[PDF] Computational Geometry Exercise Set 10 HS07




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[PDF] Computational Geometry Exercise Set 10 HS07 58795_6u10.pdf

ZurichÈTechnische HochschuleEidgenossischeÈSwiss Federal Institute of Technology ZurichPolitecnico federale di ZurigoEcole polytechnique federale de ZurichÂÂ

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ComputationalGeometryExerciseSet10HS07

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Exercise1(10points)

?????k????????????????? ???????? ?????????????????????????????????? ???k? ????S1;:::;Sk???n? ?????? ???? ???? ?????? ???????? ? a1 ?S1;:::;ak ?Sk????? ?????? ?Pk i=1ai=0????? ???? ???????????? ???? ?? ???? ???????? ??k????????? ? O(n? k

2??????n)?????k

?? ???? ???? ?O(n? k

2?)?????k????????

? ???????? ? k??? ?? ?????? ???? ?????? ???? ?? ?? ?????? ?????? ???????? ?????? ?? ?????? ?? ?? ????

Exercise2(10points)

??????????? ?? ???????????? ?????? ???? ?????????????????? ?????? ?????????? ?????????????? ???? ???? ???????? ???????? ?? ?????????? ???? ?? ??? ??? ? ?????? ?? ?????????????????? ???? ?????? ???? ?????? ???? ? n????????????????? ?????? ?????? ?? ?? ???? ???????? ?? ???? ???? ???????? ???? ??? ?????????? ???? ?????? ?? ?????????? n??????? ???????? ?????? ?????? ???????? ?????? ?????? ???pi????? ?????? ?t? ???????? ???? ? si+vit? ?????? ???????? ???????????? ?????????????? ?????????????? ???????? ?????????????? ?????????? ???????? ???????? ???????? ???? ???????? ???? ???? ?

0<<?

?? ???????? ???? ???????? ?????????????????? ?? ?????????????? ???????????????????? ?????? ???????? ???? ???????????? ?????? ?????? ?????????? ???? ???? ?????????? ?????????????????????????????? ?????? ?????????? ????? ?????? ???? ???? ?? ????????????

T=[t0;t1]?????????

???????? ?? ???? ?h(t)? ?T? ???? ?????? ?? ???????????? ???? ???? ?????????????????? ?????? ?????? ???????? ?????? ?? ?? y??????????? ?? ?????? ?????????? ?? ?????????????? ?? ?? ?????????? ????? ???????????????????? ???? ?????????? ?????? ?? ?????????????????? ?????? ???????????? ???????? ???????? ???????????? ???? ?? ???? ?? ?????????? ?? ?????? ???? ???? ?? ???? ?? ?? ?? ???? ???? ?????????? ?????? ???? ???? ?? ???? ???????? ??????? ???????????? ???????? ?????????? ???????????? ? vmax? ???????????? ?????? ?? ???? ?? ?? ????i:jvij?vmax????????? ???? ???????????????????? ???????? ?? ?????? ???????????? ?????????? ?????????? ???????????????? ?? ???? ???? ? ??vmax

Exercise3(10points)

?? ?????? ???? ???????? ?? ?? ????????n??? ?????? ???????????? ???? ?? ?????????????????? ???? ?? ? ???? ???? ???????????? ?? ?? ?????????? ??????? k??? ?? ????k ????? ?????? ?????? ????k??? ???????? ???????????? ?? ?? ?????? ?????? ?????? ???????? ???????? ?? ???? ???? ?????? ?? ???????? ???? ?? ?? ?????????? ?? ? O(n ?k)????? ???????? ???? ???????????????? ?? ???????????????????? ???? ????? ????????????? ???????? ?????? ???? ?? ?????? k ??? ????????????????? ?? ???? ?????? ?????k??? ?? ???? ?????????? ???????? ???? ???? ??k ?? ???? ?????????????????????????? ???? ?? ???? ?????? ???? ???????? ?? ???????? ??????????????? ?????? ?????????? ?????????? ?????????? ?????? ???? ???? ???????????? ???? ???? ?????? ?? ???? ???????????? ???? ???????????? ?????????? ?????????? ????? ??? li? ???? ???????????? ?????? ?????????i? ???????? ?? ???????? ?????????? ?? ???? ?e??? ???????????? ?? ?? ?????? ??????????? ??????????????? ?? ???? ? (e)=P l i:e ?????????????????????????lii ???? ? ???? (e1;:::;em)? ???????? ? ??? ???? ?????????? ???? ????????k ???????? ?? ?????????? ???? ???? ??? i:= (ei)?? ???? ???? ???? ei? ??ei+1?????????? ?????? ?? ???? ????????? i> i+1? ??????????????? ???? ?? ???? ?? i= i+1???? ? ??????? ?????? ? m- 1 ?O(nk) ??? ? ?? ????????i:= i+1- i??? ??????????????? ?????? ???? ?????????????? ?? ?? ??? ???????????? ??i> ?k ?? ????????????? 0<i? ?k ?? ?????? ?????? ???? ???? ?????? ?????????????? ???? ????????????? ?? ?? ??????O(n ?k) ??? ? ??????? ?????? ???? ???? ?????? ??????????????????? ????????????? ?? ?? ??????O(n ?k) ? ??? ???????? ???????????? ?????????? ?????? ???? ?? ?O(n ?k)????? ???????? ???? ?????????????? ???????? ?????? ?? ???? ???? ?? ???????? ?? ? O(n ?k)????? ???????? ???? ?????????????? ?????????????? ???? ?? ???? ?? ???????????? ???? ?? ?? ?????????? ?????? ???? ?????????????? ?????? ???? ???? ?? k ?

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