LeetCode Largest Rectangle in Histogram

最新推荐文章于 2024-03-25 23:26:01 发布

原创最新推荐文章于 2024-03-25 23:26:01 发布 · 284 阅读

0 ·

CC 4.0 BY-SA版权

面试题专栏收录该内容

144 篇文章

订阅专栏

本文介绍了一种求解直方图中最大矩形面积的高效算法。通过使用栈来跟踪柱状的高度，该算法能够在O(n)的时间复杂度内找到最大矩形区域的面积。示例代码展示了如何实现这一算法，并提供了具体示例。

题目：

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.

参考： http://www.geeksforgeeks.org/largest-rectangle-under-histogram/

class Solution {
public:
    //复杂度O(n)
	int largestRectangleArea(vector<int> &height) {
		int n = height.size();
		if (n == 0)
			return 0;
		int ans = 0;
		stack<int> s;
		int tp, area;
		int i = 0;
		while (i < n) {
			if (s.empty() || height[i] >= height[s.top()])
				s.push(i++);
			else  {
				int tp = s.top();
				s.pop();
				area = height[tp] * (s.empty() ? i : i - s.top() - 1);
				ans = max(ans, area);
			}
		}
		while (!s.empty()) {
			tp = s.top();
			s.pop();
			area = height[tp] * (s.empty() ? i : i - s.top() - 1);
			ans = max(ans, area);
		}
		return ans;
	}
};