隔离病毒

A virus is spreading rapidly, and your task is to quarantine the infected area by installing walls.

The world is modeled as an m x n binary grid isInfected, where isInfected[i][j] == 0 represents uninfected cells, and isInfected[i][j] == 1 represents cells contaminated with the virus. A wall (and only one wall) can be installed between any two 4-directionally adjacent cells, on the shared boundary.

Every night, the virus spreads to all neighboring cells in all four directions unless blocked by a wall. Resources are limited. Each day, you can install walls around only one region (i.e., the affected area (continuous block of infected cells) that threatens the most uninfected cells the following night). There will never be a tie.

Return the number of walls used to quarantine all the infected regions. If the world will become fully infected, return the number of walls used.

 

Example 1:

Input: isInfected = [[0,1,0,0,0,0,0,1],[0,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0]]
Output: 10
Explanation: There are 2 contaminated regions.
On the first day, add 5 walls to quarantine the viral region on the left. The board after the virus spreads is:

On the second day, add 5 walls to quarantine the viral region on the right. The virus is fully contained.

Example 2:

Input: isInfected = [[1,1,1],[1,0,1],[1,1,1]]
Output: 4
Explanation: Even though there is only one cell saved, there are 4 walls built.
Notice that walls are only built on the shared boundary of two different cells.

Example 3:

Input: isInfected = [[1,1,1,0,0,0,0,0,0],[1,0,1,0,1,1,1,1,1],[1,1,1,0,0,0,0,0,0]]
Output: 13
Explanation: The region on the left only builds two new walls.

 

Constraints:

• m == isInfected.length
• n == isInfected[i].length
• 1 <= m, n <= 50
• isInfected[i][j] is either 0 or 1.
• There is always a contiguous viral region throughout the described process that will infect strictly more uncontaminated squares in the next round.

这个题解使用了BFS和贪心算法。主要思路是每一轮选择一个感染区域进行隔离，选择的标准是该区域周围的未感染区域数量最多。具体做法是：每一轮对所有感染区域进行BFS遍历，计算每个感染区域周围的未感染区域数量，同时将感染区域的坐标标记为负数，不同的感染区域用不同的负数标记。然后选择未感染区域数量最多的感染区域，将其周围的未感染区域隔离，并将答案加上隔离区域的数量。然后将所有感染区域的标记还原，未被隔离的感染区域向周围扩散。重复以上过程直到没有感染区域。

O(mn^2 * log(mn))

O(mn)