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lec0307-trees-ann

# lec0307-trees-ann - Today’s announcements 0 MP4 available...

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Unformatted text preview: Today’s announcements: 0 MP4 available, EC due 3/4. due 3/11. 11:59p. / Toda: , (JR—4 any-334211 0 ﬂ 0 JO Binary t_r_ee, recursive deﬁnition: A binary tree I is either WM“; {3 An (important) example of a function on a binary tree: height(t) - length of longest path from root to a leaf Given a tree T. write a recursive defn of the height of T. height(T): 19 H,\m§= ' I mir‘fim’a m um = m ihz‘d‘m‘ﬁ‘w‘ﬁ *1 '3 Full Binary tree: a tree In which every node has 2 or 0 chlldren ==-==' Full tree of height; F”: o E, is an empty tree ifh>-1.thethi L.T . MIL TINT: 0N- 1L mu. M W m- . omL Mal I" nub! U I 9‘11“ Complete Binary tree: all leaves are at level height“) or height“) -1. an and all leaves at level height(t) are pushed to the iett. o “a Po: k" ' Perfect tree of height h. P": p . o P-, is an empty tree 1 ' b . if h > -1, then P!) is {'13: LR}. P2: whe TLandTRareP . R a Complete tree of hei ht h. Ch: ﬂ, . an empty tree 3 0-, o if h > -1. then 6,, is {r. TL. TR}. and either: 0 f &- E:Q._,_andms_ﬁ._t_ Check for understanding: I: every full tree complete? is every complete tree full? Rooted. drected. cidered. binary trees ADT: Insert 3 ”In Implementation: 4, root node loft and right subtroo pointers Theorem: If that. m n data “an: In a binary ho. thm from m niL null pdnm. in. cunt and. loll and up\ mun yon-nun. ...
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lec0307-trees-ann - Today’s announcements 0 MP4 available...

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