84. Largest Rectangle in Histogram（直方图最大面积 hard）

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.

用桟

 class Solution {
     public int largestRectangleArea(int[] heights) {
         Stack<Integer> stack = new Stack<Integer>();

         //array 扩容，在最后一位加上0
         int[] a = new int[heights.length+1];
         for(int i =0;i<heights.length;i++)
             a[i] = heights[i];
         a[heights.length]=0;
         //

         int answer = 0;
         int temp;
         for(int i = 0;i<a.length;){
             if(stack.isEmpty()||a[i]>a[stack.peek()]){//a[i]与桟顶元素比较
                 stack.push(i);
                 i++;
             }
             else{
                 temp = stack.pop();
                 answer = Math.max(answer,a[temp]*(stack.isEmpty()?i: i-stack.peek()-1));
                 //桟为空的时候，需要计算长度为i 高度从0到i最矮的（即桟中最小的元素，弹出后，桟就空了）
             }
         }
         return answer;
     }
 }