# Range

Class

A `Range` represents an interval—a set of values with a beginning and an end. Ranges may be constructed using the s`..`e and s`...`e literals, or with `Range::new`. Ranges constructed using `..` run from the beginning to the end inclusively. Those created using `...` exclude the end value. When used as an iterator, ranges return each value in the sequence.

```(-1..-5).to_a      #=> []
(-5..-1).to_a      #=> [-5, -4, -3, -2, -1]
('a'..'e').to_a    #=> ["a", "b", "c", "d", "e"]
('a'...'e').to_a   #=> ["a", "b", "c", "d"]
```

## Beginless/Endless Ranges

A “beginless range” and “endless range” represents a semi-infinite range. Literal notation for a beginless range is:

```(..1)
# or
(...1)
```

Literal notation for an endless range is:

```(1..)
# or similarly
(1...)
```

Which is equivalent to

```(1..nil)  # or similarly (1...nil)
Range.new(1, nil) # or Range.new(1, nil, true)
```

Beginless/endless ranges are useful, for example, for idiomatic slicing of arrays:

```[1, 2, 3, 4, 5][...2]   # => [1, 2]
[1, 2, 3, 4, 5][2...]   # => [3, 4, 5]
```

Some implementation details:

• `begin` of beginless range and `end` of endless range are `nil`;

• `each` of beginless range raises an exception;

• `each` of endless range enumerates infinite sequence (may be useful in combination with `Enumerable#take_while` or similar methods);

• `(1..)` and `(1...)` are not equal, although technically representing the same sequence.

## Custom Objects in Ranges

Ranges can be constructed using any objects that can be compared using the `<=>` operator. Methods that treat the range as a sequence (`each` and methods inherited from `Enumerable`) expect the begin object to implement a `succ` method to return the next object in sequence. The `step` and `include?` methods require the begin object to implement `succ` or to be numeric.

In the `Xs` class below both `<=>` and `succ` are implemented so `Xs` can be used to construct ranges. Note that the `Comparable` module is included so the `==` method is defined in terms of `<=>`.

```class Xs                # represent a string of 'x's
include Comparable
attr :length
def initialize(n)
@length = n
end
def succ
Xs.new(@length + 1)
end
def <=>(other)
@length <=> other.length
end
def to_s
sprintf "%2d #{inspect}", @length
end
def inspect
'x' * @length
end
end
```

An example of using `Xs` to construct a range:

```r = Xs.new(3)..Xs.new(6)   #=> xxx..xxxxxx
r.to_a                     #=> [xxx, xxxx, xxxxx, xxxxxx]
r.member?(Xs.new(5))       #=> true
```
Class Methods

Deserializes `JSON` string by constructing new `Range` object with arguments `a` serialized by `to_json`.

Constructs a range using the given `begin` and `end`. If the `exclude_end` parameter is omitted or is `false`, the range will include the end object; otherwise, it will be excluded.

Instance Methods

Iterates over the range, passing each `n`th element to the block. If begin and end are numeric, `n` is added for each iteration. Otherwise `step` invokes succ to iterate through range elements.

If no block is given, an enumerator is returned instead. Especially, the enumerator is an `Enumerator::ArithmeticSequence` if begin and end of the range are numeric.

```range = Xs.new(1)..Xs.new(10)
range.step(2) {|x| puts x}
puts
range.step(3) {|x| puts x}
```

produces:

``` 1 x
3 xxx
5 xxxxx
7 xxxxxxx
9 xxxxxxxxx

1 x
4 xxxx
7 xxxxxxx
10 xxxxxxxxxx```

See `Range` for the definition of class Xs.

Returns `true` only if `obj` is a `Range`, has equivalent begin and end items (by comparing them with `==`), and has the same `exclude_end?` setting as the range.

```(0..2) == (0..2)            #=> true
(0..2) == Range.new(0,2)    #=> true
(0..2) == (0...2)           #=> false
```

Returns `true` if `obj` is between begin and end of range, `false` otherwise (same as `cover?`). Conveniently, `===` is the comparison operator used by `case` statements.

