大二上学习数据结构lec27.pptx

DigitalSearchTreesBinaryTriesAnalogofradixsorttosearching.Keysarebinarybitstrings.Fixedlength–0110,0010,1010,1011.Variablelength–01,00,101,1011.Application–IProuting,packetclassification,firewalls.IPv4–32bitIPaddress.IPv6–128bitIPaddress.

DigitalSearchTreeAssumefixednumberofbits.Notempty=Rootcontainsonedictionarypair(anypair).Allremainingpairswhosekeybeginswitha0areintheleftsubtree.Allremainingpairswhosekeybeginswitha1areintherightsubtree.Leftandrightsubtreesaredigitalsubtreesonremainingbits.

ExampleStartwithanemptydigitalsearchtreeandinsertapairwhosekeyis0110.0110Now,insertapairwhosekeyis0010ExampleNow,insertapairwhosekeyis1001.01100010100101100010

ExampleNow,insertapairwhosekeyis1011.1001011000101001011000101011

ExampleNow,insertapairwhosekeyis0000.100101100010101110010110001010110000

Search/Insert/DeleteComplexityofeachoperationisO(#bitsinakey).#keycomparisons=O(height).Expensivewhenkeysareverylong.10010110001010110000

BinaryTrieInformationRetrieval.Atmostonekeycomparisonperoperation.Fixedlengthkeys.Branchnodes.Leftandrightchildpointers.Nodatafield(s).Elementnodes.Nochildpointers.Datafieldtoholddictionarypair.

ExampleAtmostonekeycomparisonforasearch.000100111100100010010000001111

VariableKeyLengthLeftandrightchildfields.Leftandrightpairfields.Leftpairispairwhosekeyterminatesatrootofleftsubtreeorthesinglepairthatmightotherwisebeintheleftsubtree.Rightpairispairwhosekeyterminatesatrootofrightsubtreeorthesinglepairthatmightotherwisebeintherightsubtree.Fieldisnullotherwise.

ExampleAtmostonekeycomparisonforasearch.010null000110000000011011111001000011001000101001

FixedLengthInsertInsert0111.00010011110010001001000000111101111Zerocompares.

FixedLengthInsertInsert1101.00010011110010001001000000111101111

FixedLe