<p>Given a <code>rows x cols</code>&nbsp;binary <code>matrix</code> filled with <code>0</code>&#39;s and <code>1</code>&#39;s, find the largest rectangle containing only <code>1</code>&#39;s and return <em>its area</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/09/14/maximal.jpg" style="width: 402px; height: 322px;" />
<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> 6
<strong>Explanation:</strong> The maximal rectangle is shown in the above picture.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> matrix = [[&quot;0&quot;]]
<strong>Output:</strong> 0
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> matrix = [[&quot;1&quot;]]
<strong>Output:</strong> 1
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>rows == matrix.length</code></li>
	<li><code>cols == matrix[i].length</code></li>
	<li><code>1 &lt;= row, cols &lt;= 200</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:
    int maximalRectangle(vector<vector<char>>& matrix) {
        int n = (int)matrix.size();
        int m = (int)matrix[0].size();

        auto getArea = [&](vector<int> A)->int {
            int n = (int)A.size();
            vector<int> left(n), right(n);
            stack<int> st;
            for(int i = 0; i < n; i++) {
                if(st.empty() or A[st.top()] < A[i] ) {
                    left[i] = i;
                    st.push(i);
                }
                else {
                    while(!st.empty() and A[st.top()] >= A[i]) {
                        left[i] = left[st.top()];
                        st.pop();
                    }

                    st.push(i);
                }
            }

            while(!st.empty()) st.pop();
            for(int i = n-1; i >= 0; i--) {
                if(st.empty() or A[st.top()] < A[i]) {
                    right[i] = i;
                    st.push(i);
                }
                else {
                    while(!st.empty() and A[st.top()] >= A[i]) {
                        right[i] = right[st.top()];
                        st.pop();
                    }

                    st.push(i);
                }
            }

            int maxArea = 0;
            for(int i = 0; i < n; i++) {
                int len = right[i] - left[i] + 1;
                maxArea = max(maxArea, len * A[i]);
            }
            
            return maxArea;
        };

        int maxArea = 0;
        vector<int> pre(m);
        for(int i = 0; i < n; i++) {
            vector<int> curr(m);
            for(int j = 0; j < m; j++) {
                if(matrix[i][j] == '1') {
                    curr[j] = pre[j] + 1;
                }
            }
            int area = getArea(curr);
            maxArea = max(maxArea, area);
            pre = curr;
        }
        
        return maxArea;
    }
};
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