Largest Rectangle in Histogram

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 heights = [2,1,5,6,2,3],
return 10.

solution 1:

class Solution {
public:
    int largestRectangleArea(vector<int>& heights);
};

int Solution::largestRectangleArea(vector<int>&  heights)
{
    int heightsSize = heights.size();  
	std::stack<int> s;

	int i = 0;
	int max = 0;
	while(i < heightsSize)
	{
		if(s.empty() || heights[s.top()] <= heights[i])
		{
			s.push(i);
			i++;
		} 
		else 
		{
			int index = s.top();
			s.pop();
			int tmp_max = heights[index] *(s.empty() ? i : (i - s.top() - 1));
			if(max < tmp_max)
			{
				max = tmp_max;
			}
		}
	}

	while(!s.empty())
	{
		int index = s.top();
		s.pop();
		int tmp_max = heights[index] *(s.empty() ? i : (i - s.top() - 1));
		if (max < tmp_max)
		{
			max = tmp_max;
		}
	}

	return max;
}

https://leetcode.com/problems/largest-rectangle-in-histogram/

http://www.geeksforgeeks.org/largest-rectangle-under-histogram/