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.

题意：求直方图中最大面积的矩形。

思路：单调栈的应用。维持一个单调递增的栈，网上写的可以转来：题解

[cpp]  view plain  copy

1. public class Solution {  
2.     public int largestRectangleArea(int[] height) {  
3.         Stack<Integer> stack = new Stack<Integer>();  
4.         int i = 0;  
5.         int ans = 0;  
6.         int h[] = new int[height.length+1];  
7.         h = Arrays.copyOf(height, height.length+1);  
8.         while (i < h.length) {  
9.             if (stack.isEmpty() || h[stack.peek()] <= h[i])  
10.                 stack.push(i++);  
11.             else {  
12.                 int t = stack.pop();  
13.                 ans = Math.max(ans, h[t] * (stack.isEmpty() ? i : i - stack.peek() - 1));  
14.             }  
15.         }  
16.           
17.         return ans;  
18.     }  
19. }