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with a single test instead of two per iteration.

If a function body consists of a single expression then the return keyword can be omitted.

class MyQueue<Element> {
 
 private var stack1: [Element]
 private var stack2: [Element]
 
 init() {
 stack1 = []
 stack2 = []
 }
 
 func push(_ x: Element) {
 stack1.append(x)
 }
 
 func pop() -> Element? {
 if stack2.isEmpty {
 while let elem = stack1.popLast() {
 stack2.append(elem)
 }
 }
 return stack2.popLast()
 }
 
 func peek() -> Element? {
 stack2.last ?? stack1.first
 }
 
 func empty() -> Bool {
 stack1.isEmpty && stack2.isEmpty
 }
}

with a single test instead of two per iteration. Or even simpler:

stack2 = stack1.reversed()
stack1.removeAll()

(If your queues become really large then you might want to check which of the above methods is faster.)

If a function body consists of a single expression then the return keyword can be omitted.

class MyQueue<Element> {
 
 private var stack1: [Element]
 private var stack2: [Element]
 
 init() {
 stack1 = []
 stack2 = []
 }
 
 func push(_ x: Element) {
 stack1.append(x)
 }
 
 func pop() -> Element? {
 if stack2.isEmpty {
 stack2 = stack1.reversed()
 stack1.removeAll()
 }
 return stack2.popLast()
 }
 
 func peek() -> Element? {
 stack2.last ?? stack1.first
 }
 
 func empty() -> Bool {
 stack1.isEmpty && stack2.isEmpty
 }
}

Putting it all together, we get

class MyQueue<Element> {
 
 private var stack1: [Element]
 private var stack2: [Element]
 
 init() {
 stack1 = []
 stack2 = []
 }
 
 func push(_ x: Element) {
 stack1.append(x)
 }
 
 func pop() -> Element? {
 if stack2.isEmpty {
 while let elem = stack1.popLast() {
 stack2.append(elem)
 }
 }
 return stack2.popLast()
 }
 
 func peek() -> Element? {
 return stack2.last ?? stack1.first
 }
 
 func empty() -> Bool {
 return stack1.isEmpty && stack2.isEmpty
 }
}

• I had to inspect the code in order to understand that what you have implemented is a "first in, first out" queue. This would be more obvious to a user of your code (or to you in one year) with a more specific class name, such as FIFO or FIFOQueue.

• Typical names for adding something to a FIFO and retrieving it are enqueue and dequeue.

• Swift collection types have an isEmpty property to indicate whether it contains elements or not:

  var isEmpty: Bool {
   stack1.isEmpty && stack2.isEmpty
  }
  

If a function body consists of a single expression then the return keyword can be omitted.

Putting it all together, we get

class MyQueue<Element> {
 
 private var stack1: [Element]
 private var stack2: [Element]
 
 init() {
 stack1 = []
 stack2 = []
 }
 
 func push(_ x: Element) {
 stack1.append(x)
 }
 
 func pop() -> Element? {
 if stack2.isEmpty {
 while let elem = stack1.popLast() {
 stack2.append(elem)
 }
 }
 return stack2.popLast()
 }
 
 func peek() -> Element? {
 stack2.last ?? stack1.first
 }
 
 func empty() -> Bool {
 stack1.isEmpty && stack2.isEmpty
 }
}

• I had to inspect the code in order to understand that what you have implemented is a "first in, first out" queue. This would be more obvious to a user of your code (or to you in one year) with a more specific class name, such as FIFO or FIFOQueue.

• Typical names for adding something to a FIFO and retrieving it are enqueue and dequeue.

• Swift collection types typically use "isEmpty" as the name of a property which indicates whether the collection contains elements or not:

  var isEmpty: Bool {
   stack1.isEmpty && stack2.isEmpty
  }
  

Finally, naming: I had to inspect the code in order to understand that what you have implemented is a "first in, first out" queue. This would be more obvious to a user of your code (or to you in one year) with a more specific class name, such as FIFO or FIFOQueue. Typical names for adding something to a FIFO and retrieving it are enqueue and dequeue.

Finally, naming:

• I had to inspect the code in order to understand that what you have implemented is a "first in, first out" queue. This would be more obvious to a user of your code (or to you in one year) with a more specific class name, such as FIFO or FIFOQueue.

• Typical names for adding something to a FIFO and retrieving it are enqueue and dequeue.

• Swift collection types have an isEmpty property to indicate whether it contains elements or not:

  var isEmpty: Bool {
   stack1.isEmpty && stack2.isEmpty
  }