LeetCode[Hard]------803. Bricks Falling When Hit

问题描述

We have a grid of 1s and 0s; the 1s in a cell represent bricks. A brick will not drop if and only if it is directly connected to the top of the grid, or at least one of its (4-way) adjacent bricks will not drop.

We will do some erasures sequentially. Each time we want to do the erasure at the location (i, j), the brick (if it exists) on that location will disappear, and then some other bricks may drop because of that erasure.

Return an array representing the number of bricks that will drop after each erasure in sequence.

Example 1:

Input:
grid = [[1,0,0,0],[1,1,1,0]]
hits = [[1,0]]
Output: [2]
Explanation:
If we erase the brick at (1, 0), the brick at (1, 1) and (1, 2) will drop. So we should return 2.

Example 2:

Input:
grid = [[1,0,0,0],[1,1,0,0]]
hits = [[1,1],[1,0]]
Output: [0,0]
Explanation:
When we erase the brick at (1, 0), the brick at (1, 1) has already disappeared due to the last move. So each erasure will cause no bricks dropping. Note that the erased brick (1, 0) will not be counted as a dropped brick.

Note:

1. The number of rows and columns in the grid will be in the range [1, 200].
2. The number of erasures will not exceed the area of the grid.
3. It is guaranteed that each erasure will be different from any other erasure, and located inside the grid.
4. An erasure may refer to a location with no brick - if it does, no bricks drop.

简单翻译一下，有一个包含0和1的二维数组，1表示bricks。第一行的bricks是不会掉落的，与其想联通的bricks都不会掉落。现在我要打碎一些bricks，问会有多少bricks drop。

思路：

思路：这是DFS中较难的一道题。首先我们要明白brick drop的条件：

1. grid中删除的节点为1。
2. 删除位置的节点必须和top(grid[0][])相连。
3. 删除节点的周围的brick 节点必须不能通过其他brick到达top。

所以只有同时满足以上3个条件，brick才会drop。我们先把所有要brick的节点置为0，第一行的所有brick标记为TOP(2)，然后用DFS，顺藤摸瓜找到所有与TOP联通的grid。

下一步我们恢复hits节点到1，isConnected(x, y, grid)方法用来判断第二个条件，dfs方法返回的就是因为hits的原因与TOP 断开连接的grid的个数。减一是因为要减去hit本身。

代码：

	private static final int TOP = 2;
	private static final int BRICK = 1;
	private static final int EMPTY = 0;
	private static final int[][] DIRS = { { 1, 0 }, { -1, 0 }, { 0, 1 }, { 0, -1 } };

	public int[] hitBricks(int[][] grid, int[][] hits) {
		int[] res = new int[hits.length];
		// Think backwards: remove all of the hits and then add them back;
		for (int[] hit : hits) {
			grid[hit[0]][hit[1]]--;
		}

		// Flood all the grids connecting to top with 2;
		for (int i = 0; i < grid[0].length; i++) {
			dfs(0, i, grid);
		}

		// Add back the hited Bricks
		for (int i = hits.length - 1; i >= 0; i--) {
			int x = hits[i][0], y = hits[i][1];
			grid[x][y]++;
			if (grid[x][y] == BRICK && isConnected(x, y, grid)) {
				res[i] = dfs(x, y, grid) - 1;
			}
		}

		return res;
	}

	private int dfs(int i, int j, int[][] grid) {
		if (i < 0 || i >= grid.length || j < 0 || j >= grid[0].length || grid[i][j] != BRICK) {
			return 0;
		}
		grid[i][j] = 2;
		return dfs(i + 1, j, grid) + dfs(i - 1, j, grid) + dfs(i, j + 1, grid) + dfs(i, j - 1, grid) + 1;
	}

	private boolean isConnected(int i, int j, int[][] grid) {
		if (i == 0) {
			return true;
		}
		for (int[] d : DIRS) {
			int x = i + d[0], y = j + d[1];
			if (x >= 0 && x < grid.length && y >= 0 && y < grid[0].length && grid[x][y] == TOP) {
				return true;
			}
		}
		return false;
	}

仅用于个人的学习理解，如需转载，请标明出处：
https://blog.youkuaiyun.com/sc19951007/article/details/83771000