leetcode-84. 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.

最开始的想法是寻找以每一根柱为起始的最大面积，时间复杂度为O(n^2)，超时了。

O(n)的做法见http://www.cnblogs.com/felixfang/p/3676193.html 主要思路是利用栈将直方图分解为递增段，而求解递增段的时间复杂度为O(n)。

inline int max(int a, int b)
{
    return a>b ? a : b;
}
int largestRectangleArea(vector<int>& heights) {
    int s = 0;
    heights.push_back(0);
    stack<int> h;
    for (int i = 0; i<heights.size(); i++)
    {
        if (h.empty() || heights[h.top()]<heights[i])
            h.push(i);
        else
        {
            int tmp = h.top();
            h.pop();
            if (h.empty())
                s = max(s, heights[tmp] * i);//当栈为空，表示heights[tmp]比之前i个都小(栈底最小)
            else
                s = max(s, heights[tmp] * (i - h.top() - 1));
            i--;
        }
    }
    return s;
}