#1276

Medium

auto_awesomeMath-driven solution strategy

LeetCode Problem Workspace

Number of Burgers with No Waste of Ingredients

Determine the exact counts of jumbo and small burgers using all tomato and cheese slices without leftovers, applying math-based reasoning.

math

Problem Statement

You are given two integers tomatoSlices and cheeseSlices representing available ingredients. A jumbo burger requires 4 tomato slices and 1 cheese slice, while a small burger requires 2 tomato slices and 1 cheese slice. Determine if it's possible to use all ingredients to make some combination of jumbo and small burgers without leaving any tomato or cheese slices unused.

Return an array [total_jumbo, total_small] representing the count of jumbo and small burgers that use all ingredients exactly. If no combination exists that leaves zero remaining slices, return an empty array. For example, with tomatoSlices = 16 and cheeseSlices = 7, the correct output is [1,6], while tomatoSlices = 17 and cheeseSlices = 4 results in [].

Examples

Example 1

Input: tomatoSlices = 16, cheeseSlices = 7

Output: [1,6] Explantion: To make one jumbo burger and 6 small burgers we need 4*1 + 2*6 = 16 tomato and 1 + 6 = 7 cheese. There will be no remaining ingredients.

Example details omitted.

Example 2

Input: tomatoSlices = 17, cheeseSlices = 4

Output: [] Explantion: There will be no way to use all ingredients to make small and jumbo burgers.

Example details omitted.

Example 3

Input: tomatoSlices = 4, cheeseSlices = 17

Output: [] Explantion: Making 1 jumbo burger there will be 16 cheese remaining and making 2 small burgers there will be 15 cheese remaining.

Example details omitted.

Constraints

0 <= tomatoSlices, cheeseSlices <= 107

Solution Approach

Formulate as a system of equations

Set up the equations 4 * jumbo + 2 * small = tomatoSlices and 1 * jumbo + 1 * small = cheeseSlices. This translates the ingredient allocation problem directly into a solvable linear system, allowing integer solutions to represent valid burger counts.

Check for integer feasibility and parity

Calculate small = 2 * cheeseSlices - tomatoSlices / 2 and jumbo = cheeseSlices - small. Ensure both values are non-negative integers and that tomatoSlices is even, as an odd number of tomatoes cannot satisfy 2x + 4y composition.

Return valid solution or empty array

If computed jumbo and small counts satisfy non-negativity and integer conditions, return [jumbo, small]. Otherwise, return []. This guarantees zero leftover ingredients and aligns with the math-driven pattern requirement.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

Time complexity is O(1) because calculations involve direct arithmetic without iteration. Space complexity is O(1) since only a few integer variables are stored, regardless of input size.

What Interviewers Usually Probe

Look for direct algebraic formulation rather than iterative brute force.
Check candidate solutions against ingredient parity and zero-remainder constraints.
Consider edge cases where tomatoSlices or cheeseSlices are zero or insufficient.

Common Pitfalls or Variants

Common pitfalls

Failing to check that tomatoSlices must be even for a valid solution.
Assuming negative counts are valid for jumbo or small burgers.
Ignoring integer division issues leading to fractional burger counts.

Follow-up variants

Varying burger ingredient ratios, e.g., jumbo uses 5 tomato slices instead of 4.
Limiting total number of burgers available, requiring optimization within constraints.
Adding multiple burger types beyond jumbo and small with unique ingredient requirements.

FAQ

What is the main pattern to solve Number of Burgers with No Waste of Ingredients?

The core pattern is a math-driven system of linear equations that ensures all tomato and cheese slices are used with integer counts of burgers.

Can tomatoSlices be odd for a valid solution?

No, because jumbo and small burgers require an even number of tomato slices combined; an odd total makes zero-waste impossible.

What should I return if no combination of burgers uses all ingredients?

Return an empty array, as there is no way to satisfy zero leftover constraints with the given tomatoSlices and cheeseSlices.

Does this problem require iteration over possible burger counts?

No, direct algebraic computation suffices, making the solution O(1) time and avoiding unnecessary loops.

How do I verify the computed jumbo and small counts?

Ensure both are non-negative integers and that 4 jumbo + 2 small equals tomatoSlices and jumbo + small equals cheeseSlices.

terminal

Solution

Solution 1: Mathematics

We set the number of Jumbo Burgers as $x$ and the number of Small Burgers as $y$, then we have:

1

2

3

4

5

6

class Solution:
    def numOfBurgers(self, tomatoSlices: int, cheeseSlices: int) -> List[int]:
        k = 4 * cheeseSlices - tomatoSlices
        y = k // 2
        x = cheeseSlices - y
        return [] if k % 2 or y < 0 or x < 0 else [x, y]

Continue Practicing

#1281 subtract the product and sum of digits of an integer #1266 minimum time visiting all points #1290 convert binary number in a linked list to integer