Largest Rectangle in Histogram

最新推荐文章于 2024-11-16 19:28:39 发布

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本文介绍了一种算法，用于计算给定直方图中最大矩形的面积，直方图的每个柱子宽度为1，高度由整数数组表示。通过使用栈来跟踪每个柱子的位置，算法能够高效地找到最大矩形。

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.

#include<iostream>
#include<vector>
#include<stack>
#include<algorithm>
using namespace std;
int largestRectangleArea(vector<int> &height) {
	
	stack<int>IndexStack;
	height.push_back(0);
	int maxarea = 0;
	for (int i = 0; i != height.size();)
	{
		if (IndexStack.empty() || height[i] >= height[IndexStack.top()])
			IndexStack.push(i++);
		else
		{
			int t = IndexStack.top();
			IndexStack.pop();
			maxarea = max(maxarea, height[t] * (IndexStack.empty() ? i : i - IndexStack.top() - 1));
		}
	}
	return maxarea;
}