return;
			}
			if (i - 1 >= 0 && board[i - 1][j] == 'E') bl(board, i - 1, j, m, n);
			if (j - 1 >= 0 && board[i][j - 1] == 'E')bl(board, i, j - 1, m, n);
			if (i - 1 >= 0 && j - 1 >= 0 && board[i - 1][j - 1] == 'E')bl(board, i - 1, j - 1, m, n);
			if (i + 1 < m && board[i + 1][j] == 'E')bl(board, i + 1, j, m, n);
			if (j + 1 < n && board[i][j + 1] == 'E')bl(board, i, j + 1, m, n);
			if (i + 1 < m && j + 1 < n && board[i + 1][j + 1] == 'E')bl(board, i + 1, j + 1, m, n);
			if (i - 1 >= 0 && j + 1 < n && board[i - 1][j + 1] == 'E')bl(board, i - 1, j + 1, m, n);
			if (i + 1 < m && j - 1 >= 0 && board[i + 1][j - 1] == 'E')bl(board, i + 1, j - 1, m, n);
		}
	}

	int num(vector>& board, int i, int j,int m,int n)
	{
		int count = 0;
		if (i - 1 >= 0 && board[i - 1][j] == 'M') count++;
		if (j - 1 >= 0 && board[i][j - 1] == 'M') count++;
		if (i - 1 >= 0 && j - 1 >= 0 && board[i - 1][j - 1] == 'M')count++;
		if (i + 1 < m && board[i + 1][j] == 'M')count++;
		if (j + 1 < n && board[i][j + 1] == 'M')count++;
		if (i + 1 < m && j + 1 < n && board[i + 1][j + 1] == 'M')count++;
		if (i - 1 >= 0 && j + 1 < n && board[i - 1][j + 1] == 'M')count++;
		if (i + 1 < m && j - 1 >= 0 && board[i + 1][j - 1] == 'M')count++;
		return count;
	}
};