[LeetCode]Largest Rectangle in Histogram

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.

常规的做法就是对每个点计算最大的面积值，最后得到总体的最大值，这样做的时间复杂度是O(n^2)。

巧妙利用stack的性质，可以将时间复杂度降为O(n)。参考这篇博文。

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