The latest instance of the course can be found at: O1: 2024

Luet oppimateriaalin englanninkielistä versiota. Mainitsit kuitenkin taustakyselyssä osaavasi suomea. Siksi suosittelemme, että käytät suomenkielistä versiota, joka on testatumpi ja hieman laajempi ja muutenkin mukava.

Suomenkielinen materiaali kyllä esittelee englanninkielisetkin termit.

Kieli vaihtuu A+:n sivujen yläreunan painikkeesta. Tai tästä: Vaihda suomeksi.

# Chapter 6.3: Collections and Snakes

Questions Answered: How do higher-order methods make collections easy and pleasant to work with?

Topics: Methods on collections. We’ll also continue to use function literals a lot.

What Will I Do? Read and program.

Rough Estimate of Workload:? Three or four hours.

Points Available: A35 + B100.

Related Modules: Snake (new), Election.

## Introduction

This chapter will introduce you to a diverse set of higher-order methods that you can use instead of loops, or in combination with them. All of these methods have a couple of things in common: they are provided by the collection classes of the Scala API and they take in functions that specify what to do with the elements of the target collection. The methods respond to needs such as:

• How to repeat an operation on each element of a collection?

• How to examine a collection’s overall properties (e.g., whether all of its elements are similar to each other in some respect)?

• How to select some of a collection’s elements (e.g., all the elements that match a particular criterion)?

• How to combine elements to produce a result (e.g., the sum of squares of all elements, or a combination of all the pictures in a collection)?

• How to compute a separate result from each of a collection’s element (e.g., given a vector of person objects, produce a vector or their social security numbers)?

We expect that you’ll find the upcoming methods very convenient. You can use them to write code that is expressive and to-the-point. These methods are especially typical of functional programming (more on which in 11.2), whereas imperative programming tends to favor loops.

Much of this chapter consists of small examples of API methods. In that respect, we pick up where we left off in Chapter 4.2, which introduced a variety of first-order methods on collections.

For simplicity, many of the examples below feature integer vectors. However, the same methods work for other collection types, too, and for non-integer elements.

Many of the examples use function literals (Chapter 6.2) — both in the full form and abbreviated with underscores — so before you continue, please ensure that you understand those notations.

## Repeating an Operation with `foreach`

In a sense, the most generic of all the higher-order methods on Scala collections is `foreach`. As a first example, let’s use this method to print out the squares of each number in a collection.

```val numbers = Vector(10, 5, 4, 5, -20)numbers: Vector[Int] = Vector(10, 5, 4, 5, -20)
numbers.foreach( n => println(n * n) )100
25
16
25
400
```

`foreach` takes in a function that takes in a single element (here: an `Int`), such as the anonymous function that we have in this example.

As its name suggests, `foreach` performs the given operation on each element of the collection. In this case, it computes the square of each element and prints it out.

Even though the method name contains two English words, it is (against convention and somewhat confusingly) spelled with a lower-case `E`.

You probably noticed already that `foreach` does pretty much the same thing as `repeatForEachElement`, the higher-order function you wrote in Chapter 6.1. The main difference is that `foreach` is a library method available on all collections, and you can use it in any Scala program.

`foreach` expects to be given a function that returns `Unit`. Any function that you pass to `foreach` should therefore bring about an effect of some sort, such as printing (as above) or modifying an object’s state.

### Loops vs. methods on collections

As was already mentioned, the methods in this chapter can be used for similar purposes as loops. This is especially obvious in our first method, `foreach`. After all, you can also write:

```for n <- numbers do
println(n * n)
```

And indeed these two do the same thing:

```for element <- elements do
Do something with the element.```
`elements.foreach( element => Do something with the element. )`

As a matter of fact, a `for` loop such as the above is simply a different way of writing a `foreach` call. The Scala compiler automatically translates it into a method call.

As another example, here is one of the methods from Chapter 5.5’s `AuctionHouse` class:

```def nextDay() =
for current <- this.items do
```

We could have just as well written:

```def nextDay() =
```

Which one is more elegant and easier to read depends on context and on the programmer’s personal taste.

In O1, we’ll use `foreach` often, but we’ll continue to use the `for` loop as well. Feel free to use whichever you prefer, but an educated Scala programmer needs to be familiar with both.

A+ presents the exercise submission form here.

## Examining a Collection

### Checking properties with `exists` and `forall`

The `exists` method is an easy way to determine whether or not any of the elements in the collection meets a particular criterion:

```val numbers = Vector(10, 5, 4, 5, -20)numbers: Vector[Int] = Vector(10, 5, 4, 5, -20)
numbers.exists( _ < 0 )res0: Boolean = true
numbers.exists( _ < -100 )res1: Boolean = false
```

We give `exists` a function that takes an element and returns a `Boolean` indicating whether the element meets a particular condition. Here, for instance, we pass in a function that determines whether its parameter is a negative number.

Our example collection contains (at least) one negative element. It doesn’t contain even a single element less than -100.

`forall` similarly checks whether all the elements of the collection fulfill the given criterion:

```numbers.forall( _ > 0 )res2: Boolean = false
numbers.forall( _ > -100 )res3: Boolean = true
```

In this example, we first checked whether all the elements are positive; they aren’t. Then we determined that all the elements are greater than -100.

### Getting to know `count`, `exists`, and `forall`

A+ presents the exercise submission form here.

Use the REPL or other means to work out what the `count` method does. Try `numbers.count( _ % 2 == 0 )` and similar commands.

Which of the following claims are correct, assuming that `myCriterion` is the name of a function and `elements` is a variable that refers to a collection? (Also assume that `myCriterion`’s type is compatible with the collection.)

Bear in mind that a collection may either contain some elements or it may be empty. Below, you’re expected to mark which of the following claims are always correct, no matter the size of the collection.

(When creating an empty collection for testing, make sure to include an appropriate type parameter. E.g., `Vector[String]()` or `Buffer[Int]()` rather than just `Vector()` or `Buffer()`.)

An afterthought

In the question above, why was one of the expressions written like this?

```// Version 1 (which works)
elements.forall( !myCriterion(_) )
```

Couldn’t we have simply written this?

```// Version 2 (which doesn't work)
elements.forall( !myCriterion )
```

As noted in Chapter 6.2, there are different ways to write a function literal. However, Version 2 doesn’t work, because it doesn’t actually define a function literal.

`forall`, like many other methods on collections, expects to be given a function that it can apply to each element in turn. However, the expression `!myCriterion` does not refer to any function, not even if there exists a function named `myCriterion`.

To pass in the reverse of `myCriterion`, you need to formulate a function that calls `myCriterion` and applies the negation operator `!` to the result. To that end, you can either use an underscore, as above, or the full arrow notation, as below.

```// Version 3 (which works)
elements.forall( elem => !myCriterion(elem) )
```

## Selecting Elements from a Collection

### Using `find`, `filter`, `takeWhile`, and `dropWhile`

The `find` method goes through the collection and returns the first element it finds that meets the given criterion. For instance, you could look for the first number that’s less than five:

```val numbers = Vector(10, 5, 4, 5, -20)numbers: Vector[Int] = Vector(10, 5, 4, 5, -20)
numbers.find( _ < 5 )res4: Option[Int] = Some(4)
```

Notice that `find` returns an `Option` wrapped around the value that was found. If the search results in a miss, you get `None`:

```numbers.find( _ == 100 )res5: Option[Int] = None
```

`filter` is similar to `find` except that it returns a collection of all the elements that match the criterion. Our vector contains four positive numbers:

```val numbers = Vector(10, 5, 4, 5, -20)numbers: Vector[Int] = Vector(10, 5, 4, 5, -20)
numbers.filter( _ > 0 )res6: Vector[Int] = Vector(10, 5, 4, 5)
```

In Chapter 4.2, you saw a `take` method that returns a partial collection with the given number of elements from the beginning of the original collection (say, `numbers.take(3)`). `take`’s higher-order cousin is `takeWhile`:

