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Arrays

This chapter presents one of Ruby’s most useful built-in types, arrays. You will also learn more about objects and what can happen when you have more than one name for the same object.

An array is a sequence

Like a string, an array is a sequence of values. In a string, the values are characters; in an array, they can be any type. The values in an array are called elements or sometimes items.

There are several ways to create a new array; the simplest is to enclose the elements in square brackets ([ and ]):

[10, 20, 30, 40]
['crunchy frog', 'ram bladder', 'lark vomit']

The first example is an array of four integers. The second is an array of three strings. The elements of an array don’t have to be the same type. The following array contains a string, a float, an integer, and (lo!) another array:

['spam', 2.0, 5, [10, 20]]

An array within another array is nested.

An array that contains no elements is called an empty array; you can create one with empty brackets, [].

As you might expect, you can assign array values to variables:

>> cheeses = ['Cheddar', 'Edam', 'Gouda']
=> ["Cheddar", "Edam", "Gouda"]
>> numbers = [42, 123]
=> [42, 123]
>> empty = []
=> []

>> puts "#{cheeses}, #{numbers}, #{empty}"
["Cheddar", "Edam", "Gouda"], [42, 123], []
=> nil

Arrays are mutable

The syntax for accessing the elements of an array is the same as for accessing the characters of a string—the bracket operator. The expression inside the brackets specifies the index. Remember that the indices start at 0:

>> cheeses[0]
=> "Cheddar"

Like strings, arrays are mutable. When the bracket operator appears on the left side of an assignment, it identifies the element of the array that will be assigned.

>> numbers = [42, 123]
=> [42, 123]
>> numbers[1] = 5
=> 5
>> numbers
=> [42, 5]

The one-eth element of numbers, which used to be 123, is now 5.

Figure below shows the state diagram for cheeses, numbers and empty:

State diagram.
Figure 10.1: State diagram

Arrays are represented by boxes with the word “array” outside and the elements of the array inside. cheeses refers to an array with three elements indexed 0, 1 and 2. numbers contains two elements; the diagram shows that the value of the second element has been reassigned from 123 to 5. empty refers to an array with no elements.

Array indices work similar to string indices:

  • Any integer expression can be used as an index.

  • A floating expression used as an index gets rounded down to an integer.

  • If you try to read an element that does not exist, you get back nil value.

  • If you try to write to an element that does not exist, it gets added to the array, with nil values as filler if needed.

  • If an index has a negative value, it counts backward from the end of the array.

The include? method also works on arrays.

>> cheeses = ['Cheddar', 'Edam', 'Gouda']
=> ["Cheddar", "Edam", "Gouda"]
>> cheeses.include?('Edam')
=> true
>> cheeses.include?('Brie')
=> false

Traversing an array

To traverse the elements of an array, a for loop can be used:

for cheese in cheeses
  puts cheese
end

More commonly, a block of statements is passed to one of various array built-in methods, each for example:

# preferred way for multiple statements
cheeses.each do |cheese|
  all_caps = cheese.upcase
  puts all_caps
end

# preferred way for single statement
cheeses.each { |cheese| puts cheese }

A significant difference between for loop and block form is variable scope. Similar to what we saw for user defined methods in Methods chapter, variables defined inside the block are local. In above example, cheese and all_caps are local and will raise exception if called outside the block.

for loop and each method works well if you only need to read the elements of the array. But if you want to write or update the elements, you need the indices.

# using for loop
for i in 0...numbers.length
  numbers[i] = numbers[i] * 2
end

# using each_index method
numbers.each_index { |i| numbers[i] = numbers[i] * 2 }

These traverse the array and update each element. Each time through the loop i gets the index of the next element. The assignment statement in the body uses i to read the old value of the element and to assign the new value.

Looping over an empty array never runs the body:

for x in []
  puts 'This never happens.'
end

[].each { puts 'This never happens.' }

Although an array can contain another array, the nested array still counts as a single element. The length of this array is four:

['spam', 1, ['Brie', 'Roquefort', 'Pol le Veq'], [1, 2, 3]]

Array operations

The + operator concatenates arrays:

>> a = [1, 2, 3]
=> [1, 2, 3]
>> b = [4, 5, 6]
=> [4, 5, 6]
>> c = a + b
=> [1, 2, 3, 4, 5, 6]

The * operator repeats an array a given number of times:

>> [0] * 4
=> [0, 0, 0, 0]
>> [1, 2, 3] * 3
=> [1, 2, 3, 1, 2, 3, 1, 2, 3]

The first example repeats four times. The second example repeats the array three times.

