`protocol Sequence`

Inheritance | View Protocol Hierarchy → |
---|---|

Associated Types |
`Iterator : IteratorProtocol`
A type that provides the sequence's iteration interface and encapsulates its iteration state. `SubSequence`
A type that represents a subsequence of some of the sequence's elements. |

Import | `import Swift` |

### Instance Variables

A value less than or equal to the number of elements in the sequence, calculated nondestructively.

**Complexity:** O(1)

#### Declaration

`var underestimatedCount: Int { get }`

### Instance Methods

Returns a subsequence by skipping elements while `predicate`

returns
`true`

and returning the remaining elements.

** predicate:** A closure that takes an element of the
sequence as its argument and returns a Boolean value indicating
whether the element is a match.

**Complexity:** O(*n*), where *n* is the length of the collection.

#### Declaration

`func drop(while predicate: (Self.Iterator.Element) throws -> Bool) rethrows -> Self.SubSequence`

Returns a subsequence containing all but the given number of initial elements.

If the number of elements to drop exceeds the number of elements in the sequence, the result is an empty subsequence.

```
let numbers = [1, 2, 3, 4, 5]
print(numbers.dropFirst(2))
// Prints "[3, 4, 5]"
print(numbers.dropFirst(10))
// Prints "[]"
```

** n:** The number of elements to drop from the beginning of
the sequence.

`n`

must be greater than or equal to zero.
**Returns:**A subsequence starting after the specified number of elements.

**Complexity:** O(*n*), where *n* is the number of elements to drop from
the beginning of the sequence.

#### Declaration

`func dropFirst(_ n: Int) -> Self.SubSequence`

Returns a subsequence containing all but the specified number of final elements.

The sequence must be finite. If the number of elements to drop exceeds the number of elements in the sequence, the result is an empty subsequence.

```
let numbers = [1, 2, 3, 4, 5]
print(numbers.dropLast(2))
// Prints "[1, 2, 3]"
print(numbers.dropLast(10))
// Prints "[]"
```

** n:** The number of elements to drop off the end of the
sequence.

`n`

must be greater than or equal to zero.
**Returns:**A subsequence leaving off the specified number of elements.

**Complexity:** O(*n*), where *n* is the length of the sequence.

#### Declaration

`func dropLast(_ n: Int) -> Self.SubSequence`

Returns an array containing, in order, the elements of the sequence that satisfy the given predicate.

In this example, `filter`

is used to include only names shorter than
five characters.

```
let cast = ["Vivien", "Marlon", "Kim", "Karl"]
let shortNames = cast.filter { $0.characters.count < 5 }
print(shortNames)
// Prints "["Kim", "Karl"]"
```

** isIncluded:** A closure that takes an element of the
sequence as its argument and returns a Boolean value indicating
whether the element should be included in the returned array.

**Returns:**An array of the elements that

`includeElement`

allowed.#### Declaration

`func filter(_ isIncluded: (Self.Iterator.Element) throws -> Bool) rethrows -> [Self.Iterator.Element]`

Calls the given closure on each element in the sequence in the same order
as a `for`

-`in`

loop.

The two loops in the following example produce the same output:

```
let numberWords = ["one", "two", "three"]
for word in numberWords {
print(word)
}
// Prints "one"
// Prints "two"
// Prints "three"
numberWords.forEach { word in
print(word)
}
// Same as above
```

Using the `forEach`

method is distinct from a `for`

-`in`

loop in two
important ways:

- You cannot use a
`break`

or`continue`

statement to exit the current call of the`body`

closure or skip subsequent calls. - Using the
`return`

statement in the`body`

closure will exit only from the current call to`body`

, not from any outer scope, and won't skip subsequent calls.

** body:** A closure that takes an element of the sequence as a
parameter.

#### Declaration

`func forEach(_ body: (Self.Iterator.Element) throws -> Swift.Void) rethrows`

Returns an iterator over the elements of this sequence.

#### Declaration

`func makeIterator() -> Self.Iterator`

Returns an array containing the results of mapping the given closure over the sequence's elements.

In this example, `map`

is used first to convert the names in the array
to lowercase strings and then to count their characters.

```
let cast = ["Vivien", "Marlon", "Kim", "Karl"]
let lowercaseNames = cast.map { $0.lowercaseString }
// 'lowercaseNames' == ["vivien", "marlon", "kim", "karl"]
let letterCounts = cast.map { $0.characters.count }
// 'letterCounts' == [6, 6, 3, 4]
```

** transform:** A mapping closure.

`transform`

accepts an
element of this sequence as its parameter and returns a transformed
value of the same or of a different type.
**Returns:**An array containing the transformed elements of this sequence.

#### Declaration

`func map<T>(_ transform: (Self.Iterator.Element) throws -> T) rethrows -> [T]`

Returns a subsequence, up to the specified maximum length, containing the initial elements of the sequence.

If the maximum length exceeds the number of elements in the sequence, the result contains all the elements in the sequence.

```
let numbers = [1, 2, 3, 4, 5]
print(numbers.prefix(2))
// Prints "[1, 2]"
print(numbers.prefix(10))
// Prints "[1, 2, 3, 4, 5]"
```

** maxLength:** The maximum number of elements to return.

`maxLength`

must be greater than or equal to zero.
**Returns:**A subsequence starting at the beginning of this sequence with at most

`maxLength`

elements.#### Declaration

`func prefix(_ maxLength: Int) -> Self.SubSequence`

Returns a subsequence containing the initial, consecutive elements that satisfy the given predicate.

The following example uses the `prefix(while:)`

method to find the
positive numbers at the beginning of the `numbers`

array. Every element
of `numbers`

up to, but not including, the first negative value is
included in the result.

```
let numbers = [3, 7, 4, -2, 9, -6, 10, 1]
let positivePrefix = numbers.prefix(while: { $0 > 0 })
// positivePrefix == [3, 7, 4]
```

If `predicate`

matches every element in the sequence, the resulting
sequence contains every element of the sequence.

** predicate:** A closure that takes an element of the sequence as
its argument and returns a Boolean value indicating whether the
element should be included in the result.

**Returns:**A subsequence of the initial, consecutive elements that satisfy

`predicate`

.**Complexity:** O(*n*), where *n* is the length of the collection.

#### Declaration

`func prefix(while predicate: (Self.Iterator.Element) throws -> Bool) rethrows -> Self.SubSequence`

Returns the longest possible subsequences of the sequence, in order, that don't contain elements satisfying the given predicate.

The resulting array consists of at most `maxSplits + 1`

subsequences.
Elements that are used to split the sequence are not returned as part of
any subsequence.

