<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 solve(vector<int>&heights){
     int n=heights.size();
        stack<int>st;
        vector<int>next(n,-1);
        for(int i=0;i<heights.size();i++){
            while(st.empty()==false && heights[st.top()]>heights[i]){
                next[st.top()]=i;
                st.pop();
            }
            st.push(i);
        }
        while(!st.empty()){
            st.pop();
        }
         vector<int>prev(n,-1);
         for(int i=n-1;i>=0;i--){
            while(st.empty()==false && heights[st.top()]>heights[i]){
                prev[st.top()]=i;
                st.pop();
            }
            st.push(i);
         }
         int mx=0;
         for(int i=0;i<n;i++){
            int sum=0;
            if(prev[i]==-1){
                sum+=i;
            }
            else if(prev[i]!=-1){
              sum+=(i-prev[i]-1);
            }
            if(next[i]==-1){
                sum+=(n-i-1);
            }
            else if(next[i]!=-1){
                sum+=(next[i]-i-1);
            }
            sum+=1;
            sum=sum*heights[i];
            mx=max(mx,sum);
         }
        return mx;
   }
    int maximalRectangle(vector<vector<char>>& mat) {
        int n=mat.size();
        int m=mat[0].size();
        int ans=0;
        vector<int>arr(m,0);
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                if(mat[i][j]=='1'){
                 arr[j]=arr[j]+1;
                }else{
                    arr[j]=0;
                }
            }
            ans=max(ans,solve(arr));
        }
        return ans;
    }
};
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