Abstract / Summary

Determine if a box is big or small and if it needs to be picked up based on its width, height, length, and weight.

Note

The full problem description, including helpful examples, can be found on LeetCode.

This problem is ranked as

and has an acceptance rate of about 39% (100k+ submissions).

Typical patterns to solve this problem:

• Math

Every single line of code was written by me, 100% from scratch, between August 2023 and August 2024.
However, two years later I set up this website and used various AI tools to generate most of the walkthrough / explanations below.

See this dedicated page for more details.

Overview

The provided Solution class implements a single method categorizeBox that receives four integer parameters describing a box: its three dimensions (length, width, height) and its mass. The method determines whether the box is Bulky, Heavy, Both, or Neither based on predefined thresholds. The implementation follows a straightforward decision-making process: first it evaluates two boolean conditions-bulky and heavy-and then returns a string that reflects the combination of those conditions.

Key Steps

Determining the “bulky” condition

The code defines a box as bulky when any single dimension meets or exceeds ten thousand units, or when the overall volume reaches one billion cubic units. This is expressed through a series of logical OR assignments that progressively accumulate the result in the bulky variable.

bulky  = length >= 10**4
bulky |= width  >= 10**4
bulky |= height >= 10**4
bulky |= (length * width * height) >= 10**9

The use of the compound assignment operator |= allows the condition to be built incrementally without creating additional temporary variables.

Determining the “heavy” condition

A box is considered heavy if its mass is at least one hundred units. This is a single comparison that yields a boolean value stored in heavy.

heavy  = mass >= 100

Selecting the appropriate category

After both boolean flags are computed, the method evaluates their combination using a series of if statements. The order of checks guarantees that the most specific category (“Both”) is returned first, followed by the mutually exclusive cases.

if heavy and bulky:
    return "Both"
if (not heavy) and (not bulky):
    return "Neither"
if bulky and not heavy:
    return "Bulky"
# if heavy and not bulky:
return "Heavy"

The final return statement handles the remaining scenario where the box is heavy but not bulky, relying on the fact that all other possibilities have already been excluded.

Edge Cases Handled

The implementation gracefully manages several boundary conditions:

• When a dimension is exactly ten thousand, the >= comparison classifies the box as bulky, ensuring the threshold is inclusive.
• When the volume calculation yields exactly one billion, the volume check also classifies the box as bulky, covering the case where none of the individual dimensions reach the size limit but the combined volume does.
• A mass value of exactly one hundred triggers the heavy classification, again using an inclusive comparison.
• The logical flow correctly distinguishes a box that meets both size and weight thresholds, returning “Both” rather than a single attribute.
• The final unconditional return "Heavy" captures the scenario where the box is heavy but fails all bulky criteria, including the case where the volume multiplication could overflow typical 32-bit integer ranges; Python’s arbitrary-precision integers prevent overflow, so the comparison remains reliable.

Performance Optimizations

The method is optimized for speed and minimal memory usage:

• Boolean flags are computed once and reused, avoiding repeated evaluation of the same expressions in the conditional branches.
• The use of compound assignment (|=) for the bulky condition reduces the number of temporary boolean objects that would otherwise be created if each comparison were stored separately.
• The volume calculation is performed only once, and the result is used directly in the comparison, preventing redundant multiplication.
• The decision tree is arranged so that the most restrictive condition (“Both”) is evaluated first; this can short-circuit further checks for boxes that satisfy both criteria, saving a few logical operations in common cases where boxes are both bulky and heavy.
• The final return statement eliminates the need for an explicit else clause, allowing the interpreter to exit the function as soon as a matching condition is found, which contributes to a slight reduction in branching overhead.

Imagine there is a magical box that needs to be sorted based on its size and how much it weighs. The box is called bulky if it is either very long, very wide, very tall, or if all those dimensions together make it take up a massive amount of space. The box is called heavy if it weighs one hundred units or more.

The program checks the side lengths to see if any of them are at least ten thousand. It also multiplies the length, width, and height together to see if the total space inside the box is at least one billion. If any of those things are true, the box gets a label saying it is bulky. Then, the program checks if the weight is one hundred or more to see if the box should get a label saying it is heavy.

After checking these two things, the code looks at both labels at the same time. If the box is both bulky and heavy, it gets called both. If the box is neither bulky nor heavy, it gets called neither. If the box is only bulky, it gets called bulky. If the box is only heavy, it gets called heavy. It is just like sorting toys into different bins based on their size and weight.

Several LLMs ranked my code quality on a scale from 1 (very poor) to 10 (outstanding):

Time: constant
As a rule of thumb, the maximum input size for one second execution time is

• factorial: up to 10 elements
• exponential: up to 20 elements
• polynomial: a few thousand elements
• loglinear: up to 100,000 elements
• linear: a few million elements
• logarithmic: a billion elements
• constant: practically unlimited

I wrote a basic crawler to find other solutions to that problem.
Obviously, I did that after I solved the problem myself.

In general, AlgoMonster and WalkCCC solutions are high-quality and always worth a look.
I haven't checked most of the other solutions, but they might be helpful as well.

And of course, the LeetCode forum is always a good place (or even the best) to look for alternative approaches.

(click on a column header to sort the table)

	author
author	solutions
www	AlgoMonster	Java			C++	Python		TS
	WalkCCC	Java			C++	Python
	leetcode.ca	Java		Go	C++	Python	Rust	TS
	Progiez	Java			C++	Python
github	charles-wangkai	Java
	fartem		Ruby
	fsq				C++
	muhammadfarhankt			Go
	varunu28	Java
AlgoMonster	C++, Python, Java, TypeScript
WalkCCC	C++, Python, Java
leetcode.ca	C++, Go, Java, Python, Rust, TypeScript
Progiez	C++, Java, Python
charles-wangkai	Java
fartem	Ruby
fsq	C++
muhammadfarhankt	Go
varunu28	Java

There are a few extra pages giving you some insights into my setup:

• Tech Stack - my development environment and tools
• AI - how AI helped me create this website (NOT solving the problems)
• Progress - progression over time
• Quality - code quality