```val numbers = Vector(10, 5, 4, 5, -20)numbers: Vector[Int] = Vector(10, 5, 4, 5, -20)
numbers.takeWhile( _ >= 5 )res7: Vector[Int] = Vector(10, 5)
```

As shown above, the method takes elements from the beginning of the collection until it runs into an element that doesn’t meet the given criterion.

A+ presents the exercise submission form here.

### `filter` vs. `filterNot`; `takeWhile` vs. `dropWhile`

Use the REPL or other means to work out what the `filterNot` method does. You can invoke it just like `filter` above.

Assume that `elements` is a variable that refers to a vector. Further assume that we have `def`ined a function named `myCriterion` whose type is compatible with the collection. Which of the following claims are correct?

How about `dropWhile`? You can invoke it just like `takeWhile` above.

## Assignment: Reimplementing Election (Part 1 of 2)

This was a good activity. My code is so much shorter now.

In Chapter 5.6, you wrote a number of methods for class `District` in module Election. (If you didn’t, do that now or see the example solution.) At that time, you (probably) used loops to implement the methods.

Rewrite two of the methods, namely `printCandidates` and `candidatesFrom`. For each one, there exists a simple implementation that uses one of the methods introduced above. Use those methods instead of `for` loops.

We’ll get back to the other `District` methods later.

A+ presents the exercise submission form here.

## Mapping a Collection of Elements: `map` and `flatMap`

It is remarkably often useful to “map” a collection of elements to another.

The higher-order method `map` returns a new collection whose elements have been generated by applying `map`’s parameter function to each of original collection’s elements. In the example below, we use `map` to compute each element’s absolute value and obtain a new vector that contains each of the results in order:

```val numbers = Vector(10, 5, 4, 5, -20)numbers: Vector[Int] = Vector(10, 5, 4, 5, -20)
numbers.map( _.abs )res8: Vector[Int] = Vector(10, 5, 4, 5, 20)
```

The following expression determines, for each element, whether or not it is at least five. The output vector contains the resulting Booleans in order:

```numbers.map( _ >= 5 )res9: Vector[Boolean] = Vector(true, true, false, true, false)
```

You can use `map` in combination with a wide variety of parameter functions. Like the other methods of this chapter, `map` is also available on collections other than vectors. For instance, you can call it on the `Range` object that you get by writing `1 to 10` (Chapter 5.6):

```(1 to 10).map( n => n * n )res10: IndexedSeq[Int] = Vector(1, 4, 9, 16, 25, 36, 49, 64, 81, 100)
```

One more example, this time with `Double`s as elements and a named function as a parameter:

```import scala.math.sqrtval data = Vector(100.0, 25.0, 12.3, 2, 1.21)data: Vector[Double] = Vector(100.0, 25.0, 12.3, 2.0, 1.21)
data.map(sqrt)res11: Vector[Double] = Vector(10.0, 5.0, 3.5071355833500366, 1.4142135623730951, 1.1)
```

`map`ping the square-root function to each element gives us a collection with all the roots.

### Getting to know `map`

A+ presents the exercise submission form here.

Let’s (once again) say we have a vector of numbers and mean to produce a printout of their squares. Here’s a `foreach` call and a `map` call. Compare:

```val numbers = Vector(10, -5, 20)numbers: Vector[Int] = Vector(10, -5, 20)
numbers.foreach( num => println("The square is " + num * num) )The square is 100
The square is 25
The square is 400
numbers.map( num => println("The square is " + num * num) )The square is 100
The square is 25
The square is 400
res12: Vector[Unit] = Vector((), (), ())
```

Try to figure out which of the following claims about the above example are correct. Read the feedback you get.

Suppose we mean to create a vector with the squares of those original numbers. Here’s a `foreach` call and a `map` call. Compare:

```numbers.foreach( num => num * num )numbers.map( num => num * num )res13: Vector[Int] = Vector(100, 25, 400)
```

Assess these claims:

Suppose you have a variable `buffer` of type `Buffer[Int]` that refers to a “one-dimensional” buffer of numbers. Let’s also assume the buffer contains a minimum of one element.

What happens if you now evaluate `buffer.map( x => Buffer(x, x + 1) )`? Experiment in the REPL as needed.

### The `flatMap` method

Chapter 6.1 mentioned a method that “flattens” a collection of collections:

```val nested = Vector(Vector(3, -10, -4), Vector(5, -10, 1), Vector(-1), Vector(4, 4))nested: Vector[Vector[Int]] = Vector(Vector(3, -10, -4), Vector(5, -10, 1), Vector(-1), Vector(4, 4))
nested.flattenres14: Vector[Int] = Vector(3, -10, -4, 5, -10, 1, -1, 4, 4)
```

It’s fairly common that we want to first `map` a collection to produce a nested collection, then `flatten` the result. Here’s a toy example:

```val numbers = Vector(10, 5, 4, 5, -20)numbers: Vector[Int] = Vector(10, 5, 4, 5, -20)
val experiment = numbers.map( n => Vector(-n.abs, 0, n.abs) )experiment: Vector[Vector[Int]] = Vector(Vector(-10, 0, 10), Vector(-5, 0, 5), Vector(-4, 0, 4), Vector(-5, 0, 5),
Vector(-20, 0, 20))
experiment.flattenres15: Vector[Int] = Vector(-10, 0, 10, -5, 0, 5, -4, 0, 4, -5, 0, 5, -20, 0, 20)
```

It’s possible to combine `map` and `flatten` into a single method call:

```numbers.flatMap( n => Vector(-n.abs, 0, n.abs) )res16: Vector[Int] = Vector(-10, 0, 10, -5, 0, 5, -4, 0, 4, -5, 0, 5, -20, 0, 20)
```

That is, `collection.flatMap(myFunc)` does the same as `collection.map(myFunc).flatten`.

You may well be wondering whether combining `map` with `flatten` is so useful that it merits a separate `flatMap` method. Yes, it really is. You’ll see as your programming experience grows during the rest of O1 and later.

For a somewhat more interesting example of `map` and `flatMap`, consider the following class.

```class User(val id: String, val emailAddresses: Vector[String]):
override def toString = this.id + " <" + this.emailAddresses.mkString(",") + ">"
```

Let’s imagine we’re working on an application that stores `User` objects in a vector. In the example below, our vector contains just two users, but of course there could be many more.

```val allUsers = Vector(
User("sophia", Vector("sophia.student@aalto.fi", "sophia.student@iki.fi", "sophia.student@gmail.com")),
)allUsers: Vector[User] =
Vector(sophia <sophia.student@aalto.fi,sophia.student@iki.fi,sophia.student@gmail.com>,
```

How can we now get a list of all the `id`s of all the users? What about a list of all the email addresses of all the users?

Sure, we could write a loop, but the just-introduced methods get the job done with minimal effort.

The `map` method gives us each user’s identifier if we pass in a function that maps a user object to its `id`.

```allUsers.map( _.id )res17: Vector[String] = Vector(sophia, megadestroyer)
```

We can also use `map` to access the email addresses. This gives us a nested collection (which, depending on our purposes, may or may not be convenient):

```allUsers.map( _.emailAddresses )res18: Vector[Vector[String]] = Vector(Vector(sophia.student@aalto.fi, sophia.student@iki.fi, sophia.student@gmail.com),
Vector(teemu.teekkari@aalto.fi, teemuteekkari@gmail.com))
```

Assuming we want a single “flat” collection of all the emails, we can use `flatMap` instead:

