number-of-burgers-with-no-waste-of-ingredients.py

# Time:  O(1)
# Space: O(1)

class Solution(object):
    def numOfBurgers(self, tomatoSlices, cheeseSlices):
        """
        :type tomatoSlices: int
        :type cheeseSlices: int
        :rtype: List[int]
        """
        # let the number of jumbo burger be x, the number of small burger be y:
        #   4x + 2y = t
        #   x + y = c
        #   =>
        #   x = t/2-c
        #   y = 2c-t/2
        # since x, y are natural numbers
        #   => t/2 is integer, t/2-c >= 0, 2c-t/2 >= 0
        #   => t%2 == 0, 2c <= t <= 4c
        return [tomatoSlices//2-cheeseSlices, 2*cheeseSlices - tomatoSlices//2] \
               if tomatoSlices%2 == 0 and 2*cheeseSlices <= tomatoSlices <= 4*cheeseSlices \
               else []