The following examples show the effects of the `maxSplits`

and
`omittingEmptySubsequences`

parameters when splitting a string using a
closure that matches spaces. The first use of `split`

returns each word
that was originally separated by one or more spaces.

```
let line = "BLANCHE: I don't want realism. I want magic!"
print(line.characters.split(whereSeparator: { $0 == " " })
.map(String.init))
// Prints "["BLANCHE:", "I", "don\'t", "want", "realism.", "I", "want", "magic!"]"
```

The second example passes `1`

for the `maxSplits`

parameter, so the
original string is split just once, into two new strings.

```
print(
line.characters.split(maxSplits: 1, whereSeparator: { $0 == " " })
.map(String.init))
// Prints "["BLANCHE:", " I don\'t want realism. I want magic!"]"
```

The final example passes `false`

for the `omittingEmptySubsequences`

parameter, so the returned array contains empty strings where spaces
were repeated.

```
print(
line.characters.split(
omittingEmptySubsequences: false,
whereSeparator: { $0 == " " })
).map(String.init))
// Prints "["BLANCHE:", "", "", "I", "don\'t", "want", "realism.", "I", "want", "magic!"]"
```

**Parameters:**
**maxSplits:** The maximum number of times to split the sequence, or one
less than the number of subsequences to return. If `maxSplits + 1`

subsequences are returned, the last one is a suffix of the original
sequence containing the remaining elements. `maxSplits`

must be
greater than or equal to zero. The default value is `Int.max`

.
**omittingEmptySubsequences:** If `false`

, an empty subsequence is
returned in the result for each pair of consecutive elements
satisfying the `isSeparator`

predicate and for each element at the
start or end of the sequence satisfying the `isSeparator`

predicate.
If `true`

, only nonempty subsequences are returned. The default
value is `true`

.
**isSeparator:** A closure that returns `true`

if its argument should be
used to split the sequence; otherwise, `false`

.
**Returns:** An array of subsequences, split from this sequence's elements.

#### Declaration

`func split(maxSplits: Int, omittingEmptySubsequences: Bool, whereSeparator isSeparator: (Self.Iterator.Element) throws -> Bool) rethrows -> [Self.SubSequence]`

Returns a subsequence, up to the given maximum length, containing the final elements of the sequence.

The sequence must be finite. If the maximum length exceeds the number of elements in the sequence, the result contains all the elements in the sequence.

```
let numbers = [1, 2, 3, 4, 5]
print(numbers.suffix(2))
// Prints "[4, 5]"
print(numbers.suffix(10))
// Prints "[1, 2, 3, 4, 5]"
```

** maxLength:** The maximum number of elements to return. The
value of

`maxLength`

must be greater than or equal to zero.
**Returns:**A subsequence terminating at the end of this sequence with at most

`maxLength`

elements.**Complexity:** O(*n*), where *n* is the length of the sequence.

#### Declaration

`func suffix(_ maxLength: Int) -> Self.SubSequence`

### Default Implementations

A sequence containing the same elements as this sequence,
but on which some operations, such as `map`

and `filter`

, are
implemented lazily.

**See Also:** `LazySequenceProtocol`

, `LazySequence`

#### Declaration

`var lazy: LazySequence<Self> { get }`

Returns a value less than or equal to the number of elements in the sequence, nondestructively.

**Complexity:** O(*n*)

#### Declaration

`var underestimatedCount: Int { get }`

Returns a Boolean value indicating whether the sequence contains an element that satisfies the given predicate.

You can use the predicate to check for an element of a type that
doesn't conform to the `Equatable`

protocol, such as the
`HTTPResponse`

enumeration in this example.

```
enum HTTPResponse {
case ok
case error(Int)
}
let lastThreeResponses: [HTTPResponse] = [.ok, .ok, .error(404)]
let hadError = lastThreeResponses.contains { element in
if case .error = element {
return true
} else {
return false
}
}
// 'hadError' == true
```

Alternatively, a predicate can be satisfied by a range of `Equatable`

elements or a general condition. This example shows how you can check an
array for an expense greater than $100.

```
let expenses = [21.37, 55.21, 9.32, 10.18, 388.77, 11.41]
let hasBigPurchase = expenses.contains { $0 > 100 }
// 'hasBigPurchase' == true
```

** predicate:** A closure that takes an element of the sequence
as its argument and returns a Boolean value that indicates whether
the passed element represents a match.

**Returns:**

`true`

if the sequence contains an element that satisfies
`predicate`

; otherwise, `false`

.#### Declaration

`func contains(where predicate: (Self.Iterator.Element) throws -> Bool) rethrows -> Bool`

Returns a subsequence containing all but the first element of the sequence.

The following example drops the first element from an array of integers.

```
let numbers = [1, 2, 3, 4, 5]
print(numbers.dropFirst())
// Prints "[2, 3, 4, 5]"
```

If the sequence has no elements, the result is an empty subsequence.

```
let empty: [Int] = []
print(empty.dropFirst())
// Prints "[]"
```

**Returns:** A subsequence starting after the first element of the
sequence.

**Complexity:** O(1)

#### Declaration

`func dropFirst() -> Self.SubSequence`

Returns a subsequence containing all but the last element of the sequence.

The sequence must be finite.

```
let numbers = [1, 2, 3, 4, 5]
print(numbers.dropLast())
// Prints "[1, 2, 3, 4]"
```

If the sequence has no elements, the result is an empty subsequence.

```
let empty: [Int] = []
print(empty.dropLast())
// Prints "[]"
```

**Returns:** A subsequence leaving off the last element of the sequence.

**Complexity:** O(*n*), where *n* is the length of the sequence.

#### Declaration

`func dropLast() -> Self.SubSequence`

Returns a Boolean value indicating whether this sequence and another sequence contain equivalent elements, using the given predicate as the equivalence test.

At least one of the sequences must be finite.

The predicate must be a *equivalence relation* over the elements. That
is, for any elements `a`

, `b`

, and `c`

, the following conditions must
hold:

`areEquivalent(a, a)`

is always`true`

. (Reflexivity)`areEquivalent(a, b)`

implies`areEquivalent(b, a)`

. (Symmetry)- If
`areEquivalent(a, b)`

and`areEquivalent(b, c)`

are both`true`

, then`areEquivalent(a, c)`

is also`true`

. (Transitivity)

**Parameters:**
**other:** A sequence to compare to this sequence.
**areEquivalent:** A predicate that returns `true`

if its two arguments
are equivalent; otherwise, `false`

.
**Returns:** `true`

if this sequence and `other`

contain equivalent items,
using `areEquivalent`

as the equivalence test; otherwise, `false.`

**See Also:** `elementsEqual(_:)`

#### Declaration

`func elementsEqual<OtherSequence where OtherSequence : Sequence, OtherSequence.Iterator.Element == Self.Iterator.Element>(_ other: OtherSequence, by areEquivalent: (Self.Iterator.Element, Self.Iterator.Element) throws -> Bool) rethrows -> Bool`

Returns a sequence of pairs (*n*, *x*), where *n* represents a
consecutive integer starting at zero, and *x* represents an element of
the sequence.