```allUsers.flatMap( _.emailAddresses )res19: Vector[String] = Vector(sophia.student@aalto.fi, sophia.student@iki.fi, sophia.student@gmail.com,
teemu.teekkari@aalto.fi, teemuteekkari@gmail.com)
```

The next programming assignment is not only about methods on collections, but it does provide opportunities to use them.

## Assignment: Snake

Snake is a classic computer game that originates from the 1970s. The player controls a “snake” or “worm” that turns about on a two-dimensional field, looking to eat and grow. In the 1990s, Snake renewed its popularity as a mobile game, which has in turn attracted nostalgic attention in recent years. By the time you read this, the game may have already reverted to passé retro kitch.

Snake is also a classic as a programming exercise. Let us join the tradition.

### Concepts in Snake

The key components of a game of Snake are the snake itself and the food that the snake seeks to swallow. At any given moment, there is a single item of food available for the snake, located somewhere on the playing field. When the snake eats the food — that is, when the snake’s head is about to hit it — the snake grows and a new item of food appears.

You can think of the playing field as a grid (see image). The food is located in a single space on the grid. The snake consists of segments (“pieces”), each of which takes up a space.

The only thing the player can do is press one of the arrow keys to make the snake turn in that direction. The snake can move only in the four main compass directions.

As time passes, the snake moves step by step: its first segment, or “head”, moves in the latest direction chosen by the player and the other segments follow (see the second image). However, if the head enters the food space, the snake eats the food and grows by a single segment: a new segment appears where the food was and all the other segments remain where they were.

The game is over when the snake’s head hits something other than food.

### Classes in Snake

The Snake module contains a partial implementation for the game. The overall design of the program resembles that of FlappyBug: we have a `SnakeGame` class that represents the mutable state of a game and a GUI (in `SnakeApp.scala`) that displays the state and receiving commands from the player.

So, an instance of `SnakeGame` represents a single session of Snake. Calling that instance’s methods changes its state. The `SnakeGame` object tracks:

• the next item of food: where is it on the grid?

• the location of the snake: where on the grid are its segments?

• the direction of the (head of the) snake: which of the four compass directions has it been ordered to go?

Our class needs to manipulate locations on the grid as well as directions. For that, we have tools on hand in package `o1`:

### The classes `GridPos` and `CompassDir`

Class `GridPos` represents coordinates on a grid. Each coordinate is an integer.

• This class resembles the `Pos` you know but is specifically designed for use with grids and provides some convenient methods to that end.

• We therefore distinguish between two things: which space something is located at (`GridPos`), and which spot within a particular image something should be drawn at (`Pos`).

• The `GridPos` is part of the program domain’s internal logic (i.e., the rules of Snake). The `Pos` is a feature of the GUI.

• This is similar to what we did in the Stars module, where we distinguished between a `StarCoords` on a map and a `Pos` within an image.

The class `CompassDir` represents compass directions such as north (up) and west (left):

• It’s well suited for representing the snake’s heading.

• It combines well with the methods on `GridPos`. For instance, we can ask a `GridPos` object which coordinates neighbor it in a particular direction.

Both classes are documented within the O1Library module.

### A couple of mini-assignments as groundwork

A+ presents the exercise submission form here.

A+ presents the exercise submission form here.

In `SnakeGame.scala` and `SnakeApp.scala`, find the locations where something is missing and implement the missing parts. We suggest that you proceed as follows.

### Step 0 of 5: preparations

Run the given program. You should see a playing field with a food item and a single-segment snakeling. (There is no visible grid like in the illustrations above; that’s intentional.) The snake doesn’t move yet.

Study class `SnakeGame`. Observe that there are parts missing. Note how the given code uses the classes `GridPos` and `CompassDir`. In the Scaladocs for those other classes, read at least the introductions at the top; there’s no need to wade through all the methods. (The Snake module itself has no Scaladocs. All the information you need is in this chapter and in the Scala code.)

You may want to take a look at `SnakeApp.scala`, too. As the clock ticks, the GUI calls the `advance` method of the appropriate `SnakeGame` object. `advance` is supposed to move the snake. The given version doesn’t do anything, however.

### Step 1 of 5: a mobile snake

For now, write a partial implementation for `advance`: make it move the snake’s head to the next space. Don’t worry about growing the snake yet.

Hints:

• The `segments` variable refers to a single-element vector that contains the location of the (head of the) snake. This is a `var`. Replace its value with a single-element vector containing the neighboring location towards the current heading.

• There is a convenient method in `GridPos` for determining that location.

Run the modified program. See the single segment slither.

The game ends when the snake hits an edge. You control the snake with the arrow keys (or WASD). The snake ignores the food.

### Step 2 of 5: snake snacks

Develop `advance` further. The method must now additionally move the food into a new random location whenever the snake hits it. That relocation of the food happens as part of the same movement step (i.e., the same call to `advance`) that puts the snake’s only segment in the current food space. The `advance` method should first move the snake, then the food; the food is moved only in case the snake found the food at its current location.

