Largest Rectangle in Histogram

最新推荐文章于 2020-03-05 10:52:35 发布

Paul_ZJ

最新推荐文章于 2020-03-05 10:52:35 发布

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本文介绍了一种高效算法来寻找直方图中最大的矩形面积，通过使用栈来辅助计算，确保了时间复杂度为O(n)。示例输入为高度数组[2,1,5,6,2,3]，返回结果为10。

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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`.
Java代码：

public class Solution {
    public int largestRectangleArea(int[] height) {
        height = Arrays.copyOf(height, height.length + 1);

        int maxRect = 0;
        Stack<Integer> stack = new Stack<Integer>();
        for(int i = 0; i < height.length; ++i) {
            while (!stack.isEmpty() && height[i] < height[stack.peek()]) {
                int rect = height[stack.pop()] * (stack.isEmpty() ? i : (i-stack.peek()-1));
                maxRect = Math.max(maxRect, rect);
            }
            stack.push(i);
        }

        return maxRect;
    }
}