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 height = [2,1,5,6,2,3],
return 10.

分析：设置一个stack，保存柱状图递增区间的标号，如例子中保存1,2,3，直到i=4时height[4]=2打破了一直递增的状态，因此，弹出top的元素，计算面积为6；若stack不为空或者当前元素小于等于stack中的top元素，则一直弹出top元素并更新面积的最大值。遇到末尾我们添加的-1时，由于已经没有元素比-1小，所以开始弹出stack中的元素，同时计算面积并更新最大值。参考至hackersun007的博客。运行时间31ms

class Solution {
public:
    int largestRectangleArea(vector<int>& height) {
        height.push_back(-1);
        stack<int> index;
        int i = 0, result = 0;
        while(i < height.size()){
            if(index.empty() || height[i] > height[index.top()])
                index.push(i++);
            else{
                int temp = index.top();
                index.pop();
                result = max(result, height[temp] * (index.empty() ? i :(i-index.top()-1)));
            }
        }
        return result;
    }
};