Abstract / Summary

Given the number of tomato slices and cheese slices, find how many jumbo and small burgers can be made without leftovers.

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 51% (60k+ 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 method that determines a feasible combination of two types of burgers-jumbo (using 4 tomato slices and 1 cheese slice) and small (using 2 tomato slices and 1 cheese slice)-given a total number of tomato and cheese slices. The method returns a two-element list [jumboCount, smallCount] when a solution exists, otherwise an empty list.

Core Logic

Input Normalization

t = tomatoSlices
c = cheeseSlices

The method copies the input parameters into local variables t and c. This isolates the subsequent arithmetic from the original arguments, making the later manipulations straightforward.

Feasibility Guard

if t > 4*c or t < 2*c or t % 2 == 1:
    return []

Three conditions are evaluated in a single guard:

• t > 4*c - the total tomato slices exceed the maximum possible when every cheese slice is paired with a jumbo burger (4 tomatoes per cheese).
• t < 2*c - the total tomato slices fall below the minimum possible when every cheese slice is paired with a small burger (2 tomatoes per cheese).
• t % 2 == 1 - an odd number of tomato slices cannot be expressed as a sum of even contributions (2 or 4 per burger).

If any condition holds, the method immediately returns an empty list, indicating that no integer solution exists.

Assume All Small Burgers

small = c
t -= 2*small

The algorithm starts by assuming every cheese slice forms a small burger, which consumes 2 * c tomato slices. The variable small holds the provisional count of small burgers, and t is reduced accordingly to reflect the remaining tomato slices that must be allocated to jumbo burgers.

Compute Required Jumbo Burgers

jumbo  = t // 2

After the previous subtraction, the remaining tomato count t must be an even number (guaranteed by the earlier guard). Each jumbo burger consumes an additional 2 tomato slices beyond the 2 already accounted for in the small-burger assumption. Dividing the residual t by 2 yields the exact number of jumbo burgers needed.

Adjust Small Burger Count

small -= jumbo

Every jumbo burger replaces one of the previously assumed small burgers, because both types require exactly one cheese slice. Subtracting jumbo from small yields the final count of small burgers that coexist with the computed jumbo burgers.

Return Result

return [ jumbo, small ]

The method returns the pair [jumbo, small], representing a valid distribution of burgers that matches the supplied slice counts.

Edge Cases Handled

The guard clause captures three distinct edge scenarios:

• Excess Tomatoes - When the tomato count surpasses the theoretical maximum (4 * cheeseSlices), no combination can satisfy the constraints, and the method returns an empty list.
• Insufficient Tomatoes - When the tomato count is below the theoretical minimum (2 * cheeseSlices), the constraints are likewise unsatisfiable, prompting an empty list.
• Odd Tomato Count - Because each burger contributes an even number of tomato slices, an odd total cannot be decomposed into any integer combination of the two burger types, leading to an empty list.

These checks guarantee that the subsequent arithmetic operates only on inputs that admit a solution, preventing negative counts or fractional results.

Performance Characteristics

The algorithm executes a constant number of arithmetic operations and conditional checks, regardless of the magnitude of the input values. By avoiding loops, recursion, or auxiliary data structures, the method runs in deterministic constant time with minimal memory overhead. The direct arithmetic approach eliminates the need for iterative search or combinatorial enumeration, delivering an efficient solution for the problem domain.

Imagine a magical burger shop where you have a pile of tomato slices and a pile of cheese slices. There are two kinds of burgers that can be made. A jumbo burger needs four tomato slices and one slice of cheese. A small burger needs two tomato slices and one slice of cheese.

The code starts by checking if the number of slices you have makes sense. If you have too many tomatoes, too few tomatoes, or an odd number of tomatoes, the recipe will not work because every burger must have at least two tomatoes and the total amount of tomatoes must be even.

To figure out how many burgers to make, think about starting by pretending every single slice of cheese is used for a small burger. Since small burgers use two tomatoes each, this uses up two tomatoes for every piece of cheese. After doing that, there will be some tomato slices left over. Each jumbo burger needs two more tomato slices than a small burger does. By taking those leftover tomatoes and dividing them by two, the result shows exactly how many of those small burgers need to become jumbo burgers instead. Once that swap is finished, the number of jumbo and small burgers is ready to serve.

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	C++	Python	Java					TS
	WalkCCC	C++	Python	Java
	leetcode.ca	C++	Python	Java			Go	Rust	TS
	Progiez	C++	Python	Java
github	black-shadows	C++
	charles-wangkai			Java
	fsq	C++
	Garvit244		Python
	JoshCrozier				JS
	lkwq007		Python
	suxrobGM					C#
	varunu28			Java
AlgoMonster	C++, Python, Java, TypeScript
WalkCCC	C++, Python, Java
leetcode.ca	C++, Go, Java, Python, Rust, TypeScript
Progiez	C++, Java, Python
black-shadows	C++, C++
charles-wangkai	Java
fsq	C++
Garvit244	Python
JoshCrozier	JavaScript
lkwq007	Python
suxrobGM	C#
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