This example enumerates the characters of the string "Swift" and prints each character along with its place in the string.

```
for (n, c) in "Swift".characters.enumerated() {
print("\(n): '\(c)'")
}
// Prints "0: 'S'"
// Prints "1: 'w'"
// Prints "2: 'i'"
// Prints "3: 'f'"
// Prints "4: 't'"
```

When enumerating a collection, the integer part of each pair is a counter
for the enumeration, not necessarily the index of the paired value.
These counters can only be used as indices in instances of zero-based,
integer-indexed collections, such as `Array`

and `ContiguousArray`

. For
other collections the counters may be out of range or of the wrong type
to use as an index. To iterate over the elements of a collection with its
indices, use the `zip(_:_:)`

function.

This example iterates over the indices and elements of a set, building a list of indices of names with five or fewer letters.

```
let names: Set = ["Sofia", "Camilla", "Martina", "Mateo", "Nicolás"]
var shorterIndices: [SetIndex<String>] = []
for (i, name) in zip(names.indices, names) {
if name.characters.count <= 5 {
shorterIndices.append(i)
}
}
```

Now that the `shorterIndices`

array holds the indices of the shorter
names in the `names`

set, you can use those indices to access elements in
the set.

```
for i in shorterIndices {
print(names[i])
}
// Prints "Sofia"
// Prints "Mateo"
```

**Returns:** A sequence of pairs enumerating the sequence.

#### Declaration

`func enumerated() -> EnumeratedSequence<Self>`

Returns an array containing, in order, the elements of the sequence that satisfy the given predicate.

In this example, `filter`

is used to include only names shorter than
five characters.

```
let cast = ["Vivien", "Marlon", "Kim", "Karl"]
let shortNames = cast.filter { $0.characters.count < 5 }
print(shortNames)
// Prints "["Kim", "Karl"]"
```

** isIncluded:** A closure that takes an element of the
sequence as its argument and returns a Boolean value indicating
whether the element should be included in the returned array.

**Returns:**An array of the elements that

`includeElement`

allowed.#### Declaration

`func filter(_ isIncluded: (Self.Iterator.Element) throws -> Bool) rethrows -> [Self.Iterator.Element]`

Returns the first element of the sequence that satisfies the given predicate.

The following example uses the `first(where:)`

method to find the first
negative number in an array of integers:

```
let numbers = [3, 7, 4, -2, 9, -6, 10, 1]
if let firstNegative = numbers.first(where: { $0 < 0 }) {
print("The first negative number is \(firstNegative).")
}
// Prints "The first negative number is -2."
```

** predicate:** A closure that takes an element of the sequence as
its argument and returns a Boolean value indicating whether the
element is a match.

**Returns:**The first element of the sequence that satisfies

`predicate`

,
or `nil`

if there is no element that satisfies `predicate`

.#### Declaration

`func first(where predicate: (Self.Iterator.Element) throws -> Bool) rethrows -> Self.Iterator.Element?`

Returns an array containing the non-`nil`

results of calling the given
transformation with each element of this sequence.

Use this method to receive an array of nonoptional values when your transformation produces an optional value.

In this example, note the difference in the result of using `map`

and
`flatMap`

with a transformation that returns an optional `Int`

value.

```
let possibleNumbers = ["1", "2", "three", "///4///", "5"]
let mapped: [Int?] = possibleNumbers.map { str in Int(str) }
// [1, 2, nil, nil, 5]
let flatMapped: [Int] = possibleNumbers.flatMap { str in Int(str) }
// [1, 2, 5]
```

** transform:** A closure that accepts an element of this
sequence as its argument and returns an optional value.

**Returns:**An array of the non-

`nil`

results of calling `transform`

with each element of the sequence.**Complexity:** O(*m* + *n*), where *m* is the length of this sequence
and *n* is the length of the result.

#### Declaration

`func flatMap<ElementOfResult>(_ transform: (Self.Iterator.Element) throws -> ElementOfResult?) rethrows -> [ElementOfResult]`

Returns an array containing the concatenated results of calling the given transformation with each element of this sequence.

Use this method to receive a single-level collection when your transformation produces a sequence or collection for each element.

In this example, note the difference in the result of using `map`

and
`flatMap`

with a transformation that returns an array.

```
let numbers = [1, 2, 3, 4]
let mapped = numbers.map { Array(count: $0, repeatedValue: $0) }
// [[1], [2, 2], [3, 3, 3], [4, 4, 4, 4]]
let flatMapped = numbers.flatMap { Array(count: $0, repeatedValue: $0) }
// [1, 2, 2, 3, 3, 3, 4, 4, 4, 4]
```

In fact, `s.flatMap(transform)`

is equivalent to
`Array(s.map(transform).joined())`

.

** transform:** A closure that accepts an element of this
sequence as its argument and returns a sequence or collection.

**Returns:**The resulting flattened array.

**Complexity:** O(*m* + *n*), where *m* is the length of this sequence
and *n* is the length of the result.
**See Also:** `joined()`

, `map(_:)`

#### Declaration

`func flatMap<SegmentOfResult where SegmentOfResult : Sequence>(_ transform: (Self.Iterator.Element) throws -> SegmentOfResult) rethrows -> [SegmentOfResult.Iterator.Element]`

Calls the given closure on each element in the sequence in the same order
as a `for`

-`in`

loop.

The two loops in the following example produce the same output:

```
let numberWords = ["one", "two", "three"]
for word in numberWords {
print(word)
}
// Prints "one"
// Prints "two"
// Prints "three"
numberWords.forEach { word in
print(word)
}
// Same as above
```

Using the `forEach`

method is distinct from a `for`

-`in`

loop in two
important ways:

- You cannot use a
`break`

or`continue`

statement to exit the current call of the`body`

closure or skip subsequent calls. - Using the
`return`

statement in the`body`

closure will exit only from the current call to`body`

, not from any outer scope, and won't skip subsequent calls.

