<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:
    int largestRectangleArea(vector<int>& heights) {
        std::vector<int> rightBound(heights.size(), heights.size() - 1);
        std::vector<int> leftBound(heights.size(), 0);

        std::stack<int> stR;
        for (int i = 0; i < heights.size(); i++) {
            while (!stR.empty() && heights[stR.top()] > heights[i]) {
                rightBound[stR.top()] = i - 1;
                stR.pop();
            }
            stR.push(i);
        }

        std::stack<int> stL;
        for (int i = heights.size() - 1; i >= 0; i--) {
            while (!stL.empty() && heights[stL.top()] > heights[i]) {
                leftBound[stL.top()] = i + 1;
                stL.pop();
            }
            stL.push(i);
        }

        int maxRect = 0;
        for (int i = 0; i < heights.size(); i++) {
            int rect = heights[i] * (rightBound[i] - leftBound[i] + 1);
            if (maxRect < rect) {
                maxRect = rect;
            }
            //printf("i: %d, height: %d, leftPos: %d, rightPos: %d, square: %d \n", i, heights[i], leftBound[i], rightBound[i], rect);
        }

        return maxRect;
    }
};
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