<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 {

vector<int> nextSmallerElement(vector<int> arr, int n){
    vector<int> ansArr(n, n);
    stack<int> st;

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

    return ansArr;
}


vector<int> prevSmallerElement(vector<int> arr, int n){
    vector<int> ansArr(n, -1);
    stack<int> st;

    for(int i=0; i<n; i++){
        while(!st.empty() && arr[st.top()] >= arr[i]) st.pop();
        if(!st.empty()) ansArr[i] = st.top();
        st.push(i);
    }

    return ansArr;
}



int largestAreaHistogram(vector<int> arr, int n){
    vector<int> nextArr = nextSmallerElement(arr, n);
    vector<int> prevArr = prevSmallerElement(arr, n);


    int ans = 0;
    for(int i=0; i<n; i++){
        ans = max(ans, arr[i] * (nextArr[i] - prevArr[i] - 1));
    }
    
    return ans;
}




public:
    int maximalRectangle(vector<vector<char>>& matrix) {
        int n = matrix[0].size();
        vector<int> arr(n, 0);

        int maxRectangle = 0;
        for(int j=0; j<matrix.size(); j++){
        for(int i=0; i<n; i++){
            if(matrix[j][i] == '1') arr[i] += 1;
            else if(matrix[j][i] == '0') arr[i] = 0;
        }

        maxRectangle = max(maxRectangle, largestAreaHistogram(arr, n));

        }

        return maxRectangle;
    }
};
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