** body:** A closure that takes an element of the sequence as a
parameter.

#### Declaration

`func forEach(_ body: (Self.Iterator.Element) throws -> Swift.Void) rethrows`

Returns a Boolean value indicating whether the sequence precedes another sequence in a lexicographical (dictionary) ordering, using the given predicate to compare elements.

The predicate must be a *strict weak ordering* over the elements. That
is, for any elements `a`

, `b`

, and `c`

, the following conditions must
hold:

`areInIncreasingOrder(a, a)`

is always`false`

. (Irreflexivity)- If
`areInIncreasingOrder(a, b)`

and`areInIncreasingOrder(b, c)`

are both`true`

, then`areInIncreasingOrder(a, c)`

is also`true`

. (Transitive comparability) - Two elements are
*incomparable*if neither is ordered before the other according to the predicate. If`a`

and`b`

are incomparable, and`b`

and`c`

are incomparable, then`a`

and`c`

are also incomparable. (Transitive incomparability)

**Parameters:**
**other:** A sequence to compare to this sequence.
**areInIncreasingOrder:** A predicate that returns `true`

if its first
argument should be ordered before its second argument; otherwise,
`false`

.
**Returns:** `true`

if this sequence precedes `other`

in a dictionary
ordering as ordered by `areInIncreasingOrder`

; otherwise, `false`

.

**Note:** This method implements the mathematical notion of lexicographical
ordering, which has no connection to Unicode. If you are sorting
strings to present to the end user, use `String`

APIs that perform
localized comparison instead.
**See Also:** `lexicographicallyPrecedes(_:)`

#### Declaration

`func lexicographicallyPrecedes<OtherSequence where OtherSequence : Sequence, OtherSequence.Iterator.Element == Self.Iterator.Element>(_ other: OtherSequence, by areInIncreasingOrder: (Self.Iterator.Element, Self.Iterator.Element) throws -> Bool) rethrows -> Bool`

Returns an array containing the results of mapping the given closure over the sequence's elements.

In this example, `map`

is used first to convert the names in the array
to lowercase strings and then to count their characters.

```
let cast = ["Vivien", "Marlon", "Kim", "Karl"]
let lowercaseNames = cast.map { $0.lowercaseString }
// 'lowercaseNames' == ["vivien", "marlon", "kim", "karl"]
let letterCounts = cast.map { $0.characters.count }
// 'letterCounts' == [6, 6, 3, 4]
```

** transform:** A mapping closure.

`transform`

accepts an
element of this sequence as its parameter and returns a transformed
value of the same or of a different type.
**Returns:**An array containing the transformed elements of this sequence.

#### Declaration

`func map<T>(_ transform: (Self.Iterator.Element) throws -> T) rethrows -> [T]`

Returns the maximum element in the sequence, using the given predicate as the comparison between elements.

The predicate must be a *strict weak ordering* over the elements. That
is, for any elements `a`

, `b`

, and `c`

, the following conditions must
hold:

`areInIncreasingOrder(a, a)`

is always`false`

. (Irreflexivity)- If
`areInIncreasingOrder(a, b)`

and`areInIncreasingOrder(b, c)`

are both`true`

, then`areInIncreasingOrder(a, c)`

is also`true`

. (Transitive comparability) - Two elements are
*incomparable*if neither is ordered before the other according to the predicate. If`a`

and`b`

are incomparable, and`b`

and`c`

are incomparable, then`a`

and`c`

are also incomparable. (Transitive incomparability)

This example shows how to use the `max(by:)`

method on a
dictionary to find the key-value pair with the highest value.

```
let hues = ["Heliotrope": 296, "Coral": 16, "Aquamarine": 156]
let greatestHue = hues.max { a, b in a.value < b.value }
print(greatestHue)
// Prints "Optional(("Heliotrope", 296))"
```

** areInIncreasingOrder:** A predicate that returns

`true`

if its
first argument should be ordered before its second argument;
otherwise, `false`

.
**Returns:**The sequence's maximum element if the sequence is not empty; otherwise,

`nil`

.**See Also:** `max()`

#### Declaration

```
@warn_unqualified_access
func max(by areInIncreasingOrder: (Self.Iterator.Element, Self.Iterator.Element) throws -> Bool) rethrows -> Self.Iterator.Element?
```

Returns the minimum element in the sequence, using the given predicate as the comparison between elements.

The predicate must be a *strict weak ordering* over the elements. That
is, for any elements `a`

, `b`

, and `c`

, the following conditions must
hold:

`areInIncreasingOrder(a, a)`

is always`false`

. (Irreflexivity)- If
`areInIncreasingOrder(a, b)`

and`areInIncreasingOrder(b, c)`

are both`true`

, then`areInIncreasingOrder(a, c)`

is also`true`

. (Transitive comparability) - Two elements are
*incomparable*if neither is ordered before the other according to the predicate. If`a`

and`b`

are incomparable, and`b`

and`c`

are incomparable, then`a`

and`c`

are also incomparable. (Transitive incomparability)

This example shows how to use the `min(by:)`

method on a
dictionary to find the key-value pair with the lowest value.

```
let hues = ["Heliotrope": 296, "Coral": 16, "Aquamarine": 156]
let leastHue = hues.min { a, b in a.value < b.value }
print(leastHue)
// Prints "Optional(("Coral", 16))"
```

** areInIncreasingOrder:** A predicate that returns

`true`

if its first argument should be ordered before its second
argument; otherwise, `false`

.
**Returns:**The sequence's minimum element, according to

`areInIncreasingOrder`

. If the sequence has no elements, returns
`nil`

.**See Also:** `min()`

#### Declaration

`func min(by areInIncreasingOrder: (Self.Iterator.Element, Self.Iterator.Element) throws -> Bool) rethrows -> Self.Iterator.Element?`

Returns the result of combining the elements of the sequence using the given closure.

Use the `reduce(_:_:)`

method to produce a single value from the elements
of an entire sequence. For example, you can use this method on an array
of numbers to find their sum or product.

The `nextPartialResult`

closure is called sequentially with an
accumulating value initialized to `initialResult`

and each element of
the sequence. This example shows how to find the sum of an array of
numbers.

```
let numbers = [1, 2, 3, 4]
let numberSum = numbers.reduce(0, { x, y in
x + y
})
// numberSum == 10
```

When `numbers.reduce(_:_:)`

is called, the following steps occur:

- The
`nextPartialResult`

closure is called with`initialResult`

---`0`

in this case---and the first element of`numbers`

, returning the sum:`1`

. - The closure is called again repeatedly with the previous call's return value and each element of the sequence.
- When the sequence is exhausted, the last value returned from the closure is returned to the caller.

