<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) {
        vector<int> leftMin(heights.size(), -1);
        vector<int> rightMin(heights.size(), heights.size());

        vector<int> monotonicStack;
        for(auto i = 0; i < heights.size(); ++i) {
            if(monotonicStack.empty()) {
                monotonicStack.push_back(i);
            }
            else {
                if(heights.at(i) >= heights.at(monotonicStack.back())) {
                    monotonicStack.push_back(i);
                }
                else {
                    while(!monotonicStack.empty() && heights.at(monotonicStack.back()) > heights.at(i)) {
                        rightMin[monotonicStack.back()] = i;
                        monotonicStack.pop_back();
                    }
                    monotonicStack.push_back(i);
                }
            }
        }

        monotonicStack.clear();

        for(int i = heights.size() - 1; i >= 0; --i) {
            if(monotonicStack.empty()) {
                monotonicStack.push_back(i);
            }
            else {
                while(!monotonicStack.empty() && heights.at(monotonicStack.back()) > heights.at(i)) {
                    leftMin[monotonicStack.back()] = i;
                    monotonicStack.pop_back();
                }
                monotonicStack.push_back(i);
            }
        }


        int maxArea = 0;

        bool debug = false;
        if(debug) {
            cout << "heights:" << endl;
            for(auto i : heights) {
                cout << i << ";";
            }
            cout << endl;
            cout << "leftMin:" << endl;
            for(auto i : leftMin) {
                cout << i << ";";
            }
            cout << endl;
            cout << "rightMin:" << endl;
            for(auto i : rightMin) {
                cout << i << ";";
            }
            cout << endl;
        }

        for(int i = 0; i < heights.size(); ++i) {
            maxArea = max(maxArea, heights.at(i) * (rightMin.at(i) - leftMin.at(i) - 1));
        }

        return maxArea;
    }
};
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