Leetcode 1691. Maximum Height by Stacking Cuboids  Summary and Q&A
TL;DR
This video explains how to stack cuboids for maximum height by comparing dimensions.
Key Insights
 🎮 The video illustrates the concept of dimension comparison among cuboids to devise a stacking strategy.
 ❓ It highlights the importance of both sorting and rotation in maximizing height when stacking cuboids.
 🤩 Understanding the geometric constraints is key to forming valid stacking combinations.
 The Longest Increasing Subsequence serves as an effective method for determining maximum heights in this type of problem.
 Achieving a correct implementation requires careful attention to the sorting order and condition checks.
 ❓ The cuboid stacking problem combines elements of dynamic programming with greedy algorithms for effective height maximization.
 🎮 The analysis showcased in the video ensures clarity through visual representations and practical examples.
Transcript
hey there everyone welcome back to lead coding in this video we will be solving the question number four of lead code vt contest 219 name of the problem is maximum height by stacking cuboids the problem statement is we are given n cuboids where the dimensions of the ith cuboid is given as width length and height choose a subset of cuboids and place... Read More
Questions & Answers
Q: What is the main goal of stacking cuboids in this problem?
The main goal is to select a subset of cuboids and stack them on each other to achieve the maximum height possible, while ensuring that each cuboid placed on top adheres to dimension constraints compared to the cuboid below.
Q: Can you explain the rotation of cuboids for stacking?
Yes, the rotation allows for each cuboid to be repositioned so that the largest dimension can serve as the height. This ensures the cuboid fits correctly onto another, enhancing the possibilities for stacking without breaking the dimension constraints.
Q: What algorithmic approach is suggested for solving this problem?
The solution involves sorting the dimensions of each cuboid, followed by implementing a form of the Longest Increasing Subsequence algorithm to find the maximum height achievable by valid stackings. The sorting of cuboids simplifies the detection of valid stacking sequences.
Q: Why is sorting the cuboids significant?
Sorting the cuboids is significant as it allows for an organized way to compare dimensions and ascertain valid placements for stacking. It also aids in simplifying the search for the Longest Increasing Subsequence, essential for solving the problem efficiently.
Q: What is the time complexity of the proposed solution?
The overall time complexity of the solution is O(n^2) due to the nested loops involved in calculating the Longest Increasing Subsequence after sorting the cuboids. The sorting step adds an O(n log n) complexity, but the dominating factor remains O(n^2).
Q: What are the conditions needed for one cuboid to be placed on another?
A cuboid can be placed on another if its width, length, and height dimensions are all less than or equal to the dimensions of the lower cuboid. This is critical in ensuring stability in the stacking configuration.
Summary & Key Takeaways

The video discusses the problem of stacking cuboids, adhering to specific dimension constraints, to achieve the maximum possible height.

It demonstrates how to rotate cuboids and apply a greedy approach to establish the largest dimension as the height, justifying the logic with examples.

It outlines an algorithm to sort cuboids by dimensions and utilize the Longest Increasing Subsequence method for calculating the optimal stacking arrangement.