16.unified Introduction to Computers and Programming. SOLUTIONS to Examination 4/30/04 9:05am - 10:00am

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1 16.unii Introution to Computrs n Prormmin SOLUTIONS to Exmintion /30/0 9:05m - 10:00m Pro. I. Kristin Lunqvist Sprin 00 Grin Stion: Qustion 1 (5) Qustion (15) Qustion 3 (10) Qustion (35) Qustion 5 (10) Qustion 6 (15) Qustion 7 (10) Totl 100 You v 55 minuts to tk tis xmintion. Do not in until you r instrut to o so. Tis is los ook xmintion. No xtrnl mtrils r prmitt, inluin lultors or otr ltroni vis. All nswrs must writtn in t xmintion ppr. Tis xmintion onsists o 7 qustions n 1 ps (not inluin tis ovr p). Count t numr o ps in t xmintion ppr or innin n immitly rport ny isrpny to t inviiltor. Soul you n to o so, you my ontinu your nswrs on t k o ps. Do not ort to writ your nm on p. 0

2 Prolm 1 - Quu (5 points) Consir t irulr quu o siz 10, s sown in t Fiur low (Strt stt). T irulr quu ontins lttrs A trou D. Assum t ollowin 9 oprtions tk pl in squn 1. Insrt ntry E. Insrt ntry F 3. Rmov on ntry. Rmov on ntry 5. Insrt ntry G 6. Insrt ntry H 7. Rmov on ntry 8. Insrt ntry I 9. Insrt ntry J Sow t ontnts o t irulr quu tr (Finl stt) prormin ll o t oprtions. Wr r t n til pointrs lot? Strt stt Finl stt J H pointr A B H pointr C Til pointr D Til pointr D E F G H I 1

3 Prolm MST (15 points) Usin t ivn rp low, wt is t minimum-wit spnnin tr? Wi loritm r you usin? Sow lrly, stp y stp, on t nxt p, ow t loritm is us. Finlly, rw t rsultin Minimum-wit spnnin tr r low. Givn Grp: Nm o loritm you r usin: Kruskl s loritm Minimum-wit spnnin tr: 6 3 5

4 3 3 3

5

6 Prolm 3 Bi-O (10 points) Prt ) Sow t omputtion o T(n) n t Bi-O omplxity or t o sown low. (6 points) Sttmnt Work untion Compr (Vlu1, Vlu : Flot ) rturn Flot is Rsult : Flot; Minimum : Flot :=.0; in - Compr i Vlu1 < Vlu tn ls Rsult := Vlu1; Rsult := Vlu; n i; rturn Minimum; n Compr; T(n) = = O(n) = O(1) Prt ) Wt is t rsult pss out y t prorm wn t input vlus r 10.8 n 10.? ( Points) T output is.0 us o t rturn Minimum; sttmnt. 5

7 Prolm A Tr Implmnttion (35 points) E 5 C 3 G 7 A 1 D Fiur 3. Orr Tr Prt. Din t A95 ror lrtion or t no in t tr sown in Fiur 3. (3 points) Not: T ott lin links to t prnt no, wil t soli lins link to t ilrn (mximum o two). typ No; typ No_ptr is ss No; typ No is ror n Ror; Elmnt Lt_Cil : No_ptr; Rit_Cil : No_ptr; Prnt : No_ptr; : Elmnt_typ; 6

8 Prt. Writ n loritm to prorm orr insrtion into t orr tr sown in Fiur 3. (18 points) Aloritm Crt two no pointrs Tmp, Nw_No. Allot mmory or Nw_No usin nw. Initiliz t ils o Nw_No Elmnt is st to input lmnt All pointrs r st to null I Root = null St root to Nw_No Els St Tmp to Root. St Fl to Fls Wil Fl is Fls I Tmp.Elmnt is smllr tn Elmnt Els I Tmp s no rit il Tmp.rit_il := Nw_No Nw_No.Prnt := Tmp St Fl to Tru Els Mov Tmp to Tmp.rit_il I Tmp s no lt il Tmp.lt_il := Nw_No Nw_No.Prnt := Tmp St Fl to Tru Els Mov Tmp to Tmp.lt_il 7