You can do that by updating the value of the `nextFood` variable. Use the given method `randomLocationOnGrid` to pick a new location. (See `util.scala`.)

Try running your program. Food gets eaten, but the snake doesn’t grow.

There’s a `GameSpeed` constant in `SnakeApp.scala`. You may adjust it to your liking. You could slow down the game while testing, for instance.

### Step 3 of 5: a growing snake

Finish up `advance`: 1) when the head is just about to hit the food, grow the snake, and 2) when the snake doesn’t eat, it moves. That is, each time `advance` is called, it either grows or moves the snake, but not both.

Now it’s no longer enough to replace the value of `segments` with a new single-element vector. Remove that line and write some new code.

Hints and instructions:

• Replace the value of `segments` with a new vector that contains all the snake’s locations after the move. There should be either exactly as many segments as before, or one more.

• Grow the snake from the front. When the snake’s head would end up moving to a food square, don’t move the snake at all. Instead, add a new segment where the food is; it becomes the snake’s new head. (The frontmost segment becomes the second-from-front. All existing segments stay where they are. See the illustration on the right.)

• The food must be relocated as part of the same `advance` call that brings the snake’s head to where the food is.

• To form the new vector, you can use the tools from 4.2, which were just revisited in the mini-assignment above.

• The segments are identical. You don’t have to move each segment separately. All the middle segments remain within the snake: if you take care of the first and last segments, that’s enough to create the illusion of movement.

• You may choose to reveal the additional hint below.

Hint for moving the snake segments

When the snake advances without eating, you need to construct a vector that contains the head’s new location followed by all the snake’s earlier locations except the last. The solution is fundamentally identically with what you did with an `Int` vector in the preceding mini-assignment.

Also remember that just creating a vector doesn’t store the vector anywhere. You’ll need to do that explicitly.

• Try running your program after you complete this step. The snake still doesn’t seem to grow. In fact, it does grow, but you don’t see it because the GUI draws only the head.

### Step 4 of 5: sorting out the graphics

Turn to the GUI in `SnakeApp.scala` and the `makePic` method defined there. Observe:

• The method places only a single copy of `SegmentPic` (reddish picture of a snake segment) against the background.

• `makePic` uses an auxiliary function `toPixelPos`, which is defined in the same file. That function takes in a `GridPos` and determines where in the GUI image that space should be drawn.

• `makePic` also uses a `placeCopies` method from class `Pic`. As its first parameter, that method takes a picture. As its second parameter, it takes a vector of `Pos` objects. That method works just like the familiar `place` method, except that it places multiple copies of the same image. Which doesn’t help much yet, since the given code passes in only a single-element vector.

Edit `makePic` so that it draws all the segments as identical round shapes. Here’s how:

• Use `toPixelPos` to determine each segment’s position within the image. You don’t need a loop. Use one of the collection methods from this chapter.

You have a collection of `GridPos`es. An easy way to get a collection with the corresponding `Pos`es is to call `map`.

• Call `placeCopies`, passing in a vector that contains a `Pos` for each segment.

The snake grows!

### Step 5 of 5: collisions

It is ordained by the tradition of snake gaming that snakes die if they collide with their own body. Attend to this in class `SnakeGame`: the `isOver` method should indicate that the game is over not only when the snake hits a wall but also if its head shares a location with any of the other segments. (That is, the game is over when the head is already in the same location as another segment, not before.)

You can again turn to Chapter 4.2 for tooling.

The snake has a head and a tail. Your method should determine whether the head’s location is among the tail’s locations — that is, whether the tail contains the head. As noted, the tools for doing just that are in Chapter 4.2.

A special case

What should happen when a two-segment snake turns 180 degrees? Does its head segment collide with the single tail segment or not? Or maybe the snake should be prevented from doing that altogether? You choose. The automatic tests for this assignment don’t test that case.

A+ presents the exercise submission form here.

## Summary of Key Points

• The collection classes of the Scala API define a whole bunch of higher-order methods that operate on the elements of collections.

• Methods in common use include `foreach`, `exists`, `forall`, `find`, `filter`, `map`, and `flatMap`. You’ll see more later.

• These methods provide generic solutions to common problems and are often a convenient alternative to loops.

• Processing collections in this manner is especially common in so-called functional programming, which Scala encourages.

• Links to the glossary: higher-order function; collection; level of abstraction.

Why This Chapter Matters

We’ll make frequent use of the methods introduced above. They will serve you well in upcoming programming assignments.

You’ll need to read a lot of given code that uses these methods.

You may initially struggle to recall each method. Then again, you don’t need to. You can return to this chapter for reference, or use our Scala Reference.

The important thing for now is to bear in mind the general idea: there is a wide selection of convenient higher-order methods on offer.

Bonus teaser about `for``yield` expressions

It’s already come up in the ebook that the `for``do` loops that we’ve written are just another way of writing a `foreach` method call. These two do the same thing:

