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Purely Functional Data Structures????

• ???
• 2006/05/12

2
?????

• Chapter 1. Introduction
• Chapter 2. Persistence
• Chapter 3. Some Familiar Data Structures in a
  Functional Setting

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??????????

• ??? (functional) ??????????
• ???? (imperative) ???????????

• ?????????
• ?????(destructive update)??????(assignment)?????
• ?????????
• ??? (persistent) ???

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?1 List

• (?????)
• append xs ys ??????
• Functional ???O( xs )
• Imperative ?????? O(1) ????
• ????? xs ????
• Functional ????xs,ys?xs_at_ys????????
• Persistant
• update
• ??

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?2 Binary Search Tree

• (MySet.ml)

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???? Strict vs. Lazy

• ?? (Strict) ??
• ????????????????????
• ?????
• ?? (Lazy) ??
• ????????????????????????????
• ??(amortized)???
• ???? Chapter 4 ???

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?????

• Abstraction
• ??????????????
• Abstract Data Type
• ML ?????????? signature
• Implementation
• ADT???????????????????
• ML ?????????? structure ? functor
• Object / Version
• Implementation ??????????
• ML ??????? value
• Persistent Identity
• Informal ? ??????????

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Chapter 3

• ???????????????????
• Leftist Heap
• Binomial Heap
• Red-Black Tree

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Leftist Heap

• Priority Queue
• ??????(????)?????????????
• ???????
• ???????
• ????????
• Heap / ????
• ???
• ?????? ? ?????? ?????
• ?????? O(1) ??????
• Leftist Heap
• ????rank ? ????rank ????Heap
• rank right spine ???
• ????n?Leftist Heap?Right Spine???????? log(n1)?

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Leftist Heap

• (MyHeap.ml)
• insert O(log n)
• merge O(log n)
• deleteMin O(log n)
• findMin O(1)

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Binomial Heap

• Tree ? List ??? Priority Queue ???
• ?????2????????
• ????????? Chapter9 ????
• (?????)
• (MyHeap.ml)
• insert O(log n)
• merge O(log n)
• deleteMin O(log n)
• findMin O(log n)
• ExplicitMin
• findMin O(1)

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Red Black Tree

• Binary Search Tree ??????????
• ?????????????
• ??????????????????
• ???????????????????????
• Prop. ?????????2?
• (MySet.ml)

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