9 Prt. Implmnt your loritm s n A95 prour, wi pts t root no, n t lmnt to insrt, n prorms t orr insrtion oprtion. (10 points) Prorm Co prour Insrt (Root : in out No_ptr; Elmnt : in Elmnt_Typ) is in Tmp, Nw_No : No_ptr; Insrt : Booln; Nw_No:= nw No; Nw_No.Elmnt := Elmnt; Nw_No.Lt_Cil := null; Nw_No.Rit_Cil := null; Nw_No.Prnt := null; i Root = null tn Root := Nw_No; ls Insrt := Fls; Tmp := Root; loop xit wn Insrt = Tru; i Tmp.Elmnt < Elmnt tn i Tmp.Rit_Cil /= null tn Tmp:= Tmp.Rit_Cil; ls Tmp.Rit_Cil:= Nw_No; Nw_No.Prnt := Tmp; Insrt := Tru; n i; ls i Tmp.Lt_Cil/= null tn Tmp := Tmp.Lt_Cil; ls Tmp.Lt_Cil:= Nw_No; Nw_No.Prnt := Tmp; Insrt := Tru; n i; n i; n loop; n i; n Insrt; 8

10 Prt. Upt t tr sown low, tr insrtin t lmnts n 6 usin your loritm. Sow ll t rquisit links (inluin nulls) in t irm. ( points) E5 C3 G7 A1 D A6 9

11 Prolm 5 A Exption Hnlin 1. wit A.Txt_Io, A.Intr_Txt_Io, A.Unk_Dllotion;. 5. prour Dmo_Roust_Prormmin is sutyp My_Intr is Intr; 8. typ My_Intr_Ptr is ss ll My_Intr; My_Num : My_Intr; 11. My_Num_Ptr : My_Intr_Ptr; prour Fr is 1. nw A.Unk_Dllotion(My_Intr, My_Intr_Ptr); in 17. My_Num_Ptr := nw My_Intr; Fr(My_Num_Ptr); A.Txt_Io.Put("Pls ntr n intr: ");. A.Intr_Txt_Io.Gt(My_Num); 3.. My_Num_Ptr.All := My_Num; A.Txt_Io.Put(Intr'Im(My_Num_Ptr.All)); xption 9. wn Constrint_Error => 30. A.Txt_Io.Put_Lin("Uns Pointr Hnlin"); 31. wn A.Txt_Io.Dt_Error => 3. A.Txt_Io.Put_Lin("Tryin to ntr non intr vlu"); n Dmo_Roust_Prormmin; (10 points) Prt ) Wt is t prorm vior wn t usr ntrs lotin point numr? Justiy your nswr. ( points) T prorm will nrt onstrint rror on Lin us t usr is tryin to ss lry llot mmory Prt ) Wt is t prorm vior wn t usr ntrs vli intr n Lin is ommnt out? Justiy your nswr. (6 points) Wn lin is ommnt out, t onstrint rror is ris in lin 6 or xtly t sm rson s or: t mmory s n llot. 10

12 Prolm 6 Asymptoti Complxity Divi n Conqur (15 points) Wt is t Bi-O omplxity o t loritm sown low? Dtil t stps in omputin T(n) n O(n). 3Sort(A, lt, rit) i (lt < rit) irst_split := (lt + rit) / 3 son_split := (irst_split + rit)/ 3Sort(A, lt, irst_split) 3Sort(A, irst_split+1, son_split) 3Sort(A, son_split+1, rit) 1 T(n/3) T(n/3) T(n/3) Mr(A, lt, irst_split, son_split, rit) O(n) Tror T(n) = 3T(n/3) O(n) = 3T(n/3) + O(n) + C Tror orrltin to t simplii mstr torm: n k = O(n) k = 1 T(n/) = 3T(n/3) Tror: T(n) = O(n k lo n)= O(n 1 lo 3 n) = O(n lo 3 n) 11

13 Prolm 7 (10 points) Multipl Coi Qustions. For qustion, slt t orrt nswr rom t ois, n writ t osn lttr in t ox provi nxt to qustion. 1. T tr low is :. Full inry tr. Sort inry tr. Hp Answr A Tk look t t Tr ov, wi o t ollowin sttmnts is orrt?. Vrtx 13 is t Lvl 3. T it o t tr is 3. T it o t tr is B 3. T postix nottion o *+/ is. */+. +*/. *+/ A 1

14 . Wn it oms to stk, wi o t ollowin sttmnts is ls?. T pross o ltin n ojt is ll Pop. All insrtions n ltions o lmnts tk pl t t sm n o t t strutur. Stks r FIFO struturs C 5. I v put my nm in t uppr rit ornr on ll ps o t quiz. Ys. No. I will o it y 10m toy A/B/C 13

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