<p>Given an <code>m x n</code> binary <code>matrix</code> filled with <code>0</code>&#39;s and <code>1</code>&#39;s, <em>find the largest square containing only</em> <code>1</code>&#39;s <em>and return its area</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/26/max1grid.jpg" style="width: 400px; height: 319px;" />
<pre>
<strong>Input:</strong> matrix = [[&quot;1&quot;,&quot;0&quot;,&quot;1&quot;,&quot;0&quot;,&quot;0&quot;],[&quot;1&quot;,&quot;0&quot;,&quot;1&quot;,&quot;1&quot;,&quot;1&quot;],[&quot;1&quot;,&quot;1&quot;,&quot;1&quot;,&quot;1&quot;,&quot;1&quot;],[&quot;1&quot;,&quot;0&quot;,&quot;0&quot;,&quot;1&quot;,&quot;0&quot;]]
<strong>Output:</strong> 4
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/26/max2grid.jpg" style="width: 165px; height: 165px;" />
<pre>
<strong>Input:</strong> matrix = [[&quot;0&quot;,&quot;1&quot;],[&quot;1&quot;,&quot;0&quot;]]
<strong>Output:</strong> 1
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> matrix = [[&quot;0&quot;]]
<strong>Output:</strong> 0
</pre>

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

<ul>
	<li><code>m == matrix.length</code></li>
	<li><code>n == matrix[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 300</code></li>
	<li><code>matrix[i][j]</code> is <code>&#39;0&#39;</code> or <code>&#39;1&#39;</code>.</li>
</ul>

from copy import deepcopy

class Solution:
    def maximalSquare(self, matrix: List[List[str]]) -> int:

        def max_square(start_coords, max_size) -> int:

            neighbours = set()

            for x, y in start_coords:

                next_row = x + max_size
                next_col = y + max_size

                coords = set()
                for i in range(x, next_row+1):
                    coords.add((i, next_col))

                for i in range(y, next_col+1):
                    coords.add((next_row, i))

                for r, c in coords:
                    if r >= 0 and r < ROWS and c >= 0 and c < COLS and (r,c) not in zeros:
                        neighbours.add((r,c))
                    else:
                        return max_size
                
            return max_square(start_coords, max_size + 1)
        
        ROWS = len(matrix)
        COLS = len(matrix[0])

        ones = dict()
        zeros = set()

        for i in range(ROWS):
            for j in range(COLS):

                matrix[i][j] = int(matrix[i][j])

                if matrix[i][j] == 0:
                    zeros.add((i,j))

                if matrix[i][j] == 1:
                    ones[(i,j)] = 1


        for start in list(ones.keys()):
            size = ones[start]
            start_x, start_y = start

            if start_x + size -1 >= ROWS or start_y + size -1 >= COLS:
                continue

            max_length = max_square({start}, size)
            # Cache
            if max_length > size:
                for i in range(start[0], start[0]+max_length-size+1):
                    for j in range(start[1], start[1]+max_length-size+1):
                        ones[(i,j)] = max_length - max(i-start[0], j-start[1])
                        # print(start, i, j, size, max_length)

            
        if not ones:
            return 0

        return max(ones.values())**2
        

   
47625