If the sequence has no elements, `nextPartialResult`

is never executed
and `initialResult`

is the result of the call to `reduce(_:_:)`

.

**Parameters:**
**initialResult:** The value to use as the initial accumulating value.
`initialResult`

is passed to `nextPartialResult`

the first time the
closure is executed.
**nextPartialResult:** A closure that combines an accumulating value and
an element of the sequence into a new accumulating value, to be used
in the next call of the `nextPartialResult`

closure or returned to
the caller.
**Returns:** The final accumulated value. If the sequence has no elements,
the result is `initialResult`

.

#### Declaration

`func reduce<Result>(_ initialResult: Result, _ nextPartialResult: (Result, Self.Iterator.Element) throws -> Result) rethrows -> Result`

Returns an array containing the elements of this sequence in reverse order.

The sequence must be finite.

**Complexity:** O(*n*), where *n* is the length of the sequence.

**Returns:** An array containing the elements of this sequence in
reverse order.

#### Declaration

`func reversed() -> [Self.Iterator.Element]`

Returns the elements of the sequence, sorted using the given predicate as the comparison between elements.

When you want to sort a sequence of elements that don't conform to
the `Comparable`

protocol, pass a predicate to this method that returns
`true`

when the first element passed should be ordered before the
second. The elements of the resulting array are ordered according to the
given predicate.

*strict weak ordering* over the elements. That
is, for any elements `a`

, `b`

, and `c`

, the following conditions must
hold:

`areInIncreasingOrder(a, a)`

is always`false`

. (Irreflexivity)- If
`areInIncreasingOrder(a, b)`

and`areInIncreasingOrder(b, c)`

are both`true`

, then`areInIncreasingOrder(a, c)`

is also`true`

. (Transitive comparability) - Two elements are
*incomparable*if neither is ordered before the other according to the predicate. If`a`

and`b`

are incomparable, and`b`

and`c`

are incomparable, then`a`

and`c`

are also incomparable. (Transitive incomparability)

The sorting algorithm is not stable. A nonstable sort may change the
relative order of elements for which `areInIncreasingOrder`

does not
establish an order.

In the following example, the predicate provides an ordering for an array
of a custom `HTTPResponse`

type. The predicate orders errors before
successes and sorts the error responses by their error code.

```
enum HTTPResponse {
case ok
case error(Int)
}
let responses: [HTTPResponse] = [.error(500), .ok, .ok, .error(404), .error(403)]
let sortedResponses = responses.sorted {
switch ($0, $1) {
// Order errors by code
case let (.error(aCode), .error(bCode)):
return aCode < bCode
// All successes are equivalent, so none is before any other
case (.ok, .ok): return false
// Order errors before successes
case (.error, .ok): return true
case (.ok, .error): return false
}
}
print(sortedResponses)
// Prints "[.error(403), .error(404), .error(500), .ok, .ok]"
```

You also use this method to sort elements that conform to the
`Comparable`

protocol in descending order. To sort your sequence
in descending order, pass the greater-than operator (`>`

) as the
`areInIncreasingOrder`

parameter.

```
let students: Set = ["Kofi", "Abena", "Peter", "Kweku", "Akosua"]
let descendingStudents = students.sorted(by: >)
print(descendingStudents)
// Prints "["Peter", "Kweku", "Kofi", "Akosua", "Abena"]"
```

Calling the related `sorted()`

method is equivalent to calling this
method and passing the less-than operator (`<`

) as the predicate.

```
print(students.sorted())
// Prints "["Abena", "Akosua", "Kofi", "Kweku", "Peter"]"
print(students.sorted(by: <))
// Prints "["Abena", "Akosua", "Kofi", "Kweku", "Peter"]"
```

** areInIncreasingOrder:** A predicate that returns

`true`

if its first
argument should be ordered before its second argument; otherwise,
`false`

.
**Returns:**A sorted array of the sequence's elements.

**See Also:** `sorted()`

#### Declaration

`func sorted(by areInIncreasingOrder: (Self.Iterator.Element, Self.Iterator.Element) -> Bool) -> [Self.Iterator.Element]`

Returns the longest possible subsequences of the sequence, in order, that don't contain elements satisfying the given predicate. Elements that are used to split the sequence are not returned as part of any subsequence.

The following examples show the effects of the `maxSplits`

and
`omittingEmptySubsequences`

parameters when splitting a string using a
closure that matches spaces. The first use of `split`

returns each word
that was originally separated by one or more spaces.

```
let line = "BLANCHE: I don't want realism. I want magic!"
print(line.characters.split(whereSeparator: { $0 == " " })
.map(String.init))
// Prints "["BLANCHE:", "I", "don\'t", "want", "realism.", "I", "want", "magic!"]"
```

The second example passes `1`

for the `maxSplits`

parameter, so the
original string is split just once, into two new strings.

```
print(
line.characters.split(maxSplits: 1, whereSeparator: { $0 == " " })
.map(String.init))
// Prints "["BLANCHE:", " I don\'t want realism. I want magic!"]"
```

The final example passes `true`

for the `allowEmptySlices`

parameter, so
the returned array contains empty strings where spaces were repeated.

```
print(
line.characters.split(
omittingEmptySubsequences: false,
whereSeparator: { $0 == " " }
).map(String.init))
// Prints "["BLANCHE:", "", "", "I", "don\'t", "want", "realism.", "I", "want", "magic!"]"
```

**Parameters:**
**maxSplits:** The maximum number of times to split the sequence, or one
less than the number of subsequences to return. If `maxSplits + 1`

subsequences are returned, the last one is a suffix of the original
sequence containing the remaining elements. `maxSplits`

must be
greater than or equal to zero. The default value is `Int.max`

.
**omittingEmptySubsequences:** If `false`

, an empty subsequence is
returned in the result for each pair of consecutive elements
satisfying the `isSeparator`

predicate and for each element at the
start or end of the sequence satisfying the `isSeparator`

predicate.
If `true`

, only nonempty subsequences are returned. The default
value is `true`

.
**isSeparator:** A closure that returns `true`

if its argument should be
used to split the sequence; otherwise, `false`

.
**Returns:** An array of subsequences, split from this sequence's elements.

#### Declaration

`func split(maxSplits: Int = default, omittingEmptySubsequences: Bool = default, whereSeparator isSeparator: (Self.Iterator.Element) throws -> Bool) rethrows -> [AnySequence<Self.Iterator.Element>]`

Returns a Boolean value indicating whether the initial elements of the sequence are equivalent to the elements in another sequence, using the given predicate as the equivalence test.

