leetcode 84. Largest Rectangle in Histogram

最大矩形面积算法

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本文介绍了一种求解直方图中最大矩形面积的高效算法。通过使用栈来跟踪直方图条的高度，该算法能在O(n)的时间复杂度内找到最大矩形面积。示例代码展示了如何实现这一算法。

Question

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.

Code

 public int largestRectangleArea(int[] height) {
        if (height == null || height.length == 0) {
            return 0;
        }

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

        return max;

    }