<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 {
public:
    vector<vector<char>> matrix;
    vector<vector<int>> dp;
    int n, m;

    bool isOne(int r, int c) { return (matrix[r][c] - '0' == 1); }
    int minimumValidSide(int r, int c) {
        int horizontal = 0, vertical = 0;
        for (int i = r; i < n && isOne(i, c); ++i, ++horizontal)
            ;
        for (int j = c; j < m && isOne(r, j); ++j, ++vertical)
            ;
        return min(horizontal, vertical);
    }
    int maxSquareWithUpperLeft(int r, int c) {
        if (r < 0 || r >= n || c < 0 || c >= m || !isOne(r, c))
            return 0;
        if (dp[r][c] != -1)
            return dp[r][c];
        int greatestSubSquare = maxSquareWithUpperLeft(r + 1, c + 1);
        int longestSide = minimumValidSide(r, c);
        return dp[r][c] = longestSide >= greatestSubSquare + 1 ? greatestSubSquare + 1: longestSide;
    }
    int maximalSquare(vector<vector<char>>& input) {
        matrix = input;
        n = matrix.size(), m = matrix[0].size();
        dp.assign(n, vector<int>(m, -1));
        int ans = 0;
        for (int i = 0; i < n; ++i)
            for (int j = 0; j < m; ++j)
                ans = max(ans, maxSquareWithUpperLeft(i, j));
        cout << "ans of 1 1 " << maxSquareWithUpperLeft(1, 1) << endl;
        return ans * ans;
    }
};
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