<p>You are given two integers <code>m</code> and <code>n</code> representing a <strong>0-indexed</strong> <code>m x n</code> grid. You are also given two 2D integer arrays <code>guards</code> and <code>walls</code> where <code>guards[i] = [row<sub>i</sub>, col<sub>i</sub>]</code> and <code>walls[j] = [row<sub>j</sub>, col<sub>j</sub>]</code> represent the positions of the <code>i<sup>th</sup></code> guard and <code>j<sup>th</sup></code> wall respectively.</p>

<p>A guard can see <b>every</b> cell in the four cardinal directions (north, east, south, or west) starting from their position unless <strong>obstructed</strong> by a wall or another guard. A cell is <strong>guarded</strong> if there is <strong>at least</strong> one guard that can see it.</p>

<p>Return<em> the number of unoccupied cells that are <strong>not</strong> <strong>guarded</strong>.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/03/10/example1drawio2.png" style="width: 300px; height: 204px;" />
<pre>
<strong>Input:</strong> m = 4, n = 6, guards = [[0,0],[1,1],[2,3]], walls = [[0,1],[2,2],[1,4]]
<strong>Output:</strong> 7
<strong>Explanation:</strong> The guarded and unguarded cells are shown in red and green respectively in the above diagram.
There are a total of 7 unguarded cells, so we return 7.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/03/10/example2drawio.png" style="width: 200px; height: 201px;" />
<pre>
<strong>Input:</strong> m = 3, n = 3, guards = [[1,1]], walls = [[0,1],[1,0],[2,1],[1,2]]
<strong>Output:</strong> 4
<strong>Explanation:</strong> The unguarded cells are shown in green in the above diagram.
There are a total of 4 unguarded cells, so we return 4.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= m, n &lt;= 10<sup>5</sup></code></li>
	<li><code>2 &lt;= m * n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= guards.length, walls.length &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>2 &lt;= guards.length + walls.length &lt;= m * n</code></li>
	<li><code>guards[i].length == walls[j].length == 2</code></li>
	<li><code>0 &lt;= row<sub>i</sub>, row<sub>j</sub> &lt; m</code></li>
	<li><code>0 &lt;= col<sub>i</sub>, col<sub>j</sub> &lt; n</code></li>
	<li>All the positions in <code>guards</code> and <code>walls</code> are <strong>unique</strong>.</li>
</ul>

class Solution:
    def countUnguarded(self, m: int, n: int, guards: List[List[int]], walls: List[List[int]]) -> int:
        '''
        create a grid
        add walls as 1
        then add guards as 2
        dfs each direction, marking them as 3's until you hit a wall or another guard 
        finally seach for all 0's in the grid and count them 

        '''
        def search(x,y,dirx,diry):
            nonlocal grid
            if  0 <= x < m and 0<= y < n and grid[x][y] != 2 and grid[x][y] != 1:                
                grid[x][y] = 3
                search(x+dirx,y+diry,dirx,diry)


        grid = [[0 for _ in range(n)] for _ in range(m)]
        for [x,y] in walls:
            grid[x][y] = 1
        for [x,y] in guards:
            grid[x][y] = 2
        for x,y in guards:
            search(x-1,y,-1,0)
            search(x+1,y,1,0)
            search(x,y+1,0,1)
            search(x,y-1,0,-1)
            # go left
            # go right 
            # go up 
            # go down
        
        counter = 0
        for i in range(m):
            for j in range(n):
                if grid[i][j] == 0:
                    counter +=1
        return counter
1968