The - operator performs array difference:

>> a = [2, 6, 12, 4, 5, 12]
=> [2, 6, 12, 4, 5, 12]
>> b = [12, 1, 5, 2]
=> [12, 1, 5, 2]
>> c = a - b
=> [6, 4]

array slices

Slicing also works on arrays:

>> t = ['a', 'b', 'c', 'd', 'e', 'f']
=> ["a", "b", "c", "d", "e", "f"]
>> t[1..2]
=> ["b", "c"]
>> t[0..3]
=> ["a", "b", "c", "d"]
>> t[4..-1]
=> ["e", "f"]

If you use 0 as first index, the slice starts at the beginning. If you use -1 as the second, the slice goes to the end. So if you use both, the slice is a copy of the whole array. Which is same as using the clone method.

>> t[0..-1]
=> ["a", "b", "c", "d", "e", "f"]

>> t.clone
=> ["a", "b", "c", "d", "e", "f"]

Since arrays are mutable, it is often useful to make a copy before performing operations that modify arrays.

Slicing used on the left side of an assignment can update multiple elements:

>> t = ['a', 'b', 'c', 'd', 'e', 'f']
=> ["a", "b", "c", "d", "e", "f"]
>> t[1..2] = ['x', 'y']
=> ["x", "y"]
>> t
=> ["a", "x", "y", "d", "e", "f"]

Array methods

Ruby provides methods that operate on array. For example, append adds new element(s) to the end of an array:

>> t = ['a', 'b', 'c']
=> ["a", "b", "c"]
>> t.append('d')
=> ["a", "b", "c", "d"]
>> t.append('e', 'f', 'g')
=> ["a", "b", "c", "d", "e", "f", "g"]

As can be observed from this example, the append method modifies the input array in-place.

To append all of the elements from another array, use splat operator, which turns array into an argument list:

>> t1 = ['a', 'b', 'c']
=> ["a", "b", "c"]
>> t2 = ['d', 'e']
=> ["d", "e"]
>> t1.append(*t2)
=> ["a", "b", "c", "d", "e"]

This example leaves t2 unmodified.

sort arranges the elements of the array from low to high:

>> t = ['d', 'c', 'e', 'b', 'a']
=> ["d", "c", "e", "b", "a"]
>> t.sort
=> ["a", "b", "c", "d", "e"]
>> t
=> ["d", "c", "e", "b", "a"]

Some array methods not ending with ! in their name return an array without modifying the original array. Similar to ? special character we saw in Section Boolean methods, ! at end of method name is used to indicate that the method modifies the object it was invoked upon.

So, use sort! to modify the array in-place:

>> t = ['d', 'c', 'e', 'b', 'a']
=> ["d", "c", "e", "b", "a"]
>> t.sort!
=> ["a", "b", "c", "d", "e"]
>> t
=> ["a", "b", "c", "d", "e"]

Map, filter and reduce

To add up all the numbers in an array, you can use a loop like this:

def add_all(t)
  total = 0
  t.each { |x| total += x }
  return total
end

total is initialized to 0. Each time through the loop, x gets one element from the array. The += operator provides a short way to update a variable. This augmented assignment statement,

total += x

is equivalent to

total = total + x

As the loop runs, total accumulates the sum of the elements; a variable used this way is sometimes called an accumulator.

Note that since total was defined in same scope before passing the block to each method, a local version of the variable is not created inside the block.

Adding up the elements of an array is such a common operation that Ruby provides it as a built-in method, sum:

>> t = [1, 2, 3]
=> [1, 2, 3]
>> t.sum
=> 6

An operation like this that combines a sequence of elements into a single value is sometimes called reduce.

Sometimes you want to traverse one array while building another. For example, the following method takes an array of strings and returns a new array that contains capitalized strings:

def capitalize_all(t)
  res = []
  t.each { |s| res.append(s.capitalize) }
  return res
end

res is initialized with an empty array; each time through the loop, we append the next element. So res is another kind of accumulator.

