【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.

 1 class Solution {
 2 public:
 3     int largestRectangleArea(vector<int> &height) {
 4         int max_area = 0;
 5         stack<int> s;
 6         height.push_back(0);
 7         int i = 0;
 8         while (i < height.size()) {
 9             if (s.empty() || height[s.top()] < height[i]) {
10                 s.push(i++);
11             } else {
12                 int t = s.top();
13                 s.pop();
14                 max_area = max(max_area,
15                     height[t] * (s.empty() ? i : i - s.top() - 1));
16             }
17         }
18         return max_area;
19     }
20 };

View Code

O(n²)的算法还是很好想的，但是如果借用数据结构--栈，可以使复杂度降低。

从左向右扫描数组，如果bar递增，则入栈，遇到第一个下降的bar时，开始出栈，计算从该bar(不含)到栈顶元素(含)之间形成的矩形面积，直到遇到栈里第一个低于它的bar，此时可以继续向前扫描下一个元素。

栈里维护的是递增序列。