Number of Burgers with No Waste of Ingredients - Solution & Explanation

Problem Overview: You are given the number of tomatoSlices and cheeseSlices. A jumbo burger uses 4 tomato slices and 1 cheese slice, while a small burger uses 2 tomato slices and 1 cheese slice. Your task is to determine how many jumbo and small burgers can be made so that all ingredients are used with no leftovers.

The challenge reduces to solving a small system of equations. Each burger consumes exactly one cheese slice, but tomato usage differs between burger types. If a valid combination exists, return the number of jumbo and small burgers; otherwise return an empty result.

Approach 1: Iterative Check for Solution (O(n) time, O(1) space)

The straightforward approach is to try all possible counts of jumbo burgers. Since each jumbo burger uses 4 tomato slices, the maximum possible jumbo burgers is tomatoSlices / 4. For every candidate count, compute the remaining tomato and cheese slices and check whether they can form small burgers.

The validation step is simple: remaining tomatoes must equal 2 * smallBurgers, and remaining cheese slices must match the total burgers used. Iterate through feasible jumbo counts and return the first valid pair. This method relies on basic arithmetic and loops, making it easy to reason about but slightly inefficient when the tomato count is large.

This approach mainly exercises careful iteration and arithmetic validation. It connects well with problems under math and basic constraint checking.

Approach 2: Directly Solve Using Equations (O(1) time, O(1) space)

The optimal solution models the burger counts as two variables. Let j be jumbo burgers and s be small burgers. From the ingredient rules you get two equations:

4j + 2s = tomatoSlices
j + s = cheeseSlices

Solving this system eliminates one variable. Substitute s = cheeseSlices - j into the tomato equation and simplify to compute j. Once j is known, calculate s. The only remaining checks ensure both values are non‑negative integers and satisfy the original constraints.

This approach turns the problem into a small algebra exercise and avoids iteration entirely. The runtime becomes constant because only a few arithmetic operations are performed regardless of input size. Problems like this commonly appear in math and equation solving categories where recognizing relationships between variables leads directly to the optimal solution.

Recommended for interviews: The equation-based approach is what interviewers expect. It demonstrates that you can translate constraints into algebra and derive a constant-time solution. The iterative approach still shows good reasoning and can serve as a stepping stone, but the O(1) equation solution highlights stronger problem‑solving skill.