<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>

import numpy as np
class Solution:
    def maximalSquare(self, matrix: List[List[str]]) -> int:
        '''
        M,N = len(matrix), len(matrix[0])
        cumsum = np.zeros((M+1,N+1))
        for i in range(M):
            for j in range(N):
                cumsum[i+1,j+1] = int(matrix[i][j]) + cumsum[i,j+1] + cumsum[i+1,j] - cumsum[i,j]
        
        max_size = min(M,N)
        for sz in range(max_size, 0, -1):
            for i in range(M+1-sz):
                for j in range(N+1-sz):
                    area_sum = cumsum[i+sz,j+sz] - cumsum[i,j+sz] - cumsum[i+sz,j] + cumsum[i,j]
                    if area_sum == sz*sz:
                        return sz*sz
        return 0
        '''
        M,N = len(matrix), len(matrix[0])
        dp = np.zeros((M+1,N+1)).astype(int)       
        for i in range(M):
            for j in range(N):
                if matrix[i][j] == '1':
                    dp[i+1,j+1] = 1 + min(dp[i,j+1], dp[i+1,j], dp[i,j])
        max_size = np.max(np.max(dp))
        return max_size*max_size
32775