An operation like capitalize_all is sometimes called a map because it “maps” a method (in this case the method capitalize) onto each of the elements in a sequence.

Another common operation is to select some of the elements from an array and return a subarray. For example, the following method takes an array of words and returns an array that contains words only made up of uppercase letters:

def only_upper(t)
  res = []
  t.each { |s| res.append(s) if !s.match?(/[^A-Z]/) }
  return res
end

An operation like only_upper is called a filter because it selects some of the elements and filters out the others.

Most common array operations can be expressed as a combination of map, filter and reduce.

Deleting elements

There are several ways to delete elements from an array. If you know the index of the element you want, you can use slice!:

>> t = ['a', 'b', 'c']
=> ["a", "b", "c"]
>> x = t.slice!(1)
=> "b"
>> t
=> ["a", "c"]
>> x
=> "b"

slice! modifies the array and returns the element that was removed.

To remove more than one element, you can use slicing notation:

>> t = ['a', 'b', 'c', 'd', 'e', 'f']
=> ["a", "b", "c", "d", "e", "f"]
>> t.slice!(1..4)
=> ["b", "c", "d", "e"]
>> t
=> ["a", "f"]

If you know the element you want to remove (but not the index), you can use delete:

>> t = ['a', 'b', 'c', 'b']
=> ["a", "b", "c", "b"]
>> t.delete('b')
=> "b"
>> t
=> ["a", "c"]

Observe that all elements matching the given argument is deleted. To remove multiple elements, use the - operator as discussed in Section Array operations.

Arrays and strings

A string is a sequence of characters and an array is a sequence of values, but an array of characters is not the same as a string. To convert from a string to an array of characters, you can use chars method:

>> s = 'spam'
=> "spam"
>> t = s.chars
=> ["s", "p", "a", "m"]

The chars method breaks a string into individual letters. If you want to break a string into words, you can use the split method:

>> s = 'pining for the fjords'
=> "pining for the fjords"
>> t = s.split
=> ["pining", "for", "the", "fjords"]

An optional argument called a delimiter specifies which characters to use as word boundaries. The following example uses a hyphen as a delimiter:

>> s = 'spam-spam-spam'
=> "spam-spam-spam"
>> delimiter = '-'
=> "-"
>> t = s.split(delimiter)
=> ["spam", "spam", "spam"]

join is the inverse of split. It concatenates the elements of an array.

>> t = ['pining', 'for', 'the', 'fjords']
=> ["pining", "for", "the", "fjords"]
>> delimiter = ' '
=> " "
>> s = t.join(delimiter)
=> "pining for the fjords"

>> [1, 2, [3, 4]].join
=> "1234"

In this case the delimiter is a space character, so join puts a space between elements. If you don’t pass an argument, the default delimiter is empty string.

Objects and values

If we run these assignment statements:

a = 42
b = 42

We know that a and b both refer to an integer, but we don’t know whether they refer to the same integer. There are two possible states, as shown below.

State diagram.
Figure 10.2: State diagram

In one case, a and b refer to two different objects that have the same value. In the second case, they refer to the same object.

To check whether two variables refer to the same object, you can use the equal? method.

>> a = 42
=> 42
>> b = 42
=> 42
>> a.equal?(b)
=> true

In this example, Ruby only created one integer object, and both a and b refer to it. But when you create two arrays, you get two objects:

>> a = [1, 2, 3]
=> [1, 2, 3]
>> b = [1, 2, 3]
=> [1, 2, 3]
>> a.equal?(b)
=> false

So the state diagram looks like:

State diagram.
Figure 10.3: State diagram

In this case we would say that the two arrays are equivalent, because they have the same elements, but not identical, because they are not the same object. If two objects are identical, they are also equivalent, but if they are equivalent, they are not necessarily identical.

Until now, we have been using “object” and “value” interchangeably, but it is more precise to say that an object has a value. If you evaluate [1, 2, 3], you get an array object whose value is a sequence of integers. If another array has the same elements, we say it has the same value, but it is not the same object.

Aliasing

If a refers to an object and you assign b = a, then both variables refer to the same object:

>> a = [1, 2, 3]
=> [1, 2, 3]
>> b = a
=> [1, 2, 3]
>> b.equal?(a)
=> true

The state diagram now looks like:

State diagram.
Figure 10.4: State diagram

The association of a variable with an object is called a reference. In this example, there are two references to the same object.

