<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 {
private:
    vector<int> nextSmallest(vector<int> row){
        stack<int> st;
        st.push(-1);
        int n = row.size();
        vector<int> soln(n);
        for(int i = n-1; i >= 0; i--){
            int elem = row[i];
            while(st.top() != -1 && row[st.top()] >= elem){
                st.pop();
            }
            soln[i] = st.top();
            st.push(i);
        }
        return soln;
    }

    vector<int> prevSmallest(vector<int> row){
        stack<int> st;
        st.push(-1);
        int n = row.size();
        vector<int> soln(n);
        for(int i = 0; i < n; i++){
            int elem = row[i];
            while(st.top() != -1 && row[st.top()] >= elem){
                st.pop();
            }
            soln[i] = st.top();
            st.push(i);
        }
        return soln;
    }

    int maxArea(vector<int> row){
        int maxArea = 0;

        vector<int> next = nextSmallest(row);
        vector<int> prev = prevSmallest(row);

        for(int i = 0; i < row.size(); i++){
            int nxt = next[i];
            int prv = prev[i];
            if(nxt == -1){
                nxt = row.size();
            }
            int width = nxt - prv - 1; 
            int area = width * row[i];
            if(area > maxArea){
                maxArea = area;
            }
        }
        return maxArea;
    }
public:
    int maximalRectangle(vector<vector<char>>& matrix) {
        int rowSize = matrix[0].size();
        int colSize = matrix.size();

        vector<int> histogram(rowSize, 0);
        int area = 0;

        for(int i = 0; i < colSize; i++){
            for(int j = 0; j < rowSize; j++){
                histogram[j] = (matrix[i][j] == '0') ? 0 : histogram[j] + 1;
            }
            area = max(area, maxArea(histogram));
        }
        return area;
    }
};
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