# Google Hash Code 2021 – Practice Problem 1

## Even more pizza

### Click here for Google Hash Code 2022 Practice Problem

Online Qualification Round Problem and Input Data Set

World Finals Problem and Input Data Set

### Introduction

Isn’t it fun to share pizza with friends? But, sometimes you just don’t have enough time to choose what pizza to order. Wouldn’t it be nice if someone else chose for you?

In an imaginary world…

### Problem description

Help the imaginary pizzeria choose the pizzas to deliver to Hash Code teams. And since we want everyone to enjoy their food, let’s try to deliver to each team, as many different ingredients as we can.

#### Pizza

Expecting many hungry customers, the pizzeria has already prepared some pizzas with different ingredients. Each pizza can be delivered to at most one team. There can be multiple pizzas with the exact same set of ingredients.

For example , there are 5 pizzas available in the pizzeria:

Note that Pizzas 1 and 3 have the same ingredients, even though they are mentioned in different order.

#### Teams

Teams of 2, 3, or 4 people all ordered pizzas. Each team ordered one pizza per team member, but did not specify what ingredients to put on the pizzas. The pizzeria might not deliver to a team (no pizzas are sent to that team). However, if the order is delivered, exactly one pizza should be available per person. For example, it is an error to send 3 pizzas to a 4-person team.

#### Goal

Given the description of the pizzas available, and the number of teams of 2, 3, or 4 people that have ordered, decide which pizzas to send to each of the teams. The goal is to maximize, per team, the number of different ingredients used in all their pizzas.

For example , if we deliver to a 3-person team Pizzas 0, 2 and 3, there will be 7 different ingredients (9 ingredients in total, but pepper and mushroom occur twice):

• Pizza 0
• onion
• pepper
• olive
• Pizza 2:
• chicken
• mushroom
• pepper (is already on Pizza 0)
• Pizza 3:
• tomato
• mushroom (is already on Pizza 2)
• basil

### Input data set

The input data is provided as a data set file – a plain text file containing exclusively ASCII characters with lines terminated with a single ‘\n’ character (UNIX- style line endings).

#### File format

The first line of the input file contains the following integer numbers separated by single spaces:

• M ( 1 ≤ M ≤ 100,000 ) – the number of pizzas available in the pizzeria
• T2 ( 0 ≤ T2 ≤ 50,000 ) – the number of 2-person teams
• T3 ( 0 ≤ T3 ≤ 50,000 ) – the number of 3-person teams
• T4 ( 0 ≤ T4 ≤ 50,000 ) – the number of 4-person teams

The next M lines describe the pizzas available. Each line contains (space separated):

• an integer I ( 1 ≤ I ≤ 10,000 ) – the number of ingredients,
• followed by the list of I ingredients – Each ingredient consists of lowercase ASCII letters and dash (-) characters, and its length can be between 1 and 20 characters in total. Each ingredient in a pizza is different, but the same ingredient can appear on different pizzas.

#### Example

##### Input file
```5 1 2 1
3 onion pepper olive
3 mushroom tomato basil
3 chicken mushroom pepper
3 tomato mushroom basil
2 chicken basil```
##### Description
`5 pizzas, 1 team of two, 2 teams of three, and 1 team of fourPizza 0 has the given 3 ingredientsPizza 1 has the given 3 ingredientsPizza 2 has the given 3 ingredientsPizza 3 has the given 3 ingredientsPizza 2 has the given 2 ingredients`

### Submissions

#### File format

The first line of the submission file contains a number D ( 1 ≤ D ≤ T2 + T3 + T4 ), representing the number of pizza deliveries.

The following D lines contain descriptions of each delivery. Each line contains the following integer numbers separated by single spaces:

• L ( 2 ≤ L ≤ 4 ) – the number of people in the team
• followed by the list of pizzas, P1 … PL – the space separated indexes of the pizzas delivered to that team

Even though it’s nice to deliver pizzas to all teams, it is allowed to make fewer deliveries than the number of teams. However, making more deliveries than the number of teams is an error. It is also an error to make more deliveries to 2, 3 or 4-person teams than the corresponding number
of teams provided in the input file: the number of lines with L=N, should not be greater than TN.

#### Example

```2
2 1 4
3 0 2 3```
##### Description
`Pizzas are delivered to 2 teamsA 2-person team will receive Pizza 1 and Pizza 4A 3-person team will receive Pizza 0, Pizza 2 and Pizza 3`

#### Validation

In order for the submission to be accepted:

• each pizza must be part of at most one order,
• for all N-person teams, either nobody or everybody receives a pizza,
• there are TN or less deliveries to teams of N people.

#### Scoring

For each delivery, the delivery score is the square of the total number of different ingredients of all the pizzas in the delivery. The total score is the sum of the scores for all deliveries.

For example , with the example input file and the example submission file above, there are

• 4 ingredients delivered to the two-person team (mushroom, tomato, basil, chicken). The score for that team is 42 = 16
• 7 ingredients delivered to the tree-person team. The score for that team is 72 = 49.
• (The score is 0 for the two teams that didn’t have their order delivered)

The total score is 16 + 49 = 65 .

Note that there are multiple data sets representing separate instances of the problem. The final score for your team will be the sum of your best scores for the individual data sets.

## Past editions

Hash Code started in 2014 with just 200 participants from France. In 2020, more than 100,000 participants from across Europe, the Middle East and Africa took part in the competition. You can take a look at the problems and winning teams from past editions of Hash Code below.

### Past problem statements

#### Traffic Signaling

Hash Code 2021, Online Qualification Round
Given the description of a city plan and planned paths for all cars in that city, optimize the schedule of traffic lights to minimize the total amount of time spent in traffic, and help as many cars as possible reach their destination before a given deadline.

