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

        for(int i = 0; i < n; i++) {
            while(!st.empty() && heights[st.top()] >= heights[i]) {
                rightMin[st.top()] = i;
                st.pop();
            }
            st.push(i);
        }

        for(int i = n-1; i >= 0; i--) {
            while(!st.empty() && heights[st.top()] > heights[i]) {
                leftMin[st.top()] = i;
                st.pop();
            }
            st.push(i);
        }

        int maxArea = 0;
        for(int i = 0; i < n; i++) {
            int area = heights[i] * (rightMin[i] - leftMin[i] - 1);
            maxArea = max(maxArea, area);
        }

        return maxArea;
    }
};

/*

 0, 1,  2, 3, 4, 5, 6
 ------------------
 2,  1, 5, 6, 2, 3
-1, -1, 1, 2, 1, 4 - prev smaller
 1,  6, 4, 4, 6, 6  - next smaller
 --------------------
 
 */
//2 * 3 * 2
// 5 * 1 * 2 = 10
// 2 * 3 * 2 = 12
86578