??(Heap Tree)

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??(Heap Tree)
???????
2
????

1. ??(Heap)???????????,????????
2. Heap?????????Max-heap, Min-heap, Min-max
   heap?Deap?
3. Heap???????,???Heap sort(????)?

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Definition

1. ??? ( max  tree ) ????,????????????????? ( ??????
   ) ????
2. ???? ( max heap ) ???????????????
3. ??? ( min  tree ) ????,????????????????? ( ??????
   ) ???? ???? ( min heap ) ???????????????

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????

5
????
6
????

• ????Heap,?????????????????????
• ??????,????????????,?????????
• ,??,????????????????

7
????
8
????

• ?????????????,????????????,???????????????,???2
  3?30?30??,??15?30???????????,??????????,??????????

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????

• ??Heap????,????????????????????????,???????????
  ,????????,?????????????

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?????????

• ?????????????
• ???
• ???
• ??????????????,???????
• ?????,??????????????
• Heap???????,???Heap sort(????)?

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?????????

• ???????????,??????????
• ??????
• ???????

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?????? (ReheapUp)

1. ????????????N???,??N-1?????????????,????????????
2. ????,???????????,?????????????
3. ?????? (ReheapUp),???????????,??????????,?????????
   
4. ?9-4???????,????????????,??????????????????,??????
   ???,??????????????

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?????? (ReheapUp)

• ?????????
• ?????????????,????????????1?(???)??,??9-4???
• ?????????????,???????????,?????????
• ????????-?????????,??????????????
• ?????? (ReheapUp) ?????????????,??????????,???????
  ???

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? 9-4 ????????
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?????? (ReheapUp)

• ?9-5??ReheapUp???
• ???25????12???????????????25?12???
• ????25????????21,????????
• ????????25???????42,?????????,???????

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? 9-5 ????????
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?????? (ReheapDown)

• ?????? (ReheapDown)
• ??????????,???????,???????????
• ???????????,????????
• ????????,???????????????????,???????????
• ?????? (ReheapDown) ????????,?????????????
• ??????,??????????,?????????????????
• ????????????(ReHeapDown),??9-6???

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? 9-6 ?????????
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?????? (ReheapDown)

1. ?9-7??????????????
2. ???,???10?????,?????????,?????????32,????? ???
3. ?9-7(b) ?????????,?????????????????,??10?????,????
   10???????30????
4. ??,??????,?????????

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? 9-7 ??????
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Heap???
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Heap???
??30?50? ?????????????30???, ???
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Heap???

• ????50?????Heap,?????????
• ????????Heap,??,??????????????????

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Heap???

• Heap????????????????????????,?????????Heap,??,?
  ?????????????

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Heap???
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Heap???
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Heap???

• ???40,??10????

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????

• ????,???Heap??

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????

• ???40??,??15??40(??15??????????????)

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????

• ???15????????????,??15?35(?????30)??,???15?35??
  ?

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??min-heap

• ?????Heap,?????max-heap,?max-heap?????,???????,
  ?????????????????min-heap???????,????????????,??ma
  x-heap??,???????min-heap????

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??min-heap

• ????????????max-heap????,??????????

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min-max heap

• min-max heap???min-heap?max-heap??Heap???

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min-max heap
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min-max heap

• ??min-max heap
• ??????,??????????,???min-max heap,??????????
• 1.min-max heap????min-heap,??max-heap??????
• 2.???min-heap???,????min-heap????
• 3.???max-heap???,???? max-heap????

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min-max heap???
min-max heap????max-heap??????,?????,????????min-
max heap????
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min-max heap???
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min-max heap???

• ???5,????

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min-max heap???

• ???18gt5,????????,?5?18???

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min-max heap???

• ???,??10gt5,????????,?5?10???

?????min-max heap???,???????
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min-max heap???

• ???min-max heap???????,?????????,???????????????
  ?????,??????,????????????????????????min-max
  heap??

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min-max heap???
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min-max heap???
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min-max heap???

• ???45,??????

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min-max heap???

• ???40,????????????18??40?

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min-max heap???

• ???18lt19,????????,?18?19???

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min-max heap???

• ???,??19??32?28?34?31,????????,???19??????34???

??min-max heap???,???????
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Deap

• Deap?????max-heap?min-heap???,?????
• 1.Deap??????????,??????
• 2.??????,???min-heap?????max-heap?
• 3.min-heap?max-heap?????,???????????i,????????????
  j?i??,?i??????j?

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Deap
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Deap
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Deap???
Deap????????Heap??,??????????????,?????Deap????
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Deap???

• ??????deap??

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Deap???

• ???25,??????????max-heap,????????15????????????
  ??25,??deap???,???????

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Deap???

• ??17,??????????

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Deap???

• ???????max-heap,?17???????????20,??17?20???

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Deap???

• ??40,????

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Deap???

• ????????min-heap,?40???????25(???40????????????
  ),???deap???,??40?25??,????

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Deap???

• ?????????????max-heap,???????max-heap???

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Deap???

• Deap????????Heap??,???????????????,????????????
  ?????,??????deap????

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Deap???
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Deap???
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Deap???

• ???29,???????,???????

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Deap???

• ??21,?????????22???,??????????,?????????min-hea
  p,?????22???????32,??????????????

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Deap???
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Deap???

• ??12,???????27???

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Deap???

• ??????min-heap???,?27?????????16???

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Deap???

• ??16?????30??16??30,??27???????max-heap???30,?
  ???????