structure Std.Queue (α : Type u) : Type u

• eList : List α

  The enqueue list, which stores elements that have just been pushed (with the most recently enqueued elements at the head).

• dList : List α

  The dequeue list, which buffers elements ready to be dequeued (with the head being the next item to be yielded by dequeue?).

A functional queue data structure, using two back-to-back lists. If we think of the queue as having elements pushed on the front and popped from the back, then the queue itself is effectively eList ++ dList.reverse.

def Std.Queue.empty {α : Type u} : Std.Queue α

O(1). The empty queue.

Equations

• Std.Queue.empty = { eList := [], dList := [] }

instance Std.Queue.instEmptyCollectionQueue {α : Type u} : EmptyCollection (Std.Queue α)

Equations

• Std.Queue.instEmptyCollectionQueue = { emptyCollection := Std.Queue.empty }

instance Std.Queue.instInhabitedQueue {α : Type u} : Inhabited (Std.Queue α)

Equations

• Std.Queue.instInhabitedQueue = { default := ∅ }

def Std.Queue.isEmpty {α : Type u} (q : Std.Queue α) : Bool

O(1). Is the queue empty?

Equations

• Std.Queue.isEmpty q = (List.isEmpty q.dList && List.isEmpty q.eList)

def Std.Queue.enqueue {α : Type u} (v : α) (q : Std.Queue α) : Std.Queue α

O(1). Push an element on the front of the queue.

Equations

• Std.Queue.enqueue v q = { eList := v :: q.eList, dList := q.dList }

def Std.Queue.enqueueAll {α : Type u} (vs : List α) (q : Std.Queue α) : Std.Queue α

O(|vs|). Push a list of elements vs on the front of the queue.

Equations

• Std.Queue.enqueueAll vs q = { eList := vs ++ q.eList, dList := q.dList }

def Std.Queue.dequeue? {α : Type u} (q : Std.Queue α) : Option (α × Std.Queue α)

O(1) amortized, O(n) worst case. Pop an element from the back of the queue, returning the element and the new queue.

Equations

• One or more equations did not get rendered due to their size.

def Std.Queue.toArray {α : Type u} (q : Std.Queue α) : Array α

Equations

• Std.Queue.toArray q = List.toArray q.dList ++ Array.reverse (List.toArray q.eList)