62 lines
1.9 KiB
Text
62 lines
1.9 KiB
Text
/-
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Copyright (c) 2019 Microsoft Corporation. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Daniel Selsam
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Simple queue implemented using two lists.
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Note: this is only a temporary placeholder.
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-/
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prelude
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import Init.Data.List
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namespace Std
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/--
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A functional queue data structure, using two back-to-back lists.
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If we think of the queue as having elements pushed on the front and
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popped from the back, then the queue itself is effectively `eList ++ dList.reverse`.
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-/
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structure Queue (α : Type u) where
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/-- The enqueue list, which stores elements that have just been pushed
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(with the most recently enqueued elements at the head). -/
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eList : List α := []
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/-- The dequeue list, which buffers elements ready to be dequeued
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(with the head being the next item to be yielded by `dequeue?`). -/
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dList : List α := []
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namespace Queue
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variable {α : Type u}
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/-- `O(1)`. The empty queue. -/
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def empty : Queue α := {}
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instance : EmptyCollection (Queue α) := ⟨.empty⟩
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instance : Inhabited (Queue α) := ⟨∅⟩
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/-- `O(1)`. Is the queue empty? -/
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def isEmpty (q : Queue α) : Bool :=
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q.dList.isEmpty && q.eList.isEmpty
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/-- `O(1)`. Push an element on the front of the queue. -/
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def enqueue (v : α) (q : Queue α) : Queue α :=
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{ q with eList := v::q.eList }
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/-- `O(|vs|)`. Push a list of elements `vs` on the front of the queue. -/
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def enqueueAll (vs : List α) (q : Queue α) : Queue α :=
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{ q with eList := vs ++ q.eList }
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/--
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`O(1)` amortized, `O(n)` worst case. Pop an element from the back of the queue,
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returning the element and the new queue.
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-/
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def dequeue? (q : Queue α) : Option (α × Queue α) :=
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match q.dList with
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| d::ds => some (d, { q with dList := ds })
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| [] =>
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match q.eList.reverse with
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| [] => none
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| d::ds => some (d, { eList := [], dList := ds })
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def toArray (q : Queue α) : Array α :=
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q.dList.toArray ++ q.eList.toArray.reverse
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