<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> nextSmallestElement(vector<int> arr) {
        stack<int> s;
        vector<int> ans(arr.size());

        s.push(-1);

        for (int i = arr.size() - 1; i >= 0; i--) {
            while (s.top() != -1 && arr[s.top()] >= arr[i]) {
                s.pop();
            }
            ans[i] = s.top();
            s.push(i);
        }

        return ans;
    }

    vector<int> previousSmallestElements(vector<int>& arr) {
        vector<int> ans(arr.size());

        stack<int> st;
        st.push(-1);

        for (int i = 0; i < arr.size(); i++) {

            while (st.top() != -1 && arr[st.top()] >= arr[i]) {
                st.pop();
            }
            ans[i] = (st.empty() ? -1 : st.top());
            st.push(i);
        }

        return ans;
    }

    int largestRectangleArea(vector<int>& heights) {

        // 1️⃣ step 1
        vector<int> next = nextSmallestElement(heights);

        // 2️⃣ step 2
        vector<int> prev = previousSmallestElements(heights);

        // 3️⃣ Area

        // this can store max area of the rectangle
        int maxArea = INT_MIN;

        // iterate the main array
        for (int i = 0; i < heights.size(); i++) {

            // calculate the length of rectangle which is current height
            int length = heights[i];

            // jab bhi hme next[i] ki value -1 milegi to iska mtlb uske aage koi
            // usse chhota element nhi hai to usme hm main array ka size put kar
            // dege
            if (next[i] == -1) {
                next[i] = heights.size();
            }

            // calculate exact width of rectangle
            int width = next[i] - prev[i] - 1;

            // here is max area
            maxArea = max(maxArea, length * width);
        }

        return maxArea;
    }
};
87306