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Unformatted text preview: Announcements: MPSavaila Ie. Due 10/29. 11:59p. EC due 10/22.11/59p. .
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Today: +0 agar; W Balanced BST— Weiss, 4.4 http://www.qmatica .com/DataStructures/Trees/BSThtmI Warmups:
1. Fill in the blanks to give the recursive deﬁnition of 8 BST:
A binary tree T is a binary search tree (BST) if:
 T is empty. or
oTis{;p.I‘_._T‘}and
x TL ) key(x) i key(r).
x E TR 9 key(x) 4 key(r).
and W
2. Correct the following speciﬁcation for ADT dictionary:
insert(ke data) traverseo > aﬁnd rerpove(&> void ’ du‘lk
3. T F BSTs have better worstcase performance than SLL J
4. How much would you pay for a BST ‘find' whose running time is 9(log n)? S, 'A’
N .
5. What data structure is used to support a level ordgr'daversa o a binary tree? ) $9 (ML something new... which tree makes you happiest? Hrz skorttfwa «oh .3
gym '32:,
\ e a» The “height balancebof a tree 1' is:
g = he_ight(T,)  heigbt(TR) A tree T is “height bala_gced" if: «"1": I NTt;T¢u&h (tiLO. \m ww 9mm ubmd’m m U: 0003.0 Binary Search Tree  is this tree “height balanced”? ea» 4“. m 4; u a W3 «.4. wangfvpﬁcuhm 0% Qoﬁ ovJw “was / a chm *H “14% “L
M, W (Xv/Nd”? WOLDMWSWQ’YIMZGJ stm M 4m Mam
balanced trees  rotations thither h” M mt balanced trees  rotations balanced trees  rotations balanced trees  rotations summary: 1. there are 4 kinds: left. right. leftright. rightleft (symmetric!)
local operations (subtrees not affected) 2.
3. constant time operations
4. BST characteristic maintained height balanced trees  we have a special name: Three issues to consider as we move toward implementation: Rotating
Maintaining height Detecting imbalance ...
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 Spring '09
 Heeren

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