<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 largestRectangleArea(vector<int>& heights) {
        int n=heights.size();
        stack<int> st;
        int leftSmall[n],rightSmall[n];
        for(int i=0;i<n;i++){
            while(!st.empty() && heights[st.top()]>=heights[i]){
                st.pop();
            }

            if(st.empty()){
                leftSmall[i]=0;
            }else{
                leftSmall[i]=st.top()+1;
            }
            st.push(i);
        }

        while(!st.empty()) st.pop();

        for(int i=n-1;i>=0;i--){
            while(!st.empty()&& heights[st.top()]>=heights[i]){
                st.pop();
            }

            if(st.empty()) rightSmall[i]=n-1;
            else rightSmall[i]=st.top()-1;

            st.push(i);
        }

        int maxA=0;
        for(int i=0;i<n;i++){
            maxA=max(maxA,heights[i]*(rightSmall[i]-leftSmall[i]+1));
        }
        return maxA;
    }

    int maximalRectangle(vector<vector<char>>& matrix) {
        int n=matrix.size();
        int m=matrix[0].size();
        vector<int> height(m,0);
        int maxArea=0;
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                if(matrix[i][j]=='1'){
                    height[j]++;
                }
                else{
                    height[j]=0;
                }
            }
            int area=largestRectangleArea(height);
            maxArea=max(area,maxArea);
        }
        return maxArea;
    }
};
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