Largest Rectangle in Histogram -- 待看

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.

此題難度很大，個人並未想出來。第一反應是F(i,j)但是超時錯誤。此處借鑑他人。並理解了下代碼。以及相關題目Maximal Rectangle，利用此題結論。先做的Maximal Rectangle，直接被打擊，後面度娘下，發現此題很刁鑽，利用了本題的思路。否則有的超時！！

借鑑自：http://blog.csdn.net/sbitswc/article/details/33451347

  int largestRectangleArea(vector<int> &height) 
{

	stack<int> st;
 
	int max_area = 0;
	height.push_back(0);//技巧

	for(int i = 0;i < height.size();)
	{
		if(st.empty() || height[i] > height[st.top()])
		{
			st.push(i);
			i++;
 
		}
		else
		{
			int temp_index = st.top();
			st.pop();
			max_area = max(max_area, height[temp_index]*(st.empty()? i:i-st.top()-1));  
			//cout<<height[temp_index]*(st.empty()? i:i-st.top()-1)<<endl;
			//此題關鍵的地方 最後一句索引與高度的獲取。在棧裏面的是最小遞增序列（當前）
		}

	}
	return max_area;

}