The predicate must be a *equivalence relation* over the elements. That
is, for any elements `a`

, `b`

, and `c`

, the following conditions must
hold:

`areEquivalent(a, a)`

is always`true`

. (Reflexivity)`areEquivalent(a, b)`

implies`areEquivalent(b, a)`

. (Symmetry)- If
`areEquivalent(a, b)`

and`areEquivalent(b, c)`

are both`true`

, then`areEquivalent(a, c)`

is also`true`

. (Transitivity)

**Parameters:**
**possiblePrefix:** A sequence to compare to this sequence.
**areEquivalent:** A predicate that returns `true`

if its two arguments
are equivalent; otherwise, `false`

.
**Returns:** `true`

if the initial elements of the sequence are equivalent
to the elements of `possiblePrefix`

; otherwise, `false`

. If
`possiblePrefix`

has no elements, the return value is `true`

.

**See Also:** `starts(with:)`

#### Declaration

`func starts<PossiblePrefix where PossiblePrefix : Sequence, PossiblePrefix.Iterator.Element == Self.Iterator.Element>(with possiblePrefix: PossiblePrefix, by areEquivalent: (Self.Iterator.Element, Self.Iterator.Element) throws -> Bool) rethrows -> Bool`

Returns a subsequence, up to the given maximum length, containing the final elements of the sequence.

The sequence must be finite. If the maximum length exceeds the number of elements in the sequence, the result contains all the elements in the sequence.

```
let numbers = [1, 2, 3, 4, 5]
print(numbers.suffix(2))
// Prints "[4, 5]"
print(numbers.suffix(10))
// Prints "[1, 2, 3, 4, 5]"
```

** maxLength:** The maximum number of elements to return. The
value of

`maxLength`

must be greater than or equal to zero.
**Complexity:**O(

*n*), where

*n*is the length of the sequence.

#### Declaration

`func suffix(_ maxLength: Int) -> AnySequence<Self.Iterator.Element>`

#### Where Base.Iterator == Iterator

Returns an array containing, in order, the elements of the sequence that satisfy the given predicate.

In this example, `filter`

is used to include only names shorter than five
characters.

```
let cast = ["Vivien", "Marlon", "Kim", "Karl"]
let shortNames = cast.filter { $0.characters.count < 5 }
print(shortNames)
// Prints "["Kim", "Karl"]"
```

** includeElement:** A closure that takes an element of the
sequence as its argument and returns a Boolean value indicating
whether the element should be included in the returned array.

**Returns:**An array of the elements that

`includeElement`

allowed.#### Declaration

`func filter(_ isIncluded: (Self.Base.Iterator.Element) throws -> Bool) rethrows -> [Self.Base.Iterator.Element]`

Returns an iterator over the elements of this sequence.

#### Declaration

`func makeIterator() -> Self.Base.Iterator`

Returns an array containing the results of mapping the given closure over the sequence's elements.

In this example, `map`

is used first to convert the names in the array to
lowercase strings and then to count their characters.

```
let cast = ["Vivien", "Marlon", "Kim", "Karl"]
let lowercaseNames = cast.map { $0.lowercaseString }
// 'lowercaseNames' == ["vivien", "marlon", "kim", "karl"]
let letterCounts = cast.map { $0.characters.count }
// 'letterCounts' == [6, 6, 3, 4]
```

** transform:** A mapping closure.

`transform`

accepts an
element of this sequence as its parameter and returns a transformed
value of the same or of a different type.
**Returns:**An array containing the transformed elements of this sequence.

#### Declaration

`func map<T>(_ transform: (Self.Base.Iterator.Element) throws -> T) rethrows -> [T]`

#### Where Iterator == Self

Returns an iterator over the elements of this sequence.

#### Declaration

`func makeIterator() -> Self`

#### Where Iterator.Element : Comparable

Returns a Boolean value indicating whether the sequence precedes another
sequence in a lexicographical (dictionary) ordering, using the
less-than operator (`<`

) to compare elements.

This example uses the `lexicographicallyPrecedes`

method to test which
array of integers comes first in a lexicographical ordering.

```
let a = [1, 2, 2, 2]
let b = [1, 2, 3, 4]
print(a.lexicographicallyPrecedes(b))
// Prints "true"
print(b.lexicographicallyPrecedes(b))
// Prints "false"
```

** other:** A sequence to compare to this sequence.

**Returns:**

`true`

if this sequence precedes `other`

in a dictionary
ordering; otherwise, `false`

.**Note:** This method implements the mathematical notion of lexicographical
ordering, which has no connection to Unicode. If you are sorting
strings to present to the end user, use `String`

APIs that
perform localized comparison.
**See Also:** `lexicographicallyPrecedes(_:by:)`

#### Declaration

`func lexicographicallyPrecedes<OtherSequence where OtherSequence : Sequence, OtherSequence.Iterator.Element == Self.Iterator.Element>(_ other: OtherSequence) -> Bool`

Returns the maximum element in the sequence.

This example finds the smallest value in an array of height measurements.

```
let heights = [67.5, 65.7, 64.3, 61.1, 58.5, 60.3, 64.9]
let greatestHeight = heights.max()
print(greatestHeight)
// Prints "Optional(67.5)"
```

**Returns:** The sequence's maximum element. If the sequence has no
elements, returns `nil`

.

**See Also:** `max(by:)`

#### Declaration

```
@warn_unqualified_access
func max() -> Self.Iterator.Element?
```

Returns the minimum element in the sequence.

This example finds the smallest value in an array of height measurements.

```
let heights = [67.5, 65.7, 64.3, 61.1, 58.5, 60.3, 64.9]
let lowestHeight = heights.min()
print(lowestHeight)
// Prints "Optional(58.5)"
```

**Returns:** The sequence's minimum element. If the sequence has no
elements, returns `nil`

.

**See Also:** `min(by:)`

#### Declaration

```
@warn_unqualified_access
func min() -> Self.Iterator.Element?
```

Returns the elements of the sequence, sorted.

You can sort any sequence of elements that conform to the
`Comparable`

protocol by calling this method. Elements are sorted in
ascending order.

The sorting algorithm is not stable. A nonstable sort may change the relative order of elements that compare equal.

Here's an example of sorting a list of students' names. Strings in Swift
conform to the `Comparable`

protocol, so the names are sorted in
ascending order according to the less-than operator (`<`

).

```
let students: Set = ["Kofi", "Abena", "Peter", "Kweku", "Akosua"]
let sortedStudents = students.sorted()
print(sortedStudents)
// Prints "["Abena", "Akosua", "Kofi", "Kweku", "Peter"]"
```

To sort the elements of your sequence in descending order, pass the
greater-than operator (`>`

) to the `sorted(by:)`

method.

```
let descendingStudents = students.sorted(by: >)
print(descendingStudents)
// Prints "["Peter", "Kweku", "Kofi", "Akosua", "Abena"]"
```

**Returns:** A sorted array of the sequence's elements.

**See Also:** `sorted(by:)`

#### Declaration

`func sorted() -> [Self.Iterator.Element]`

#### Where Iterator.Element : Equatable

Returns a Boolean value indicating whether the sequence contains the given element.

