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Unformatted text preview: Announcements:
MP 6 regrade window closes tonight. 11 :59p. Late penalty waived.
MP7 available. Due soon. Start now. Today: graphs, but first... Disjoint Sets ADT: U m‘gn . F '
(“I } nning times)
) . Path Compression: mart mans Path Compression: int DS::Find(int i) I
it (3(1] < 0) return 1: else return : Find(s[i]):
} ——' r  void DS::UnionBySizo(int rootl. int toot2) ( int nchizo  slrootlloslrootzlt
_ it (isBiqqor(root1.toot2)) I slzootzl rootl;
slrootll nowSizc:
1
also {
clrootl]  rootZ:
clrootzl nousizo: Trace the code below.
Use Path Compression. Union by Height. and a pencil. If (Find(A) != Find(B) Union (Find (A) , Find (B) ) :
If (Find(D) ! Find(E) 9
Union(Find(D),Find(E)); If (Find(A) ! Find(C)
Union (Find (A) ,Find (C) ) :
If (Find(C) != Find(B)
Union(Find(C).Find(B)): If (Find(B) ! Find(F)) Union (Find (8) ,Find(F) ) 3 © (é) é
If (Find(D) ! Find(F)) Union (Find (D) .Find(F) ) 0. What‘s the tree height of the final tree? Name the last 4 data structures we‘ve discussed:
Which of those 4 islare dictionaries? Give 2 applications of a Heap: What's the buildHeap algorithm and how fast is it? The umernet. 2003
CS Networking Discovery:
wmm muttr Is most (natal? IOW: thh vmtnx has mm)ch
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. characters in the play
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an octet on stage at all times
What Is the smallest set 0! actors you could select so as to assure
. that there is aMays someone on stage who can hotd the sword? . IOW:
Findavenex ooverinthegtaph
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CS: HCI Discovery: Find the Is! otpoqale who are
my Month' Month. but no!
nine. IOW:
Given a vertax 5. ﬁnd all vowoos whose 3mm»!
distame Is 2 from s. @or HARD? cO I! Rush Hour CS: State diagram Discovety:
Find me samba d (we!
"DVDS. IOW: Find them pom
' ' n' 't 2 @ HARD? This graph can be used to quickly
calculate whether a given number is
divisible by 7. 1.Start at the circle node at the top. 2.For each digit d in the given
number. follow d blue (solid) edges in
succession. As you move from one
digit to the next. follow 1 red (dashed)
edge. 3.If you end up back at the circle
node. your number is divisible by 7. 3073
17.93 d . . u“'b v v V ' Q) "3..
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CS: Graphics Discovery:
Ifwe can act! some Manges.
when; should we put them? IOW:
Roﬂno mo mosh In ammo!
high curvature. r HARD? . v“ .
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‘ 'A‘AV.V§‘ Final Exam Scheduler
CS: Conﬂict Graph Discovety: What's the mm olﬂnal
periods we can have «we
want to avocd comm? IOW:
Findthe butﬂdlabols we modtoookxthovonlmd
momphsonommm m an the same oolov
(Vane): Who) EASY or HARD? ®®®
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eomaewfoe ©®®®©®®®® e How do we get from here to there? Need: I. POM/nan 'v/(X4d/1ZI/(2/1l/
2. ét(gp/r 1.07/9/ Pmpnz‘a’f [on
3. 7;‘(zs’er5a/ q. fZ/Bnrf'f/IMS. Incident edges(6) Graph Vocabulary: (/1  Degree(6)
Adjacent vertloes(6)
O o 0 O
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Complete subgraph(G,) 
O O O 0 Connected oomponent(G) 
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6. Spanning tree(G1)  Graphs: theory that will help us in analysis (arm/’3 time5 often reported in terms of n, the numéer of
Valtires, (Sat (Ivy 0/2?» depend on m, the "under of c.4325. How many edges? At least:
0 [iv/1' I I) connected — All]  M
notoonnected Almost simple  not simple  Reletlonshlp to degree sum: Edegﬂr) =
sEV ...
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 Spring '09
 Heeren
 Graph Theory, Disjoint sets, Disjointset data structure, path compression, int rootl. int, slzootzl rootl

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