#### Assembling smartphones

Hash Code 2020, Final Round
In this problem statement, we will explore the idea of operating an automated assembly line for smart phones.
Building a smart phone is a complex process that involves assembling numerous components, including the screen, multiple cameras, microphones, speakers, a processing unit, and a storage unit.
In order to automate the building of a smart phone, we will be using robotic arms that can move around the assembly workspace performing all necessary tasks.

#### Book scanning

Hash Code 2020, Online Qualification Round
Books allow us to discover fantasy worlds and better understand the world we live in. They enable us to learn about everything from photography to compilers… and of course a good book is a great way to relax!
Google Books is a project that embraces the value books bring to our daily lives. It aspires to bring the world’s books online and make them accessible to everyone. In the last 15 years, Google Books has collected digital copies of 40 million books in more than 400 languages , partly by scanning books from libraries and publishers all around the world.
In this competition problem, we will explore the challenges of setting up a scanning process for millions of books stored in libraries around the world and having them scanned at a scanning facility.

Hash Code 2019, Final Round
Google has a large codebase, containing billions of lines of code across millions of source files. From these source files, many more compiled files are produced, and some compiled files are then used to produce further compiled files, and so on.
Given then huge number of files, compiling them on a single server would take a long time. To speed it up, Google distributes the compilation steps across multiple servers.
In this problem, we will explore how to effectively use multiple compilation servers to optimize compilation time.

#### Photo slideshow

Hash Code 2019, Online Qualification Round
As the saying goes, “a picture is worth a thousand words.” We agree – photos are an important part of contemporary digital and cultural life. Approximately 2.5 billion people around the world carry a camera – in the form of a smart phone – in their pocket every day. We tend to make good use of it, too, taking more photos than ever (back in 2017, Google Photos announced it was backing up more than 1.2 billion photos and videos per day).
The rise of digital photography creates an interesting challenge: what should we do with all of these photos? In this competition problem, we will explore the idea of composing a slideshow out of a photo collection.

#### City Plan

Hash Code 2018, Final Round
The population of the world is growing and becoming increasingly concentrated in cities. According to the World Bank, global urbanization (the percentage of the world’s population that lives in cities) crossed 50% in 2008 and reached 54% in 2016.
The growth of urban areas creates interesting architectural challenges. How can city planners make efficient use of urban space? How should residential needs be balanced with access to public utilities, such as schools and parks?

#### Self-driving rides

Hash Code 2018, Online Qualification Round
Millions of people commute by car every day; for example, to school or to their workplace.
Self-driving vehicles are an exciting development for transportation. They aim to make traveling by car safer and more available while also saving commuters time.
In this competition problem, we’ll be looking at how a fleet of self-driving vehicles can efficiently get commuters to their destinations in a simulated city.

#### Router placement

Hash Code 2017, Final Round
Who doesn’t love wireless Internet? Millions of people rely on it for productivity and fun in countless cafes, railway stations and public areas of all sorts. For many institutions, ensuring wireless Internet access is now almost as important a feature of building facilities as the access to water and electricity. Typically, buildings are connected to the Internet using a fiber backbone. In order to provide wireless Internet access, wireless routers are placed around the building and connected using fiber cables to the backbone. The larger and more complex the building, the harder it is to pick router locations and decide how to lay down the connecting cables.

#### Streaming videos

Hash Code 2017, Online Qualification Round
Have you ever wondered what happens behind the scenes when you watch a YouTube video? As more and more people watch online videos (and as the size of these videos increases), it is critical that video-serving infrastructure is optimized to handle requests reliably and quickly. This typically involves putting in place cache servers, which store copies of popular videos. When a user request for a particular video arrives, it can be handled by a cache server close to the user, rather than by a remote data center thousands of kilometers away. Given a description of cache servers, network endpoints and videos, along with predicted requests for individual videos, decide which videos to put in which cache server in order to minimize the average waiting time for all requests.

#### Schedule Satellite Operations

Hash Code 2016, Final Round
[download id=”2596″]A satellite equipped with a high-resolution camera can be an excellent source of geo imagery. While harder to deploy than a plane or a Street View car, a satellite — once launched — provides a continuous stream of fresh data. Terra Bella is a division within Google that deploys and manages high-resolution imaging satellites in order to capture rapidly-updated imagery and analyze them for commercial customers. With a growing constellation of satellites and a constant need for fresh imagery, distributing the work between the satellites is a major challenge. Given a set of imaging satellites and a list of image collections ordered by customers, schedule satellite operations so that the total value of delivered image collections is as high as possible.

#### Optimize Drone Deliveries

Hash Code 2016, Online Qualification Round
The Internet has profoundly changed the way we buy things, but the online shopping of today is likely not the end of that change; after each purchase we still need to wait multiple days for physical goods to be carried to our doorstep. Given a fleet of drones, a list of customer orders and availability of the individual products in warehouses, schedule the drone operations so that the orders are completed as soon as possible.

#### Route Loon Balloons

Hash Code 2015, Final Round
Project Loon aims to bring universal Internet access using a fleet of high altitude balloons equipped with LTE transmitters. Circulating around the world, Loon balloons deliver Internet access in areas that lack conventional means of Internet connectivity. Given the wind data at different altitudes, plan altitude adjustments for a fleet of balloons to provide Internet coverage to select locations.

#### Optimize a Data Center

Hash Code 2015, Online Qualification Round
For over ten years, Google has been building data centers of its own design, deploying thousands of machines in locations around the globe. In each of these of locations, batteries of servers are at work around the clock, running services we use every day, from Google Search and YouTube to the Judge System of Hash Code. Given a schema of a data center and a list of available servers, your task is to optimize the layout of the data center to maximize its availability.

#### Street View Routing

Hash Code 2014, Final Round