<p>An <code>n x n</code> grid is composed of <code>1 x 1</code> squares where each <code>1 x 1</code> square consists of a <code>&#39;/&#39;</code>, <code>&#39;\&#39;</code>, or blank space <code>&#39; &#39;</code>. These characters divide the square into contiguous regions.</p>

<p>Given the grid <code>grid</code> represented as a string array, return <em>the number of regions</em>.</p>

<p>Note that backslash characters are escaped, so a <code>&#39;\&#39;</code> is represented as <code>&#39;\\&#39;</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2018/12/15/1.png" style="width: 200px; height: 200px;" />
<pre>
<strong>Input:</strong> grid = [&quot; /&quot;,&quot;/ &quot;]
<strong>Output:</strong> 2
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2018/12/15/2.png" style="width: 200px; height: 198px;" />
<pre>
<strong>Input:</strong> grid = [&quot; /&quot;,&quot;  &quot;]
<strong>Output:</strong> 1
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2018/12/15/4.png" style="width: 200px; height: 200px;" />
<pre>
<strong>Input:</strong> grid = [&quot;/\\&quot;,&quot;\\/&quot;]
<strong>Output:</strong> 5
<strong>Explanation: </strong>Recall that because \ characters are escaped, &quot;\\/&quot; refers to \/, and &quot;/\\&quot; refers to /\.
</pre>

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

<ul>
	<li><code>n == grid.length == grid[i].length</code></li>
	<li><code>1 &lt;= n &lt;= 30</code></li>
	<li><code>grid[i][j]</code> is either <code>&#39;/&#39;</code>, <code>&#39;\&#39;</code>, or <code>&#39; &#39;</code>.</li>
</ul>

from collections import defaultdict

class Solution:
    def regionsBySlashes(self, grid: List[str]) -> int:
        '''
        nxn grid where each square is a 
        / \ or a blank 
        given the grid represented as a string array, return the number of 
        regions 

        ex. [' /', 
             '/ ']
        number of regions is 2
        this as a grid is 
        [[0, 1],
         [1, 0]]
        [[0, 0, 0, 1],
         [0, 0, 1, 0],
         [0, 1, 0, 0],
         [1, 0, 0, 0]]
        the number of island is 2
        
        ex. [' /',
             '  ']
        number of regions is 1 (can have incompleted lines)
        [[0, 1],
        [0, 0]]
        [0, 0, 0, 1],
        [0, 0, 1, 0]

        ex. ['/\',
             '\/]
        5 number of regions 
        can I represent this in a 2D matrix?
        [0, 1, 0, 1, 0],
        [0, 1, 0, 0]
        trying to figure out the number of islands
        
        [0, 1, 1, 0],
        [1, 0, 0, 1],
        [0, 1, 1, 0]
        Match: 
        Matrix Creation and then Num of Islands

        Plan:
        1. Create a dictionary that maps the slash and the 3x3 corresponding
        2. For each row, build the 3x(n * 3) where n is the number of characters ( , /, and \\)
        3. Then we append those onto the 2D matrix
        4. We perform Num of Islands (DFS) on it
        '''

        mappingDict = {
            ' ': [[0, 0, 0], [0, 0, 0], [0, 0, 0]],
            '/': [[0, 0, 1], [0, 1, 0], [1, 0, 0]],
            '\\':[[1, 0, 0], [0, 1, 0], [0, 0, 1]]
        }

        regionMatrix = [] 
        for row in grid:
            index = 0 
            newRow = [[],[],[]]
            while index < len(row):
                curChar = row[index] 
                newMatrix = mappingDict[curChar] if (curChar == ' ' or curChar == '/') else mappingDict['\\']
                for i, newMatrixRow in enumerate(newMatrix):
                    newRow[i].extend(newMatrixRow)
                index = index + 1
            regionMatrix.extend(newRow)
        
        visited = set()
        ROW = len(regionMatrix)
        COL = len(regionMatrix[0])

        def dfs(r, c):
            nonlocal visited, ROW, COL, regionMatrix
            if (r not in range(ROW) or c not in range(COL) or (r, c) in visited or regionMatrix[r][c] == 1):
                return 
            visited.add((r,c))
            dirs = [[1, 0], [-1, 0], [0, 1], [0, -1]]
            for dr, dc in dirs:
                dfs(r + dr, c + dc)

        print(regionMatrix)
        numIslands = 0
        for i in range(ROW):
            for j in range(COL):
                if regionMatrix[i][j] == 0 and (i, j) not in visited:
                    dfs(i, j)
                    numIslands += 1

        return numIslands

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