<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 {
int N;
int M;
int max_square;
vector<vector<int>> memo;
vector<vector<char>> mat;
public:
    int maximalSquare(vector<vector<char>>& matrix) {
        N = matrix.size();
        M = matrix[0].size();
        mat = matrix;
        max_square = 0; 
        memo.assign(N, vector<int>(M,0));

        int p = solve(N-1, M-1);
        return pow(max_square, 2);
    }

    int solve(int i, int j){
        if (i < 0 || j < 0) return 0;

        int& ans = memo[i][j];
        if (ans) return ans;

        /*
        [
            ["1","0","1","0","0"],
            ["1","0","1","1","1"],
            ["1","1","1","1","1"],
            ["1","0","0","1","0"]
            ]

             [0 , 0 , 0 , 0 , 0 ]
             [0 , 0 , 0 , 0 , 0 ]
             [0 , 0 , 0 , 0 , 0 ]
             [0 , 0 , 0 , 0 , 0 ]

        */
        int t = solve(i-1,j);
        int l = solve(i, j-1);
        int tl = solve(i-1,j-1);
        if (mat[i][j] == '1') ans = 1 + min(min(t,l), tl);
        max_square = max(max_square, ans);
        return ans;
    }
};
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