This example checks to see whether a favorite actor is in an array storing a movie's cast.

```
let cast = ["Vivien", "Marlon", "Kim", "Karl"]
print(cast.contains("Marlon"))
// Prints "true"
print(cast.contains("James"))
// Prints "false"
```

** element:** The element to find in the sequence.

**Returns:**

`true`

if the element was found in the sequence; otherwise,
`false`

.#### Declaration

`func contains(_ element: Self.Iterator.Element) -> Bool`

Returns a Boolean value indicating whether this sequence and another sequence contain the same elements in the same order.

At least one of the sequences must be finite.

This example tests whether one countable range shares the same elements as another countable range and an array.

```
let a = 1...3
let b = 1...10
print(a.elementsEqual(b))
// Prints "false"
print(a.elementsEqual([1, 2, 3]))
// Prints "true"
```

** other:** A sequence to compare to this sequence.

**Returns:**

`true`

if this sequence and `other`

contain the same elements
in the same order.**See Also:** `elementsEqual(_:by:)`

#### Declaration

`func elementsEqual<OtherSequence where OtherSequence : Sequence, OtherSequence.Iterator.Element == Self.Iterator.Element>(_ other: OtherSequence) -> Bool`

Returns the longest possible subsequences of the sequence, in order, around elements equal to the given element.

The resulting array consists of at most `maxSplits + 1`

subsequences.
Elements that are used to split the sequence are not returned as part of
any subsequence.

The following examples show the effects of the `maxSplits`

and
`omittingEmptySubsequences`

parameters when splitting a string at each
space character (" "). The first use of `split`

returns each word that
was originally separated by one or more spaces.

```
let line = "BLANCHE: I don't want realism. I want magic!"
print(line.characters.split(separator: " ")
.map(String.init))
// Prints "["BLANCHE:", "I", "don\'t", "want", "realism.", "I", "want", "magic!"]"
```

The second example passes `1`

for the `maxSplits`

parameter, so the
original string is split just once, into two new strings.

```
print(line.characters.split(separator: " ", maxSplits: 1)
.map(String.init))
// Prints "["BLANCHE:", " I don\'t want realism. I want magic!"]"
```

The final example passes `false`

for the `omittingEmptySubsequences`

parameter, so the returned array contains empty strings where spaces
were repeated.

```
print(line.characters.split(separator: " ", omittingEmptySubsequences: false)
.map(String.init))
// Prints "["BLANCHE:", "", "", "I", "don\'t", "want", "realism.", "I", "want", "magic!"]"
```

**Parameters:**
**separator:** The element that should be split upon.
**maxSplits:** The maximum number of times to split the sequence, or one
less than the number of subsequences to return. If `maxSplits + 1`

subsequences are returned, the last one is a suffix of the original
sequence containing the remaining elements. `maxSplits`

must be
greater than or equal to zero. The default value is `Int.max`

.
**omittingEmptySubsequences:** If `false`

, an empty subsequence is
returned in the result for each consecutive pair of `separator`

elements in the sequence and for each instance of `separator`

at the
start or end of the sequence. If `true`

, only nonempty subsequences
are returned. The default value is `true`

.
**Returns:** An array of subsequences, split from this sequence's elements.

#### Declaration

`func split(separator: Self.Iterator.Element, maxSplits: Int = default, omittingEmptySubsequences: Bool = default) -> [AnySequence<Self.Iterator.Element>]`

Returns a Boolean value indicating whether the initial elements of the sequence are the same as the elements in another sequence.

This example tests whether one countable range begins with the elements of another countable range.

```
let a = 1...3
let b = 1...10
print(b.starts(with: a))
// Prints "true"
```

Passing a sequence with no elements or an empty collection as
`possiblePrefix`

always results in `true`

.

```
print(b.starts(with: []))
// Prints "true"
```

** possiblePrefix:** A sequence to compare to this sequence.

**Returns:**

`true`

if the initial elements of the sequence are the same as
the elements of `possiblePrefix`

; otherwise, `false`

. If
`possiblePrefix`

has no elements, the return value is `true`

.**See Also:** `starts(with:by:)`

#### Declaration

`func starts<PossiblePrefix where PossiblePrefix : Sequence, PossiblePrefix.Iterator.Element == Self.Iterator.Element>(with possiblePrefix: PossiblePrefix) -> Bool`

#### Where Iterator.Element : Sequence

Returns the elements of this sequence of sequences, concatenated.

In this example, an array of three ranges is flattened so that the elements of each range can be iterated in turn.

```
let ranges = [0..<3, 8..<10, 15..<17]
// A for-in loop over 'ranges' accesses each range:
for range in ranges {
print(range)
}
// Prints "0..<3"
// Prints "8..<10"
// Prints "15..<17"
// Use 'joined()' to access each element of each range:
for index in ranges.joined() {
print(index, terminator: " ")
}
// Prints: "0 1 2 8 9 15 16"
```

**Returns:** A flattened view of the elements of this
sequence of sequences.

**See Also:** `flatMap(_:)`

, `joined(separator:)`

#### Declaration

`func joined() -> FlattenSequence<Self>`

Returns the concatenated elements of this sequence of sequences, inserting the given separator between each element.

This example shows how an array of `[Int]`

instances can be joined, using
another `[Int]`

instance as the separator:

```
let nestedNumbers = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
let joined = nestedNumbers.joined(separator: [-1, -2])
print(Array(joined))
// Prints "[1, 2, 3, -1, -2, 4, 5, 6, -1, -2, 7, 8, 9]"
```

** separator:** A sequence to insert between each of this
sequence's elements.

**Returns:**The joined sequence of elements.

**See Also:** `joined()`

#### Declaration

`func joined<Separator where Separator : Sequence, Separator.Iterator.Element == Self.Iterator.Element.Iterator.Element>(separator: Separator) -> JoinedSequence<Self>`

#### Where Iterator.Element == String

Returns a new string by concatenating the elements of the sequence, adding the given separator between each element.

The following example shows how an array of strings can be joined to a single, comma-separated string:

```
let cast = ["Vivien", "Marlon", "Kim", "Karl"]
let list = cast.joined(separator: ", ")
print(list)
// Prints "Vivien, Marlon, Kim, Karl"
```

** separator:** A string to insert between each of the elements
in this sequence. The default separator is an empty string.

