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.

此题需要注意数组overflow情况，即新创建的数组的最后一个元素一定要为0！代码如下：

public class Solution {

    public int largestRectangleArea(int[] heights) {

        int max = 0;

        if(heights.length==0) return max;

        int[] h = new int[heights.length+1];

        for(int i=0;i<heights.length;i++){

            h[i] = heights[i];

        }

        Stack<Integer> s =new Stack<Integer>();

        for(int i=0;i<h.length;i++){

            if(s.isEmpty()||h[s.peek()]<=h[i]){

                s.push(i);

            }else{

                while(!s.isEmpty()&&h[s.peek()]>h[i]){

                    int top= s.pop();

                    int area = h[top]*(s.isEmpty()?i:i-s.peek()-1);

                    max = Math.max(max,area);

                }

                s.push(i);

            }

        }

        return max;

    }

}