queue access element element

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????????

• ??? queue ??? access element ??????????????????
  element ????
• ????????????????????????? ????????????????????????
  ????????????? (????????????????????)
• Printer queue ???????????????????????

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Priority

• ????????? ???????????????????????????? (??
  priority ??????????????)
• ????????????????????? ????????????????????????????
  ???????????
• ????????????????? ?????? Comparable interface
  ???? Comparator interface

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Comparator interface

• ?????? Comparable ??????????
• int compare(Object o1, Object o2)

???????? class ???????? ???? ????subclass ???
??????? throw CastCastException
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??? interface
// Postcondition ????????????????????? priority
queue ???
// Postcondition ???????? true ??? priority
queue ?????????????? //????????????????? false
// Postcondition element ????????????? priority
queue
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// Precondition ????????????????????? ?????????
throw // NoSuchElementException //
Postcondition ??????????????????????????????????
?? PriorityQueue ???
// Precondition ????????????????????? ?????????
throw // NoSuchElementException //
Postcondition ???????????????????????????????
PriorityQueue ??? // ?????????????????????????????
????????????????????????
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??????? implement ??????????

• ???????????? ???????? prioriry
• ?????????????? ????????????? priority ??????????
• ??? ArrayList ???????????
• getMin ?????? constant time
• add ??? removeMin ????? linear time -????????????

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??????? implement (???)

• ??? LinkedList
• getMin ??? removeMin ???? constant time
• add ?????? linear time
• Ok ?????? ???????

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??? Comparable ??? default
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?????
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???????? previous ?

• ???????? 1,2,4,5 ?????????? add 3
• Loop ??????????? itr.next() ???? 4
• ?????? iterator ?????????????? 5 ??????
• ??????? ???? previous() ?????? ???????????? 3

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protected int compare (Object elem1, Object
elem2)   return (comparatornull
? ((Comparable)elem1).compareTo(elem2)
comparator.compare (elem1, elem2)) //
method compare   ??? comparator null, return
elem1.compareTo (elem2) ?????????? return
comparator.compare (elem1, elem2)
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?????????????????

• ???????????

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public void add (Object element) set.add
(element) // method add   public Object
getMin ( ) return set.first( ) // method
getMin   public Object removeMin ( ) Object
temp set.first( ) set.remove (set.first(
)) return temp // method removeMin   ????
3 method ????? worstTime(n) ???? LOGARITHMIC ???
n.
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?????????? ?????????? Heap
ppublic class Heap implements PriorityQueue  

???????????? JAVA
COLLECTIONS
FRAMEWORK  
 
 
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Complete Binary tree ???????????????
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Heap ??? complete binary tree

• ???????? empty tree ????
• ???????? root ??????????????? (???????? minHeap)
  ???
• left ??? right subtree ?????? heap ????
• (?????? binary search tree ??)

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Complete binary tree ?????????????????
 
???????????? child, parent
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???????????????? Heap (GPA ????????????? highest
priority)
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// ?? constructor ?????? string ???? input
???????????? toString ???? ?????????????   //
Postcondition ???????????????????? lt 0, 0,
???? gt 0 ?????????????? GPA ??? // this Student
????????????????????? ??????? ??????????? GPA ???
o1
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????????? Heap ???
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index ???????????????
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index ???????????????
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?? method ?? Heap
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// Postcondition element ????????????????????
heap // ???? worst case O(n) //
??????????????????????????
??????????????? ??????
??????????? percolateUp
//????????????????????
//???????????????????????????????
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????????????????? 30 ????
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Percolate up ???...
??????? 30 ???????????????????????????????????????
?? ??????????????????? heap
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// Postcondition ??? heap ???????????????????????
?????? ?????????????????????? //O(log n)
????????????????????????????
protected void percolateUp()   int
parent int child size-1 Object
temp while (childgt0)   parent
(child-1)/2 if(compare(heapparent,hea
pchild) lt0) break
temp heapparent heapparent
heapchild heapchild temp
child parent // while   //
method percolateUp
???????????????? ?????????????????????????????????
??????????
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Average time -percolateUp

• ??????????????????????????????????????????????????
  ????
• ??????????????????????????
• ?????????????????????????????????? heap
  ?????????????????? constant time

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public Object getMin()   if (size 0)
throw new NoSuchElementException(Empty)
return heap0     // method
getMin
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removeMin() ???????????
???????????? complete binary tree ????????????
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// Precondition ????????????????????? ?????????
throw // NoSuchElementException //
Postcondition ???????????????????????????????
PriorityQueue ??? // ?????????????????????????????
???????????????????????? // ??????????????????????
O(log n)
??????? percolateDown
//????????????????????? root
//?????????????????????????
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                107 48 ?????
removeMin( ) ???????? 48 ???????????? 26 ????
size ???????????????? ??????????? percolateDown
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32 50 85
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PercolateDown ???

