题目：​​原题链接​​（困难）

标签：动态规划、回溯算法

解法一（动态规划）：

class Solution:
    def pileBox(self, box: List[List[int]]) -> int:
        # 依据长宽高总和排序箱子
        # O(NlogN)
        box.sort(key=lambda x: sum(x), reverse=True)

        # 初始化状态表格
        dp = [b[2] for b in box]

        # 状态转移
        for i in range(1, len(box)):
            w1, d1, h1 = box[i]
            max_height = 0
            for j in range(i - 1, - 1, -1):
                w2, d2, h2 = box[j]
                if w1 < w2 and d1 < d2 and h1 < h2:
                    max_height = max(max_height, dp[j])

            dp[i] = max(dp[i], max_height + h1)

        return max(dp)