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1276. Number of Burgers with No Waste of Ingredients

Description

Given two integers tomatoSlices and cheeseSlices. The ingredients of different burgers are as follows:

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

Return [total_jumbo, total_small] so that the number of remaining tomatoSlices equal to 0 and the number of remaining cheeseSlices equal to 0. If it is not possible to make the remaining tomatoSlices and cheeseSlices equal to 0 return [].

 

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 2:

Input: tomatoSlices = 17, cheeseSlices = 4
Output: []
Explantion: There will be no way to use all ingredients to make small and jumbo burgers.

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.

 

Constraints:

  • 0 <= tomatoSlices, cheeseSlices <= 107

Solutions

Solution 1: Mathematics

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

\[\begin{aligned} 4x + 2y &= tomatoSlices \\ x + y &= cheeseSlices \end{aligned}\]

Transforming the above two equations, we can get:

\[\begin{aligned} y = (4 \times cheeseSlices - tomatoSlices) / 2 \\ x = cheeseSlices - y \end{aligned}\]

Where $x$ and $y$ must be non-negative integers.

The time complexity is $O(1)$, and the space complexity is $O(1)$.

  • class Solution {
        public List<Integer> numOfBurgers(int tomatoSlices, int cheeseSlices) {
            int k = 4 * cheeseSlices - tomatoSlices;
            int y = k / 2;
            int x = cheeseSlices - y;
            return k % 2 != 0 || y < 0 || x < 0 ? List.of() : List.of(x, y);
        }
    }
    
  • class Solution {
    public:
        vector<int> numOfBurgers(int tomatoSlices, int cheeseSlices) {
            int k = 4 * cheeseSlices - tomatoSlices;
            int y = k / 2;
            int x = cheeseSlices - y;
            return k % 2 || x < 0 || y < 0 ? vector<int>{} : vector<int>{x, y};
        }
    };
    
  • 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]
    
    
  • func numOfBurgers(tomatoSlices int, cheeseSlices int) []int {
    	k := 4*cheeseSlices - tomatoSlices
    	y := k / 2
    	x := cheeseSlices - y
    	if k%2 != 0 || x < 0 || y < 0 {
    		return []int{}
    	}
    	return []int{x, y}
    }
    
  • function numOfBurgers(tomatoSlices: number, cheeseSlices: number): number[] {
        const k = 4 * cheeseSlices - tomatoSlices;
        const y = k >> 1;
        const x = cheeseSlices - y;
        return k % 2 || y < 0 || x < 0 ? [] : [x, y];
    }
    
    
  • impl Solution {
        pub fn num_of_burgers(tomato_slices: i32, cheese_slices: i32) -> Vec<i32> {
            let k = 4 * cheese_slices - tomato_slices;
            let y = k / 2;
            let x = cheese_slices - y;
            if k % 2 != 0 || y < 0 || x < 0 {
                Vec::new()
            } else {
                vec![x, y]
            }
        }
    }
    
    

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