• ???? 48 ???????????????????
• ???????????????????? ??????????????????? heap

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protected void percolateDown(int start)  
int parent start int child 2parent1
Object temp while (childltsize)
if(childltsize-1compare(heapchild,heapchild1
) gt0) child if
(compare(heapparent,heapchild) lt0)
break temp heapchild
heapchild heapparent heapparent
temp parent child child
2parent1 // while   // method
percolateDown
// Postcondition ??? heap ???????????????????????
?? // ???????????????? ??????????????????? O(log
n) ???????
?????????????????? ???????????????????????????????
??
????????????????? ?????? child ?????????????
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???????
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?????????

• ?? compress file ?????????????????????????????????
  ?
• ??? M ???? ??????????????????? compress
  ????????????????? 100000 character
  ??????????????? a ??? e ????????
• ??? E ??? version ??? compress ????

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????????? (???)

• ??????? 1 character ????? 16 bit
• ?????? 100000 character -_- ?????????????
• ???????????????? bit

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???????
????? bit ????????? 3 ???
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????????????
????? bit ????????????3??? ??? 001010
?????????????? aababa ???? cbda ?????
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?????????????????????

• ??? prefix-free encoding
• ???????? binary tree
• ??????????????? 0
• ?????????????? 1
• ??? character ?????????

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??????? character ??????? path ???????????????????
?
a 010 b 11 c 00 d 10 e 011
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??????????????????
????????????? ?????????? character
??????????????? bit ??????????????????
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????? Huffman tree

• ????????? binary tree ??????????????
  ???????????????????????????????????????????
  character
• ??????????????????????????????????????????????
  ???????? bit ??????????

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????????????????????

• a ?? 5000
• b ?? 10000
• c ?? 20000
• d ?? 31000
• e ?? 34000

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?????? (character,???????)???Priority Q

• Priority Q ?????? ????????????????????????????
• ????? node ??? priority Q ???? left, right,
  parent ?????????
• ?????? ??????????????? (a5000) (b 10000) (c
  20000) (d 31000) (e 34000)
• ????? ????? Huffman tree ???

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• ???????????????????????????? ?????????????????????
  ?? ?????????????????????? ????????????????????????
  ??????????

0
1

• ????????????????????????? priority Q
  ?????????????? ( 15000) (c 20000) (d 31000)
  (e 34000)

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• ???????????????????????????? ????????????

• ????????????????????????? priority Q
  ???????????????? (d 31000) (e 34000) ( 35000)

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• ???????????????????????????? ????????????

• ?????????????? tree ????????
• ????????????????????????? priority Q
  ???????????????? ( 35000) ( 65000)

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• ????????????????????????? ????????????

• priority Q ?????????? ( 100000)

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???????
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Huffman ???? Greedy Algorithm

• ????????????????????????????????? ??????????????
  min ?????? tree
• ??????????????? ???????? optimal solution ??????
  ?????????????? prefix-free code ????????

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Huffman class

• ????????? input ????????????????? Huffman
• ?????????? Entry ?????????

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??????????????????????
???????? access ???????
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???????????? c ?? index 99
??????????? Entry
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// Postcondition This Huffman object ???
initialize
// Postcondition ???? ?????????????? s
??????????????????
// Postcondition priority queue
???????????????????? input //file ??????? worst
case O(n)
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// Postcondition ????? huffman tree ????worst
case ?????????
// Postcondition ????? huffman code
???????????????? // ????worst case ?????????
// Postcondition Huffman codes???????????????????
??????????????????? // ????worst case ???? O
(n).
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Fields ?? Huffman class

• Gui
• priority queue
• file reader
• file writer
• input file name ??????????????????????? 2 ??
• ????????????
• encode ?????????
• boolean ??????????????????????????

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Method processInput

• ????? priority Q
• ????? Huffman tree
• ????????????
• ??????????????????????????????????????

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Method createPQ

• ????? leafEntries
• update freq field ???????? Entry
• ?????????????????? priority queue ???????? freq

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Method createHuffmanTree

• Loop ?????? size ??? priority queue ??????? 1
• ?????????????????????????

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Method calculateHuffmanCodes

• Loop ?? leafEntries
• ????? Entry ????
• ???????????????? empty string
• ?? parent ???? ??????????????? parent
  ??????????????? string ??????? (???????????????
  prepend) ???????????? root

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????????????????????
????????????????????????
???????????
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??????? f
????????????????????????
f ????? int ???? 102 ????????????? set ???
leafEntries102.code 1010
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Method saveToFile

• Loop ?? leafEntries
• ??? character ??? code ???????????????
• ?????????? input file ?????
• ??????? input ?????????????? ??? save ?????????

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?? web ????????
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????? output file ?? ???????? Huffman tree
?????????????????????????
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???????? priority queue