An object with more than one reference has more than one name, so we say that the object is aliased.

If the aliased object is mutable, changes made with one alias affect the other:

>> b[0] = 42
=> 42
>> a
=> [42, 2, 3]

Although this behavior can be useful, it is error-prone. In general, it is safer to avoid aliasing when you are working with mutable objects.

For immutable objects like integers, aliasing is not as much of a problem. In this example:

a = 42
b = 42

It almost never makes a difference whether a and b refer to the same integer or not.

Array arguments

When you pass an array to a method, the method gets a reference to the array. If the method modifies the array, the caller sees the change. For example, delete_head removes the first element from an array:

def delete_head(t)
  t.slice!(0)
end

Here’s how it is used:

>> letters = ['a', 'b', 'c']
=> ["a", "b", "c"]
>> delete_head(letters)
=> "a"
>> letters
=> ["b", "c"]

The parameter t and the variable letters are aliases for the same object. The stack diagram looks like:

Stack diagram.
Figure 10.5: Stack diagram

Since the array is shared by two frames, I drew it between them.

It is important to distinguish between operations that modify arrays and operations that create new arrays. For example, the append method modifies an array, but the + operator creates a new array.

Here’s an example using append:

>> t1 = [1, 2]
=> [1, 2]
>> t2 = t1.append(3)
=> [1, 2, 3]
>> t1
=> [1, 2, 3]
>> t2
=> [1, 2, 3]

Here’s an example using the + operator:

>> t3 = t1 + [4]
=> [1, 2, 3, 4]
>> t1
=> [1, 2, 3]
>> t3
=> [1, 2, 3, 4]

The result of the operator is a new array, and the original array is unchanged.

This difference is important when you write methods that are supposed to modify arrays. For example, this method does not delete the head of an array:

def bad_delete_head(t)
  t = t[1..-1]              # WRONG!
end

The slicing creates a new array and the assignment makes t refer to it, but that doesn’t affect the caller.

>> t4 = [1, 2, 3]
=> [1, 2, 3]
>> bad_delete_head(t4)
=> [2, 3]
>> t4
=> [1, 2, 3]

At the beginning of bad_delete_head, t and t4 refer to the same array. At the end, t refers to a new array, but t4 still refers to the original, unmodified array.

An alternative is to write a method that creates and returns a new array. For example, tail returns all but the first element of an array:

def tail(t)
  return t[1..-1]
end

This method leaves the original array unmodified. Here’s how it is used:

>> letters = ['a', 'b', 'c']
=> ["a", "b", "c"]
>> rest = tail(letters)
=> ["b", "c"]
>> rest
=> ["b", "c"]

Debugging

Careless use of arrays (and other mutable objects) can lead to long hours of debugging. Here are some common pitfalls and ways to avoid them:

  1. Array methods like sort and slice have two versions, one that returns the result and the other having ! in their name to indicate argument is modified in-place. Methods like append and delete have only one version that always modify the argument.

    If you are used to writing array code like this:

    numbers.append(4)

    It is tempting to write array code for in-place sorting like this:

    numbers.sort           # WRONG!

    Because sort doesn’t modify array in-place, the next operation you perform with numbers is likely to fail.

    Before using array methods and operators, you should read the documentation carefully and then test them in interactive mode.

  2. Pick an idiom and stick with it.

    Part of the problem with arrays is that there are too many ways to do things. For example, to remove an element from an array, you can use pop, delete, slice!, or - operator.

    To add an element, you can use the append method or the + operator. Assuming that t is an array and x is an array element, these are correct:

    t.append(x)
t = t + [x]
t += [x]

    And these are wrong:

    t.append([x])          # WRONG!
t + [x]                # WRONG!
t = t + x              # WRONG!

    Try out each of these examples in interactive mode to make sure you understand what they do. Notice that only the last one causes a runtime error; the other two are legal, but they do the wrong thing.

  3. Make copies to avoid aliasing.

    If you want to use a method like delete that modifies the argument, but you need to keep the original array as well, you can make a copy.

    >> t = [3, 1, 2]
=> [3, 1, 2]
>> t2 = t.clone
=> [3, 1, 2]
>> t2.delete(1)
=> 1
>> t
=> [3, 1, 2]
>> t2
=> [3, 2]

Glossary

  • array:
    A sequence of values.

