<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:
    vector<int> nextSmaller(vector<int> &arr){
        stack<int> s;
        s.push(-1);
        int n = arr.size();
        vector<int> ans(n);
        for(int i=n-1; i>=0; i--){
            int item = arr[i];
            while(s.top() != -1 && arr[s.top()] >= item)
                s.pop();
            if(s.top() == -1)
                ans[i] = n;
            else
                ans[i] = s.top();
            s.push(i);
        }
        return ans;
    }

    vector<int> prevSmaller(vector<int> &arr){
        stack<int> s;
        s.push(-1);
        int n = arr.size();
        vector<int> ans(n);
        for(int i=0; i<n; i++){
            int item = arr[i];
            while(s.top() != -1 && arr[s.top()] >= item)
                s.pop();
            ans[i] = s.top();
            s.push(i);
        }
        return ans;
    }

    int largestArea(vector<int> arr){
        vector<int> prev = prevSmaller(arr);
        vector<int> next = nextSmaller(arr);
        int maxArea = INT_MIN;
        for(int i=0; i<arr.size(); i++){
            int length = arr[i];
            int breadth = next[i] - prev[i] - 1;
            int newArea = length * breadth;
            maxArea = max(maxArea, newArea);
        }
        return maxArea;
    }

    int maximalRectangle(vector<vector<char>>& matrix) {
        int maxi = INT_MIN;
        vector<int> histogram(matrix[0].size(), 0);
        for(int i=0; i<matrix.size(); i++){
            for(int j=0; j<histogram.size(); j++){
                if(matrix[i][j] == '1')
                    histogram[j]++;
                else
                    histogram[j] = 0;
            }
            maxi = max(maxi, largestArea(histogram));
        }
        return maxi;
    }
};
21951