<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>& nums) {
        int n = nums.size();
        vector<int> prevSmall(n, -1);
        vector<int> nextSmall(n, n);
        stack<int> st;
        for(int i = 0 ; i < n; i++){
            while(!st.empty() && nums[st.top()] > nums[i]){
                nextSmall[st.top()] = i;
                st.pop();
            }
            st.push(i);
        }
        while(!st.empty()) st.pop();
        for(int i = n-1 ; i >= 0; i--){
            while(!st.empty() && nums[st.top()] > nums[i]){
                prevSmall[st.top()] = i;
                st.pop();
            }
            st.push(i);
        }

        int maxArea = 0;
        for(int i = 0; i < n; i++){
            maxArea = max(maxArea, nums[i] * (nextSmall[i] - prevSmall[i] - 1));
        }
        return maxArea;
    }
    int maximalRectangle(vector<vector<char>>& matrix) {
        vector<int> height(matrix[0].size(), 0);
        int maxArea = 0;
        for(int i = 0 ; i < matrix.size(); i++){
            for(int j = 0 ; j < matrix[0].size(); j++){
                height[j] = matrix[i][j] == '0' ? 0 : ++height[j];
            }
            maxArea = max(maxArea, largestRectangleArea(height));
        }
        return maxArea;
    }
};
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