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Number of Burgers with No Waste of Ingredients

Number: 1401

Difficulty: Medium

Paid? No

Companies: N/A

Problem Description

Given two integers tomatoSlices and cheeseSlices, determine the number of Jumbo and Small burgers that can be made such that no ingredient is wasted. A Jumbo Burger requires 4 tomato slices and 1 cheese slice, while a Small Burger requires 2 tomato slices and 1 cheese slice. Return [total_jumbo, total_small] if it’s possible to use all ingredients with no leftovers. Otherwise, return an empty list.

Key Insights

  • Formulate the ingredient equations:
    • Total tomato slices: 4 * jumbo + 2 * small = tomatoSlices.
    • Total cheese slices: jumbo + small = cheeseSlices.
  • Solve the system by substitution to compute:
    • jumbo = tomatoSlices/2 - cheeseSlices.
    • small = cheeseSlices - jumbo.
  • The number of tomato slices must be even; otherwise, no valid combination exists.
  • Both jumbo and small counts must be non-negative.
  • Edge cases include when ingredients are zero or in combinations that don’t satisfy the equations.

Space and Time Complexity

Time Complexity: O(1) - Only constant time arithmetic operations are used. Space Complexity: O(1) - Only a fixed number of variables are used.

Solution

We start by checking if tomatoSlices is even since both burger types require an even number of tomato slices per burger. Next, we derive a system of linear equations based on the given burger ingredient requirements. Let jumbo be the number of Jumbo Burgers and small be the number of Small Burgers.

The equations are:

  1. 4 * jumbo + 2 * small = tomatoSlices
  2. jumbo + small = cheeseSlices

From the second equation, we express small as cheeseSlices - jumbo. Substitute this into the first equation: 4 * jumbo + 2 * (cheeseSlices - jumbo) = tomatoSlices
Simplify: 4 * jumbo + 2 * cheeseSlices - 2 * jumbo = tomatoSlices
=> 2 * jumbo + 2 * cheeseSlices = tomatoSlices
=> jumbo = (tomatoSlices / 2) - cheeseSlices

Then, small can be computed as: small = cheeseSlices - jumbo

Finally, to ensure a valid solution, both jumbo and small must be non-negative. If they are not, or if tomatoSlices is odd, the answer is an empty list.

Code Solutions

# Function to find the number of burgers with no waste
def numOfBurgers(tomatoSlices, cheeseSlices):
    # Check if tomatoSlices is even
    if tomatoSlices % 2 != 0:
        return []
    
    # Compute number of jumbo burgers using the derived formula
    jumbo = (tomatoSlices // 2) - cheeseSlices
    # Compute number of small burgers
    small = cheeseSlices - jumbo
    
    # Validate that both counts are non-negative
    if jumbo < 0 or small < 0:
        return []
    return [jumbo, small]

# Example usage:
print(numOfBurgers(16, 7))  # Expected output: [1, 6]
print(numOfBurgers(17, 4))  # Expected output: []
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