```case 79
when 1..50   then   puts "low"
when 51..75  then   puts "medium"
when 76..100 then   puts "high"
end
# Prints "high"

case "2.6.5"
when ..."2.4" then puts "EOL"
when "2.4"..."2.5" then puts "maintenance"
when "2.5"..."2.7" then puts "stable"
when "2.7".. then puts "upcoming"
end
# Prints "stable"
```

Returns a hash, that will be turned into a `JSON` object and represent this object.

Returns the object that defines the beginning of the range.

```(1..10).begin   #=> 1
```

By using binary search, finds a value in range which meets the given condition in O(log n) where n is the size of the range.

You can use this method in two use cases: a find-minimum mode and a find-any mode. In either case, the elements of the range must be monotone (or sorted) with respect to the block.

In find-minimum mode (this is a good choice for typical use case), the block must return true or false, and there must be a value x so that:

• the block returns false for any value which is less than x, and

• the block returns true for any value which is greater than or equal to x.

If x is within the range, this method returns the value x. Otherwise, it returns nil.

```ary = [0, 4, 7, 10, 12]
(0...ary.size).bsearch {|i| ary[i] >= 4 } #=> 1
(0...ary.size).bsearch {|i| ary[i] >= 6 } #=> 2
(0...ary.size).bsearch {|i| ary[i] >= 8 } #=> 3
(0...ary.size).bsearch {|i| ary[i] >= 100 } #=> nil

(0.0...Float::INFINITY).bsearch {|x| Math.log(x) >= 0 } #=> 1.0
```

In find-any mode (this behaves like libc’s bsearch(3)), the block must return a number, and there must be two values x and y (x <= y) so that:

• the block returns a positive number for v if v < x,

• the block returns zero for v if x <= v < y, and

• the block returns a negative number for v if y <= v.

This method returns any value which is within the intersection of the given range and x…y (if any). If there is no value that satisfies the condition, it returns nil.

```ary = [0, 100, 100, 100, 200]
(0..4).bsearch {|i| 100 - ary[i] } #=> 1, 2 or 3
(0..4).bsearch {|i| 300 - ary[i] } #=> nil
(0..4).bsearch {|i|  50 - ary[i] } #=> nil
```

You must not mix the two modes at a time; the block must always return either true/false, or always return a number. It is undefined which value is actually picked up at each iteration.

Identical to `Enumerable#count`, except it returns Infinity for endless ranges.

Returns `true` if `obj` is between the begin and end of the range.

This tests `begin <= obj <= end` when `exclude_end?` is `false` and `begin <= obj < end` when `exclude_end?` is `true`.

If called with a `Range` argument, returns `true` when the given range is covered by the receiver, by comparing the begin and end values. If the argument can be treated as a sequence, this method treats it that way. In the specific case of `(a..b).cover?(c...d)` with `a <= c && b < d`, the end of the sequence must be calculated, which may exhibit poor performance if `c` is non-numeric. Returns `false` if the begin value of the range is larger than the end value. Also returns `false` if one of the internal calls to `<=>` returns `nil` (indicating the objects are not comparable).

```("a".."z").cover?("c")  #=> true
("a".."z").cover?("5")  #=> false
("a".."z").cover?("cc") #=> true
("a".."z").cover?(1)    #=> false
(1..5).cover?(2..3)     #=> true
(1..5).cover?(0..6)     #=> false
(1..5).cover?(1...6)    #=> true
```

Iterates over the elements of range, passing each in turn to the block.

The `each` method can only be used if the begin object of the range supports the `succ` method. A `TypeError` is raised if the object does not have `succ` method defined (like `Float`).

If no block is given, an enumerator is returned instead.

```(10..15).each {|n| print n, ' ' }
# prints: 10 11 12 13 14 15

(2.5..5).each {|n| print n, ' ' }
# raises: TypeError: can't iterate from Float
```

Returns the object that defines the end of the range.

```(1..10).end    #=> 10
(1...10).end   #=> 10
```
An alias for to_a

Returns `true` only if `obj` is a `Range`, has equivalent begin and end items (by comparing them with `eql?`), and has the same `exclude_end?` setting as the range.

```(0..2).eql?(0..2)            #=> true
(0..2).eql?(Range.new(0,2))  #=> true
(0..2).eql?(0...2)           #=> false
```

Returns `true` if the range excludes its end value.

