- ?s?????s

1
??µ?? ?ed?µ????

• - ?s?????sµ??a ??ad??? ???d?a (balanced binary
  trees)
• ???d?a ??a??t?s?? m-d??µ??
• ????d??stata ???d?a (multidimensional trees)

2
???sµ??

• st???e?? (??µß??)
• a?µ?
• ?p?d??d??
• pa?d??, ??????, p???????, ap??????
• µ???p?t?
• ???? (ß????)
• ep?ped?
• f???a, es?te????? ??µß??

3
Stat??? a?apa??stas? d?ad???? d??d??? (µe p??a?a)

• ?as??eta? st?? p??????µe?? ?d??t?ta (t??
  s?µp????µ???? d?ad???? d??d???)
• ???ß??µa spat??? ????? ?ta? ?e?p??? p????
  st???e?a (??a ?a ???e? t? d??d?? p???e?)
• ??a d??d?? µe n st???e?a ?a µp????se ?a apa?t?se?
  p??a?a µe?????? µ???? ?a? 2n-1 (? pe??pt?s? t??
  de???? ????? d?ad???? d??d???)

4
S??dedeµ??? a?apa??stas? d?ad???? d??d??? (µe
de??te?)

• ? p?? d?µ?f???? ???p???s?
• ???e st???e?? a?t?st???e? se ??a ??µß? µe ??a
  ped?? ded?µ???? (data) ?a? d?? ped?a s??d?sµ??
  (LeftChild, RightChild)

5
???s??s? d??d??? (s??.)

• ???d?ateta?µ??? A, B, D, C, E, G, F, H, I
• ?etad?ateta?µ???D, B, G, E, H, I, F, C, A
• ??d?d?ateta?µ???B, D, A, G, E, C, H, F, I
• ?at? se??? ep?p?d??A, B, C, D, E, F, G, H, I

6
??a??af? st???e??? ap? ??? (1)

• 3 pe??pt?se??
• ? ??µß?? p (p?? pe????e? t? st???e??) e??a? f????
• ?? p ??e? µ??? ??a µ? ?e?? ?p?d??d??
• ?? p ??e? a???ß?? d?? µ? ?e?? ?p?d??d?a

7
???a?? ???d??
8
?pa??de?t? !
9
??a ?a??te?? ???d??
10
?s?????sµ??a ???d?a

• St????
• ?a µ?? af?s??µe t? ??a ??ad? t?? d??d??? ?a ???e?
  ?at? p??? µe?a??te?? t?? ?????. ?a d?? ?p?d??d?a
  ?????µe ?a ????? pe??p?? t? ?d?? ????.

11
? ??s?

• ???d?a AVL
• Adel'son
• Vel'skii
• Landis

12
???d?a AVL

• ? d?af??? t?? ???? t?? a??ste??? ?a? t?? de????
  ?p?d??d??? de? p??pe? ?a ?epe??? t? 1. ??t?
  p??pe? ?a ?s??e? a?ad??µ??? ??a ????? t???
  ??µß??? t?? d??d???.

13
???d?a AVL

• ???p?? ?e?t?????a?
• ? a?a??t?s? e??a? ?d?a ?p?? ?a? se ??a ap??
  d?ad??? d??d?? a?a??t?s??.
• ?et? ap? ???e e?sa???? ?a? d?a??af? p??pe? ?a
  ???e? ??e???? ??a t? a? ??a??p??e?ta? ?
  pe?????sµ?? t?? AVL (d?af??? t?? ???? t??
  ?p?d??d???).

14
???d?a AVL

• Se pe??pt?s? p?? de? ?p???e? p??ß??µa st? d?µ?
  t?? d??d???, t?te de? apa?te?ta? ?aµ?a ????
  e????e?a.
• ??af??et??? ?a p??pe? ?a ?????? d?µ???? a??a???
  st? d??d?? ?ste ?a p?????e? p??? ??a d??d?? AVL.

15
?e??st??f??

• ????µe d?? e?d? pe??st??f??
• ?p?? pe??st??f?
• ?e??st??f??ta? d?? ??µß??
• ??p?? pe??st??f?
• ?e??st??f??ta? t?e?? ??µß??
• ???ta ?a d??µe t? e??a? a?t?? ?? pe??st??f?? ?a?
  st? s????e?a ?a e?et?s??µe t? ???s? t???

16
?p?? ?e??st??f?
?e??pt?s? 1
17
?p?? ?e??st??f?
?e??pt?s? 2
18
?p?? ?e??st??f? - ?a??de??µa
h
h1
??t? e??a? ??a d??d?? AVL
19
?p?? ?e??st??f? - ?a??de??µa
h
h2
??sa???? 02
?et? t?? e?sa???? t?? ??µß?? 2 t? d??d?? p??
p????pte? ??? e??a? AVL
20
?p?? ?e??st??f? - ?a??de??µa
x
y
h
h
h1
C
B
A
21
?et? t?? ?e??st??f?
y
x
A
B
C
22
?p?? ?e??st??f?

• ?e????? f???? t? p??ß??µa se ???eta? µe ap??
  pe??st??f?

k2
k1
k1
Z
k2
h
X
h2
X
Y
h
h2
Y
Z
?? µp????µe ?a ?????µe ??p?? pe??st??f? !
23
??p?? ?e??st??f?
?e??pt?s? 3
24
??p?? ?e??st??f?
?e??pt?s? 4
25
??p?? ?e??st??f? - ?a??de??µa
??t? e??a? ??a d??d?? AVL
h
h1
??a??af? t?? ??µß?? 94
26
??p?? ?e??st??f? - ?a??de??µa
h2
h
?a?aß???eta? ? ???sµ?? t?? AVL
27
??p?? ?e??st??f? - ?a??de??µa
x
y
z
C
A
B1
B2
28
?et? t? ??p?? ?e??st??f?
z
x
y
A
B1
B2
C
29
???d?a ?????? ???µ??
Page 166
???d?? 5 d??µ??
30
?a??de??µa
???d?? 5 d??µ?? 31 ??µß?? 3 ep?peda
??ad??? d??d?? 31 ??µß?? 5 ep?peda