```numbers.foreach( n => println("The square is " + n * n) )
```
```for n <- numbers do
println("The square is " + n * n) )
```

Scala’s `for` construct can be used for a bunch of other things, too. (But you don’t have to in O1.) For instance, you can write a `map` method call as a `for` expression. These two do the same thing:

```val squares = numbers.map( n => n * n )
```
```val squares = for n <- numbers yield n * n
```

`yield` is a reserved word that you can use to make a `for` expression produce a result other than `Unit`.

And below, you’ll find a `flatMap` call and a `for``yield` structure that’s equivalent to it. Both code fragments traverse a `numbers` vector twice and produce all possible two-element sums:

```val sums = for first <- numbers; second <- numbers yield first + second
```
```val sums = numbers.flatMap( first => numbers.map( second => first + second ) )
```

You may split a `for``yield` expression across multiple lines. Here’s one way to do that:

```val sums =
for
first <- numbers
second <- numbers
yield first + second
```

## Feedback

Please note that this section must be completed individually. Even if you worked on this chapter with a pair, each of you should submit the form separately.

## Credits

Thousands of students have given feedback and so contributed to this ebook’s design. Thank you!

The ebook’s chapters, programming assignments, and weekly bulletins have been written in Finnish and translated into English by Juha Sorva.

The appendices (glossary, Scala reference, FAQ, etc.) are by Juha Sorva unless otherwise specified on the page.

The automatic assessment of the assignments has been developed by: (in alphabetical order) Riku Autio, Nikolas Drosdek, Joonatan Honkamaa, Antti Immonen, Jaakko Kantojärvi, Niklas Kröger, Kalle Laitinen, Teemu Lehtinen, Jaakko Nakaza, Strasdosky Otewa, Timi Seppälä, Teemu Sirkiä, Anna Valldeoriola Cardó, and Aleksi Vartiainen.

The illustrations at the top of each chapter, and the similar drawings elsewhere in the ebook, are the work of Christina Lassheikki.

The animations that detail the execution Scala programs have been designed by Juha Sorva and Teemu Sirkiä. Teemu Sirkiä and Riku Autio did the technical implementation, relying on Teemu’s Jsvee and Kelmu toolkits.

The other diagrams and interactive presentations in the ebook are by Juha Sorva.

The O1Library software has been developed by Aleksi Lukkarinen and Juha Sorva. Several of its key components are built upon Aleksi’s SMCL library.

The pedagogy of using O1Library for simple graphical programming (such as `Pic`) is inspired by the textbooks How to Design Programs by Flatt, Felleisen, Findler, and Krishnamurthi and Picturing Programs by Stephen Bloch.

The course platform A+ was originally created at Aalto’s LeTech research group as a student project. The open-source project is now shepherded by the Computer Science department’s edu-tech team and hosted by the department’s IT services. Markku Riekkinen is the current lead developer; dozens of Aalto students and others have also contributed.

The A+ Courses plugin, which supports A+ and O1 in IntelliJ IDEA, is another open-source project. It has been designed and implemented by various students in collaboration with O1’s teachers.

For O1’s current teaching staff, please see Chapter 1.1.

Additional credits appear at the ends of some chapters.

Posting submission...