<p>Given an array of integers <code>heights</code> representing the histogram&#39;s bar height where the width of each bar is <code>1</code>, return <em>the area of the largest rectangle in the histogram</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/01/04/histogram.jpg" style="width: 522px; height: 242px;" />
<pre>
<strong>Input:</strong> heights = [2,1,5,6,2,3]
<strong>Output:</strong> 10
<strong>Explanation:</strong> The above is a histogram where width of each bar is 1.
The largest rectangle is shown in the red area, which has an area = 10 units.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/01/04/histogram-1.jpg" style="width: 202px; height: 362px;" />
<pre>
<strong>Input:</strong> heights = [2,4]
<strong>Output:</strong> 4
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= heights.length &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= heights[i] &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution {
public:
    vector<int> calPosSmaller(vector<int>& heights) {
        vector<int> ret(heights.size(), 0);
        stack<int> st;
        st.push(0);
        int i = 1;
        while(i < heights.size()) {
            while(!st.empty()) {
                if (heights[i] < heights[st.top()]) {
                    ret[st.top()] = i;
                    st.pop();
                } else {
                    break;
                }
            }
            st.push(i);
            i++;
        }
        while(!st.empty()) {
            ret[st.top()] = heights.size();
            st.pop();
        }
        return ret;
    }

    int largestRectangleArea(vector<int>& heights) {
        if(heights.size() == 1) return heights[0];
        vector<int> right = calPosSmaller(heights);
        vector<int> vec1 = heights;
        reverse(vec1.begin(), vec1.end());
        vector<int> left = calPosSmaller(vec1);

        for(int i = 0; i < heights.size(); i++) {
            left[i] = heights.size() - left[i] -1;
            //if(left[i] < 0) left[i] = 0;
        }
        reverse(left.begin(), left.end());

        int ret = 0;
        for (int i = 0; i < heights.size(); i++) {
            int area = (right[i] - left[i] - 1) * heights[i];
            if(area > ret) ret = area;
        }
        return ret;
    }
};
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