Largest Rectangle in Histogram -- LeetCode

[Question]

Given n non-negative integers representing the histogram's bar height where the width of each bar is 1, find the area of largest rectangle in the histogram.

Above is a histogram where width of each bar is 1, given height = [2,1,5,6,2,3].

The largest rectangle is shown in the shaded area, which has area = 10 unit.

For example,
Given height = [2,1,5,6,2,3],
return 10.

[Analysis]
If we can calculate each rectangle with max height of H[i], we can get the maximum area. To calculate such rectangles, for each H[i], we need to get the first H[j] where H[j]<H[i], j<i and the first H[k]<H[i], where k>i. 

Using a stack can help to find such j and k. The Time Complexity is O(N).

[Solution]
class Solution {
public:
    int largestRectangleArea(vector<int>& heights) {
        stack<int> st;
        int area=0;
        heights.push_back(0);
        for(int i=0; i<heights.size(); i++) {
            while(!st.empty() && heights[st.top()]>heights[i] ) {
                int h = heights[st.top()];
                st.pop();
                int j=st.empty()?-1:st.top();
                area = max(area, (i-j-1)* h);
            }
            //--this loop is not necessary but save calculation above.
            while (!st.empty() && heights[st.top()]==heights[i])
                st.pop();
            st.push(i);
        }
        return area;
    }
};