<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>

class Solution:
    def maximalSquare(self, matrix: List[List[str]]) -> int:
        m = len(matrix)
        n = len(matrix[0])
        dp_row = [[0 for i in range(n)] for j in range(m)]
        for i in reversed(range(m)):
            for j in reversed(range(n)):
                if matrix[i][j] == '1' and j<n-1:
                    dp_row[i][j] = 1 + dp_row[i][j+1]
                elif matrix[i][j] == '1':
                    dp_row[i][j] = 1
        
        dp_col = [[0 for i in range(n)] for j in range(m)]
        for i in reversed(range(m)):
            for j in reversed(range(n)):
                if matrix[i][j] == '1' and i<m-1:
                    dp_col[i][j] = 1 + dp_col[i+1][j]
                elif matrix[i][j] == '1':
                    dp_col[i][j] = 1
        
        dp_area = [[0 for i in range(n)] for j in range(m)]
        res = 0
        for i in reversed(range(m)):
            for j in reversed(range(n)):
                if matrix[i][j] == '1' and i<m-1 and j<n-1:
                    if (min(dp_row[i][j]-1, dp_col[i][j]-1))**2 >= dp_area[i+1][j+1]:
                        dp_area[i][j] = (sqrt(dp_area[i+1][j+1]) + 1)**2
                    else:
                        dp_area[i][j] = min(dp_row[i][j], dp_col[i][j])**2
                elif matrix[i][j] == '1' and i==m-1:
                    dp_area[i][j] = 1
                elif matrix[i][j] == '1' and j==n-1:
                    dp_area[i][j] = 1
                if dp_area[i][j] > res:
                    res = dp_area[i][j]
        print(dp_col)
        print(dp_row)
        print(dp_area)
        return int(res)


        
26175