<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 maxArea(vector<int> &nums) {
        int n = nums.size();
        // for(int i=0;i<n;i++) cout << nums[i] << " ";
        // cout << endl;
        vector<int> left(n, -1);
        vector<int> right(n, -1);
        
        stack<int> st;
        
        for(int i=0;i<n;i++) {
            while(!st.empty() && nums[st.top()]>=nums[i]) {
                st.pop();
            }
            if(!st.empty()) left[i] = st.top();
            st.push(i);
        }
        
        while(!st.empty()) st.pop();
        
        for(int i=n-1;i>=0;i--) {
            while(!st.empty() && nums[st.top()]>=nums[i]) {
                st.pop();
            }
            if(!st.empty()) right[i] = st.top();
            st.push(i);
        }
        
        int ans = 0;
        for(int i=0;i<n;i++) {
            int left_index, right_index;
            if(left[i]==-1) left_index = i;
            else left_index = i-left[i]-1;
            
            if(right[i]==-1) right_index = n-1-i;
            else right_index = right[i]-i-1;
            
            ans = max(ans, (left_index+right_index+1)*nums[i]);
        }
        
        return ans;
    }
    
    int maximalRectangle(vector<vector<char>>& matrix) {
        int n = matrix.size();
        int m = matrix[0].size();
        
        vector<vector<int>> dp(n, vector<int> (m, 0));
        
        int ans = 0;
        
        for(int i=0;i<n;i++) {
            for(int j=0;j<m;j++) {
                if(i==0) dp[i][j] = matrix[i][j]-'0';
                else {
                    if(matrix[i][j]=='1') {
                        dp[i][j] = 1+dp[i-1][j];
                    }
                    else {
                        dp[i][j] = 0;
                    }
                }
            }
            // cout << maxArea(dp[i]) << endl;
            ans = max(ans, maxArea(dp[i]));
        }
        
        return ans;
    }
};
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