**Returns:**A single, concatenated string.

#### Declaration

`func joined(separator: String = default) -> String`

#### Where SubSequence : Sequence, SubSequence.SubSequence == SubSequence, SubSequence.Iterator.Element == Iterator.Element

Returns a subsequence by skipping the initial, consecutive elements that satisfy the given predicate.

The following example uses the `drop(while:)`

method to skip over the
positive numbers at the beginning of the `numbers`

array. The result
begins with the first element of `numbers`

that does not satisfy
`predicate`

.

```
let numbers = [3, 7, 4, -2, 9, -6, 10, 1]
let startingWithNegative = numbers.drop(while: { $0 > 0 })
// startingWithNegative == [-2, 9, -6, 10, 1]
```

If `predicate`

matches every element in the sequence, the result is an
empty sequence.

** predicate:** A closure that takes an element of the sequence as
its argument and returns a Boolean value indicating whether the
element should be included in the result.

**Returns:**A subsequence starting after the initial, consecutive elements that satisfy

`predicate`

.**Complexity:** O(*n*), where *n* is the length of the collection.
**See Also:** `prefix(while:)`

#### Declaration

`func drop(while predicate: (Self.Iterator.Element) throws -> Bool) rethrows -> AnySequence<Self.Iterator.Element>`

Returns a subsequence containing all but the given number of initial elements.

If the number of elements to drop exceeds the number of elements in the sequence, the result is an empty subsequence.

```
let numbers = [1, 2, 3, 4, 5]
print(numbers.dropFirst(2))
// Prints "[3, 4, 5]"
print(numbers.dropFirst(10))
// Prints "[]"
```

** n:** The number of elements to drop from the beginning of
the sequence.

`n`

must be greater than or equal to zero.
**Returns:**A subsequence starting after the specified number of elements.

**Complexity:** O(1).

#### Declaration

`func dropFirst(_ n: Int) -> AnySequence<Self.Iterator.Element>`

Returns a subsequence containing all but the given number of final elements.

The sequence must be finite. If the number of elements to drop exceeds the number of elements in the sequence, the result is an empty subsequence.

```
let numbers = [1, 2, 3, 4, 5]
print(numbers.dropLast(2))
// Prints "[1, 2, 3]"
print(numbers.dropLast(10))
// Prints "[]"
```

** n:** The number of elements to drop off the end of the
sequence.

`n`

must be greater than or equal to zero.
**Returns:**A subsequence leaving off the specified number of elements.

**Complexity:** O(*n*), where *n* is the length of the sequence.

#### Declaration

`func dropLast(_ n: Int) -> AnySequence<Self.Iterator.Element>`

Returns a subsequence, up to the specified maximum length, containing the initial elements of the sequence.

If the maximum length exceeds the number of elements in the sequence, the result contains all the elements in the sequence.

```
let numbers = [1, 2, 3, 4, 5]
print(numbers.prefix(2))
// Prints "[1, 2]"
print(numbers.prefix(10))
// Prints "[1, 2, 3, 4, 5]"
```

** maxLength:** The maximum number of elements to return. The
value of

`maxLength`

must be greater than or equal to zero.
**Returns:**A subsequence starting at the beginning of this sequence with at most

`maxLength`

elements.**Complexity:** O(1)

#### Declaration

`func prefix(_ maxLength: Int) -> AnySequence<Self.Iterator.Element>`

Returns a subsequence containing the initial, consecutive elements that satisfy the given predicate.

The following example uses the `prefix(while:)`

method to find the
positive numbers at the beginning of the `numbers`

array. Every element
of `numbers`

up to, but not including, the first negative value is
included in the result.

```
let numbers = [3, 7, 4, -2, 9, -6, 10, 1]
let positivePrefix = numbers.prefix(while: { $0 > 0 })
// positivePrefix == [3, 7, 4]
```

If `predicate`

matches every element in the sequence, the resulting
sequence contains every element of the sequence.

** predicate:** A closure that takes an element of the sequence as
its argument and returns a Boolean value indicating whether the
element should be included in the result.

**Returns:**A subsequence of the initial, consecutive elements that satisfy

`predicate`

.**Complexity:** O(*n*), where *n* is the length of the collection.
**See Also:** `drop(while:)`

#### Declaration

`func prefix(while predicate: (Self.Iterator.Element) throws -> Bool) rethrows -> AnySequence<Self.Iterator.Element>`

A type that provides sequential, iterated access to its elements.

A sequence is a list of values that you can step through one at a time. The most common way to iterate over the elements of a sequence is to use a

`for`

-`in`

loop:While seemingly simple, this capability gives you access to a large number of operations that you can perform on any sequence. As an example, to check whether a sequence includes a particular value, you can test each value sequentially until you've found a match or reached the end of the sequence. This example checks to see whether a particular insect is in an array.

The

`Sequence`

protocol provides default implementations for many common operations that depend on sequential access to a sequence's values. For clearer, more concise code, the example above could use the array's`contains(_:)`

method, which every sequence inherits from`Sequence`

, instead of iterating manually:## Repeated Access

The

`Sequence`

protocol makes no requirement on conforming types regarding whether they will be destructively consumed by iteration. As a consequence, don't assume that multiple`for`

-`in`

loops on a sequence will either resume iteration or restart from the beginning:In this case, you cannot assume either that a sequence will be consumable and will resume iteration, or that a sequence is a collection and will restart iteration from the first element. A conforming sequence that is not a collection is allowed to produce an arbitrary sequence of elements in the second

`for`

-`in`

loop.To establish that a type you've created supports nondestructive iteration, add conformance to the

`Collection`

protocol.## Conforming to the Sequence Protocol

Making your own custom types conform to

`Sequence`

enables many useful operations, like`for`

-`in`

looping and the`contains`

method, without much effort. To add`Sequence`

conformance to your own custom type, add a`makeIterator()`

method that returns an iterator.Alternatively, if your type can act as its own iterator, implementing the requirements of the

`IteratorProtocol`

protocol and declaring conformance to both`Sequence`

and`IteratorProtocol`

are sufficient.Here's a definition of a

`Countdown`

sequence that serves as its own iterator. The`makeIterator()`

method is provided as a default implementation.## Expected Performance

A sequence should provide its iterator in O(1). The

`Sequence`

protocol makes no other requirements about element access, so routines that traverse a sequence should be considered O(n) unless documented otherwise.See Also:`IteratorProtocol`

,`Collection`