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Day44 柱状图中最大的矩形

给定 n 个非负整数,用来表示柱状图中各个柱子的高度。每个柱子彼此相邻,且宽度为 1

https://leetcode-cn.com/problems/largest-rectangle-in-histogram/

求在该柱状图中,能够勾勒出来的矩形的最大面积。

示例1:

Java解法

package sj.shimmer.algorithm.m2;

/**
 * Created by SJ on 2021/3/10.
 */

class D44 {
    public static void main(String[] args) {
        System.out.println(largestRectangleArea(new int[]{2,1,5,6,2,3}));
    }

    public static int largestRectangleArea(int[] heights) {
        if (heights == null) {
            return 0;
        }
        int length = heights.length;
        long sum = 0;
        int height = 0;
        for (int i = 0; i < length; i++) {
            int left = i;
            int right = i;
            if (height == heights[i]) {
                continue;
            }
            height = heights[i];
            while (left >= 0 && heights[left] >= height) {
                left--;
            }
            while (right < length && heights[right] >= height) {
                right++;
            }
            long temp = height * (right - left - 1);
            sum = sum > temp ? sum : temp;
        }
        return (int) sum;
    }
}

官方解

https://leetcode-cn.com/problems/largest-rectangle-in-histogram/solution/zhu-zhuang-tu-zhong-zui-da-de-ju-xing-by-leetcode-/

主要思路就是:枚举(宽或者高)

  1. 单调栈

    • 时间复杂度:O(N)
  • 空间复杂度:O(N)
  1. 单调栈 + 常数优化

    • 时间复杂度:O(N)
    • 空间复杂度:O(N)
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