<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>

#include <algorithm>

using namespace std;
class Solution {
public:
//Algo one - scan the matrix for squares of size 1x1, 2x2, 3x3...up to min(n,m)*min(n,m); each step takes n*m comparisons, times n. So around O(n3)
    int maximalSquare(vector<vector<char>>& matrix) {

        int maxSide = 0; 
        //m*n matrix 
        int m = matrix.size() - 1;
        int n = matrix[0].size() - 1;

        for(int i = 0; i < matrix.size(); i++)
            for(int j = 0; j < matrix[0].size(); j++)
                if(matrix[i][j] == '1') maxSide = 1; 

        if(m == 0 || n == 0) return maxSide; 

        vector<vector<char>> small(m, vector<char>(n, '0'));
        while(m >= 1 && n >=1)
        {
            bool hasSq = false; 
            for(int r = 0; r < m; r++)
            {
                for(int c = 0; c < n; c++)
                {
                    if(matrix[r][c] == '1' && matrix[r+1][c] == '1' && matrix[r][c+1] == '1' && matrix[r+1][c+1] == '1')
                    {
                        small[r][c] = '1'; 
                        hasSq = true;
                    }
                }
            }
            if(hasSq == true) maxSide++; 
            for(int r = 0; r < m; r++){
                for(int c = 0; c < n; c++){
                    matrix[r][c] = small[r][c];
                    small[r][c] = '0';
                }
                std::cout << endl; 
            }
            m--; n--; 
        }
        return maxSide*maxSide; 

    }
};
23300