CSE 2321 Lecture 23: Lecture 23

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LECTURE23
Determing precise formulafees runningtime Fcn
is difficult
Simplify by using abig 0expression
0gcn is an upper bound on Fcn
PROPERTIES of big 0
Simplicity
fon 0cgCND
gcn is abig 0bound on fch
gnis simple if
It is asingle term AND yo
Coefficient is 1
ex sum 0
fees Ciao initt
for Cj Ojen jtt
sunt arr iCj
is fun aGnat CntCwhere
CCz tCz C2Cz and cCCz
het gcn cn't Cnt C
gnIna
g3 nn2
Then fCh a0cg CND for each il2,3
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f0cg CI13
Note gga are not simple
g3 is simple
fe the running time is 0Cgs
CND
which is 0Cha
Tightness
we want the tightest big 0
bound we can prove If Fcn OCnD
then we cannot find afunc
thCn that grows at least as
fast as fcn but grows slowes
than gcn
gcn is tight bound on fcn if
fcn 0cgCND AND
If fCn Ohen then it is
also true that gcn OChCnD
ex 2Running time fees alg in exCD
Fcn NZ CntC
we had gz nzn2
Let goCh n3
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