Advanced Algorithms End Term: 1 September 2024, Set QDB3 (May 2024 term)

We are given a non-empty list of N ordered triplets where each triplet holds three integers and represents a cuboid-shaped disk. These integers denote each disk’s width, depth, and height, respectively. Your goal is to stack up the disks and to maximize the total height of the stack. A disk must have a strictly smaller width, depth, and height than any other disk below it.
Our goal is to design an algorithm that returns the total height of the optimal stack, starting with the top disk and ending with the bottom disk. Note that you can’t rotate disks. You can assume that there will only be one stack with the greatest total height. We also use 1-based indexing in the subquestions.
Based on the above data, answer the given subquestions.

Can the disk with dimensions [2,1,2] be placed above [3,2,3]?

We are given a non-empty list of N ordered triplets where each triplet holds three integers and represents a cuboid-shaped disk. These integers denote each disk’s width, depth, and height, respectively. Your goal is to stack up the disks and to maximize the total height of the stack. A disk must have a strictly smaller width, depth, and height than any other disk below it.
Our goal is to design an algorithm that returns the total height of the optimal stack, starting with the top disk and ending with the bottom disk. Note that you can’t rotate disks. You can assume that there will only be one stack with the greatest total height. We also use 1-based indexing in the subquestions.
Based on the above data, answer the given subquestions.

Can the disk with dimensions [2,2,2] be placed above [3,2,3]?

We are given a non-empty list of N ordered triplets where each triplet holds three integers and represents a cuboid-shaped disk. These integers denote each disk’s width, depth, and height, respectively. Your goal is to stack up the disks and to maximize the total height of the stack. A disk must have a strictly smaller width, depth, and height than any other disk below it.
Our goal is to design an algorithm that returns the total height of the optimal stack, starting with the top disk and ending with the bottom disk. Note that you can’t rotate disks. You can assume that there will only be one stack with the greatest total height. We also use 1-based indexing in the subquestions.
Based on the above data, answer the given subquestions.

Suppose the input consists of the following triplets: [[3, 8, 8], [2, 1, 9], [4, 1, 1], [2, 3, 6]]. What’s the answer?