Google Hash Code 2021 Practice Problem

Representing the data

In order to determine how to achieve the best deliveries, a query that would be executed a lot is how many unique ingredients would result from the reunion of the sets which contain the ingredients of some specific pizzas. Since there can be many pizzas in a dataset, and many unique ingredients(10000), it is important for this operation to be fast and memory efficient. For this reason, a unique number is associated to each ingredient. Each Pizza object will contain a bitset of length equal to the number of unique ingredients in all the data set. For each index i, if bitset[i] equals 1, then that ingredient is present in that specific pizza. This means that the number of unique ingredients in a delivery can be computed in O(n), with n / 8 bytes of memory used per pizza, where n is the number of unique ingredients in the dataset.

Solution 1

This solution is a combination of greedy and backtracking. The pizza vector is sorted descendingly based on the number of ingredients they contain. Then, a list is created from this vector, since the simulation will imply a lot of deletions, which list is capable of executing in O(1). At each step, the first element of the list is selected. Then, the program gets the best deliveries of 2, 3, and 4 pizzas which contain the first element. Those are selected by applying backtracking on the next b elements from the list. This b is defined as a constant, and it can be increased depending on how beefy your computer is. Obviously, the more you can increase it, the better results you will get. For this attempt, I set it to 10. The score for each delivery is calculated as (nr_unique_ingredients - (nr_ingredients_wasted *0,67)).

Score

File	Score
a_example.in	74
b_little_bit_of_everything.in	8193
c_many_ingredients.in	686298420
d_many_pizzas.in	5915208
e_many_teams.in	8358631
Total	700580526

Solution 2: Parallel post-processing

This solution is similar to solution 1, but after the result is obtained, we go over the deliveries, and try to obtain a better score by swapping pizza i from one delivery with pizza j from another. For the bigger datasets this could take days, so this operation is done on two threads to achieve more in the same time. Also, this operation is set to stop after a certain time limit was exceeded(this time, I set it to 30 minutes).

Score

File	Score
a_example.in	74
b_little_bit_of_everything.in	9097
c_many_ingredients.in	693570291
d_many_pizzas.in	6469059
e_many_teams.in	9168995
Total	709217516