```(1..5).exclude_end?     #=> false
(1...5).exclude_end?    #=> true
```

Returns the first object in the range, or an array of the first `n` elements.

```(10..20).first     #=> 10
(10..20).first(3)  #=> [10, 11, 12]
```

Compute a hash-code for this range. Two ranges with equal begin and end points (using `eql?`), and the same `exclude_end?` value will generate the same hash-code.

See also `Object#hash`.

An alias for member?

Convert this range object to a printable form (using `inspect` to convert the begin and end objects).

Returns the last object in the range, or an array of the last `n` elements.

Note that with no arguments `last` will return the object that defines the end of the range even if `exclude_end?` is `true`.

```(10..20).last      #=> 20
(10...20).last     #=> 20
(10..20).last(3)   #=> [18, 19, 20]
(10...20).last(3)  #=> [17, 18, 19]
```

Returns the maximum value in the range, or an array of maximum values in the range if given an Integer argument.

For inclusive ranges with an end, the maximum value of the range is the same as the end of the range.

If an argument or block is given, or `self` is an exclusive, non-numeric range, calls `Enumerable#max` (via `super`) with the argument and/or block to get the maximum values, unless `self` is a beginless range, in which case it raises a `RangeError`.

If `self` is an exclusive, integer range (both start and end of the range are integers), and no arguments or block are provided, returns last value in the range (1 before the end). Otherwise, if `self` is an exclusive, numeric range, raises a `TypeError`.

Returns `nil` if the begin value of the range larger than the end value. Returns `nil` if the begin value of an exclusive range is equal to the end value. Raises a `RangeError` if called on an endless range.

Examples:

```(10..20).max                        #=> 20
(10..20).max(2)                     #=> [20, 19]
(10...20).max                       #=> 19
(10...20).max(2)                    #=> [19, 18]
(10...20).max{|x, y| -x <=> -y }    #=> 10
(10...20).max(2){|x, y| -x <=> -y } #=> [10, 11]
```

Returns `true` if `obj` is an element of the range, `false` otherwise.

```("a".."z").include?("g")   #=> true
("a".."z").include?("A")   #=> false
("a".."z").include?("cc")  #=> false
```

If you need to ensure `obj` is between `begin` and `end`, use `cover?`

```("a".."z").cover?("cc")  #=> true
```

If begin and end are numeric, `include?` behaves like `cover?`

```(1..3).include?(1.5) # => true
```

Returns the minimum value in the range. Returns `nil` if the begin value of the range is larger than the end value. Returns `nil` if the begin value of an exclusive range is equal to the end value.

Can be given an optional block to override the default comparison method `a <=> b`.

```(10..20).min    #=> 10
```

Returns a two element array which contains the minimum and the maximum value in the range.

Can be given an optional block to override the default comparison method `a <=> b`.

Returns the number of elements in the range. Both the begin and the end of the `Range` must be `Numeric`, otherwise nil is returned.

```(10..20).size    #=> 11
('a'..'z').size  #=> nil
(-Float::INFINITY..Float::INFINITY).size #=> Infinity
```

Iterates over the range, passing each `n`th element to the block. If begin and end are numeric, `n` is added for each iteration. Otherwise `step` invokes succ to iterate through range elements.

If no block is given, an enumerator is returned instead. Especially, the enumerator is an `Enumerator::ArithmeticSequence` if begin and end of the range are numeric.

```range = Xs.new(1)..Xs.new(10)
range.step(2) {|x| puts x}
puts
range.step(3) {|x| puts x}
```

produces:

``` 1 x
3 xxx
5 xxxxx
7 xxxxxxx
9 xxxxxxxxx

1 x
4 xxxx
7 xxxxxxx
10 xxxxxxxxxx```

See `Range` for the definition of class Xs.

Returns an array containing the items in the range.

```(1..7).to_a  #=> [1, 2, 3, 4, 5, 6, 7]
(1..).to_a   #=> RangeError: cannot convert endless range to an array
```

Stores class name (`Range`) with `JSON` array of arguments `a` which include `first` (integer), `last` (integer), and `exclude_end?` (boolean) as `JSON` string.

Convert this range object to a printable form (using `to_s` to convert the begin and end objects).