84. Largest Rectangle in Histogram（难）

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本文介绍了一种高效算法，用于解决寻找直方图中最大矩形面积的问题。通过使用栈来跟踪直方图柱的高度，该算法能够在O(n)的时间复杂度内找到最大矩形的面积。

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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.

解释参考点击打开链接

class Solution {
public:
	int largestRectangleArea(vector<int>& heights) {
		heights.push_back(0);
		int largestArea = 0;
		int i = 0;
		stack<int> stk;
		while (i < heights.size()){
			if (stk.empty() || heights[stk.top()] <= heights[i]){
				stk.push(i);
				i++;
			}
			else{
				int t = stk.top(); stk.pop();
				largestArea = max(largestArea, heights[t] * (stk.empty() ? i : (i - stk.top() - 1)));
			}
		}
		return largestArea;
	}
};