<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> PSE(vector<int> nums){
        vector<int> result(nums.size() , -1);
        stack<pair<int,int>> st;
        for(int i = 0 ; i < nums.size() ; i++){

            while(!st.empty() && st.top().first >= nums[i]) st.pop();
            if(!st.empty()) result[i] = st.top().second;
            st.push({nums[i],i});
        }
        return result;
    }

    vector<int> NSE(vector<int> nums) {
        vector<int> result(nums.size(), nums.size());
        stack<pair<int, int>> st;

        for (int i = nums.size() - 1; i >= 0; i--) {
            while (!st.empty() && st.top().first >= nums[i]) {
                st.pop();
            }
            if (!st.empty()) {
                result[i] = st.top().second;
            }
            st.push({nums[i], i});
        }

        return result;
    }
    

    int largestRectangleArea(vector<int>& heights) {
        if(heights.size() == 0) return 0;
        vector<int> nse = NSE(heights);
        vector<int> pse = PSE(heights);
        int ans = 0;
        for(int i = 0; i < heights.size() ; i++){
            ans = max(ans, (heights[i] * (nse[i] - pse[i]-1)));
        }
        return ans;
    }
};

auto init = []() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  return '$';
}();
90701