Largest Rectangle in Histogram

Problem Statement

Given an array of integers heights representing the histogram's bar height where the width of each bar is 1, return the area of the largest rectangle in the histogram.

Leetcode link

Example 1:

Input: heights = [2,1,5,6,2,3]
Output: 10
Explanation: 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.

Example 2:

Input: heights = [2,4]
Output: 4

Constraints:

• 1 <= heights.length <= 10⁵
• 0 <= heights[i] <= 10⁴

Code

Python

def largestRectangleArea(self, height):
    height.append(0)
    stack = [-1]
    ans = 0
    for i in xrange(len(height)):
        while height[i] < height[stack[-1]]:
            h = height[stack.pop()]
            w = i - stack[-1] - 1
            ans = max(ans, h * w)
        stack.append(i)
    height.pop()
    return ans

C++

class Solution {
public:
    int largestRectangleArea(vector<int>& heights) {
        heights.push_back(0);

        stack <int>st;
        int area=0;

        for(int i=0;i<heights.size();i++){
            while(!st.empty() && heights[st.top()]>heights[i]){
                int h=heights[st.top()];
                st.pop();

                if(st.empty()){
                    area=max(area,h*i);
                }
                else{
                    int l=i-st.top()-1;
                    area=max(area,h*l);
                }
            }
            st.push(i);
        }
        return area;
    }
};