Number of Burgers with No Waste of Ingredients - Problem

Math Medium

Given two integers tomatoSlices and cheeseSlices, determine how many burgers can be made with no waste of ingredients.

The ingredients required for different burgers are:

Jumbo Burger: 4 tomato slices and 1 cheese slice
Small Burger: 2 tomato slices and 1 cheese slice

Return [total_jumbo, total_small] such that the number of remaining tomatoSlices equals 0 and the number of remaining cheeseSlices equals 0. If it is not possible to achieve zero waste, return [].

Input & Output

Example 1 — Basic Case

$ Input: tomatoSlices = 16, cheeseSlices = 7

› Output: [1,6]

💡 Note: 1 jumbo burger (4 tomatoes + 1 cheese) + 6 small burgers (12 tomatoes + 6 cheese) = 16 tomatoes + 7 cheese total

Example 2 — Only Small Burgers

$ Input: tomatoSlices = 10, cheeseSlices = 5

› Output: [0,5]

💡 Note: 0 jumbo burgers + 5 small burgers (10 tomatoes + 5 cheese) uses all ingredients perfectly

Example 3 — Impossible Case

$ Input: tomatoSlices = 4, cheeseSlices = 17

› Output: []

💡 Note: Not enough tomatoes to satisfy minimum requirement (2 tomatoes per cheese slice). 4 < 2×17 = 34

Constraints

0 ≤ tomatoSlices ≤ 10⁷
0 ≤ cheeseSlices ≤ 10⁷

Visualization

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Asked in

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The key insight is recognizing this as a system of linear equations. We have 4j + 2s = tomatoSlices and j + s = cheeseSlices. The optimal approach solves directly: j = (tomatoSlices - 2×cheeseSlices) ÷ 2. Time: O(1), Space: O(1)

Common Approaches

✓ Brute Force - Try All Combinations

⏱️ Time: O(cheeseSlices) Space: O(1)

Iterate through all possible numbers of jumbo burgers (0 to cheeseSlices) and check if the remaining ingredients can make the exact number of small burgers needed.

Mathematical Solution - System of Equations

⏱️ Time: O(1) Space: O(1)

Set up two equations: 4j + 2s = tomatoes and j + s = cheese, then solve algebraically for j and s. Check if solutions are non-negative integers.

Brute Force - Try All Combinations — Algorithm Steps

For each possible jumbo count from 0 to cheeseSlices
Calculate required small burgers = cheeseSlices - jumbo
Check if tomato equation holds: 4*jumbo + 2*small = tomatoSlices
Return first valid combination or empty array

Visualization

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Step-by-Step Walkthrough

Try jumbo = 0

Check if all small burgers work

Try jumbo = 1

Check if remaining makes valid small burgers

Found Solution

Return first valid combination

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

void solution(int tomatoSlices, int cheeseSlices, int* result, int* size) {
    for (int jumbo = 0; jumbo <= cheeseSlices; jumbo++) {
        int small = cheeseSlices - jumbo;
        if (4 * jumbo + 2 * small == tomatoSlices) {
            result[0] = jumbo;
            result[1] = small;
            *size = 2;
            return;
        }
    }
    *size = 0;
}

int main() {
    int tomatoSlices, cheeseSlices;
    scanf("%d", &tomatoSlices);
    scanf("%d", &cheeseSlices);
    
    int result[2];
    int size;
    solution(tomatoSlices, cheeseSlices, result, &size);
    
    printf("[");
    for (int i = 0; i < size; i++) {
        if (i > 0) printf(",");
        printf("%d", result[i]);
    }
    printf("]\n");
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(cheeseSlices)

Single loop from 0 to cheeseSlices checking each combination

✓ Linear Growth

Space Complexity

O(1)

Only using a few variables for calculations

✓ Linear Space

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Number of Burgers with No Waste of Ingredients - Problem

Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Brute Force - Try All Combinations — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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