[LeetCode]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.

思考：记录每个矩形最左最右比自己高的矩形下标，左右相减即为长，乘以矩形高，即为当前矩形可以组成矩形最大面积。求最大值。

struct Node{
	int height;
	int left;
	int right;
	int area;
};
class Solution {
public:
    int largestRectangleArea(vector<int> &height) {
        // IMPORTANT: Please reset any member data you declared, as
        // the same Solution instance will be reused for each test case.
		
		int i;
		int maxarea=0;
		int len=height.size();
		Node *h=new Node[len+2];
		for(i=1;i<=len;i++)
		{
			h[i].height=height[i-1];
			h[i].left=i;
			h[i].right=i;
		}
	
		h[0].height=-1;
		h[len+1].height=-1;
		for(i=1;i<=len;i++)
		{
			while(h[i].height<=h[h[i].left-1].height)
				h[i].left=h[h[i].left-1].left;
		}
	
		for(i=len;i>=1;i--)
		{
			while(h[i].height<=h[h[i].right+1].height)
				h[i].right=h[h[i].right+1].right;
		}
		for(i=1;i<=len;i++)
		{
			h[i].area=h[i].height*(h[i].right-h[i].left+1);
			if(maxarea<h[i].area)
				maxarea=h[i].area;
		}

		delete []h;
		return maxarea;
	}
};