  • element:
    One of the values in an array (or other sequence), also called items.

  • nested array:
    An array that is an element of another array.

  • accumulator:
    A variable used in a loop to add up or accumulate a result.

  • augmented assignment:
    A statement that updates the value of a variable using an operator like +=.

  • reduce:
    A processing pattern that traverses a sequence and accumulates the elements into a single result.

  • map:
    A processing pattern that traverses a sequence and performs an operation on each element.

  • filter:
    A processing pattern that traverses an array and selects the elements that satisfy some criterion.

  • object:
    Something a variable can refer to. An object has a type and a value.

  • equivalent:
    Having the same value.

  • identical:
    Being the same object (which implies equivalence).

  • reference:
    The association between a variable and its value.

  • aliasing:
    A circumstance where two or more variables refer to the same object.

  • delimiter:
    A character or string used to indicate where a string should be split.

Exercises

Exercise 1
Write a method called nested_sum that takes an array of arrays of integers and adds up the elements from all of the nested arrays. For example:

>> t = [[1, 2], [3], [4, 5, 6]]
=> [[1, 2], [3], [4, 5, 6]]
>> nested_sum(t)
=> 21

Exercise 2
Write a method called cumsum that takes an array of numbers and returns the cumulative sum; that is, a new array where the ith element is the sum of the first i+1 elements from the original array. For example:

>> t = [1, 2, 3]
=> [1, 2, 3]
>> cumsum(t)
[1, 3, 6]

Exercise 3
Write a method called middle that takes an array and returns a new array that contains all but the first and last elements. For example:

>> t = [1, 2, 3, 4]
=> [1, 2, 3, 4]
>> middle(t)
[2, 3]

Exercise 4
Write a method called chop! that takes an array, modifies it by removing the first and last elements, and returns nil. For example:

>> t = [1, 2, 3, 4]
=> [1, 2, 3, 4]
>> chop!(t)
=> nil
>> t
=> [2, 3]

Exercise 5
Write a method called sorted? that takes an array as a parameter and returns true if the array is sorted in ascending order and false otherwise. For example:

>> sorted?([1, 2, 2])
=> true
>> sorted?(['b', 'a'])
=> false

Exercise 6
Two words are anagrams if you can rearrange the letters from one to spell the other. Write a method called anagram? that takes two strings and returns true if they are anagrams.

Exercise 7
Write a method called has_duplicates? that takes an array and returns true if there is any element that appears more than once. It should not modify the original array.

Exercise 8
This exercise pertains to the so-called Birthday Paradox, which you can read about at https://en.wikipedia.org/wiki/Birthday_paradox.

If there are 23 students in your class, what are the chances that two of you have the same birthday? You can estimate this probability by generating random samples of 23 birthdays and checking for matches. Hint: you can generate random birthdays with the rand method.

Exercise 9
Write a method that reads the file words.txt and builds an array with one element per word. Write two versions of this method, one using the append method and the other using the idiom t = t + [x]. Which one takes longer to run? Why?

Exercise 10
To check whether a word is in the word array, you could use the include? method, but it would be slow because it searches through the words in order.

Because the words are in alphabetical order, we can speed things up with a bisection search (also known as binary search), which is similar to what you do when you look a word up in the dictionary. You start in the middle and check to see whether the word you are looking for comes before the word in the middle of the array. If so, you search the first half of the array the same way. Otherwise you search the second half.

Either way, you cut the remaining search space in half. If the word array has 113,809 words, it will take about 17 steps to find the word or conclude that it’s not there.

Write a method called in_bisect? that takes a sorted array and a target value and returns true if the word is in the array and false if it’s not.

Or you could read the documentation of the bsearch method and use that!

Exercise 11
Two words are a “reverse pair” if each is the reverse of the other. Write a program that finds all the reverse pairs in the word array.

Exercise 12
Two words “interlock” if taking alternating letters from each forms a new word. For example, “shoe” and “cold” interlock to form “schooled”. Credit: This exercise is inspired by an example at http://puzzlers.org.

  1. Write a program that finds all pairs of words that interlock. Hint: don’t enumerate all pairs!

  2. Can you find any words that are three-way interlocked; that is, every third letter forms a word, starting from the first, second or third?