COMSC 2613 Summer 2000

Transcription

1 Programmg II Fal Exam COMSC 63 Summer Istructos: Name:. Prt your ame the space provded Studet Id:. Prt your studet detfer the space Secto: provded. Date: 3. Prt the secto umber of the secto whch you are erolled the space provded. 4. Prt the date the space provded. 5. You have mutes to complete ths examato. 6. You may use a calculator. 7. Referece materals are prohbted. You must complete ths test wthout the ad of course otes or referece texts. 8. Questos requrg wrtte aswers must be aswered usg stadard Amerca Eglsh. Aswers cotag spellg or grammatcal errors wll be gve o credt. 9. Aswers must be coded legbly. Aswers that caot be read by your structor wll be gve o credt.. You must do your ow wor. Scorg:. The table to the rght lsts the umber of raw pots avalable for each problem ad the total umber of raw pots that ca be eared o ths test.. Your score wll be ormalzed to a fracto of 3 pots. If s your ormalzed score, r s your raw score, ad T s the total umber r of raw pots, the 3. T Problem Avalable Mssed Eared Total 578 Norm. 3

2 Programmg II Fal Exam COMSC 63 Summer. ( pots) Fd a closed-form expresso for. > ), ( ( ) ( ) ( )( ) ( ) ( ) ( )( ) + + ( ) +

3 Programmg II Fal Exam COMSC 63 Summer L+.. (4 pots) Use mathematcal ducto to prove that ( ) Bass Step. Show that ( ) Left sde: ( ) Rght sde: Left sde Rght sde () Iducto Step. Assume that + ( ) for,, K,. Prove that ( ) ( + ) ( ) ( ) + ( + ) ( ) + + ( ) ( + ) 3

4 Programmg II Fal Exam COMSC 63 Summer 3. (3 pots) Draw a tree dagram of the heap that results from sertg the detfers gve Table. Use fucto heapsert to sert the detfers the order specfed Table. Table. Idetfers to be serted Order Idetfer obda ade mare laura are jula ree halle Order Idetfer grace fate elae dese cosette belle alce alce fate belle ree grace elae cosette obda laura mare halle ade jula are dese Fgure. Aswer to Problem 3. 4

5 Programmg II Key 3 Revso COMSC 63 Summer 4. (3 pots) Draw a tree dagram of the heap mplemeted array H, show Table, after the mmum elemet has bee removed. Elemet H[] cotas the setel ad s ever removed from the heap by deletg the mmum elemet. Table. Array H Idex Elemet Value Idex Elemet Value SMALL (3 pots) Wrte C declaratos for a lst mplemeted usg a dyamcally allocated array that ca be used to store arbtrarly log detfers. Be sure to clude ay declaratos that are requred to support terato fuctos lsttop, lsteol, ad lstsucc. Code Value typedef struct lst_t { 4 t sze; 3 t cout; 3 char **L; 9 t pos; 3 } Total Fgure. Aswer for Problem 3. 5

6 Programmg II Key 3 Revso COMSC 63 Summer 6. (64 pots) Code fucto lstcreate that creates a empty lst of character strgs. Use the defto of the achor ad elemets you defed problem 5. Code Value lst_t *lstcreate(t sze) 7 { lst_t *l(lst_t)malloc(szeof(lst_t)); 6 l->szesze; 6 l->cout; 6 l->l(char**)calloc(sze,szeof(char*)) 9 l->pos-; 6 retur l; 3 } Total 64 6

7 Programmg II Key 3 Revso COMSC 63 Summer 7. (93 pots) Code fucto lstsert that serts a detfer to a lst defed by data structures you specfed problem 5. Isert detfers alphabetcal order. Employ fucto maed to allocate storage for detfers passed to fucto lstsert. You may also assume the exstece of fuctos lstfull, lsterror, ad maed whose hose prototypes are gve below. t lstfull(lst_t *l); vod lsterror(char *msg,t le); char *maed(char *d); Code Value vod lstsert(lst_t *l, char *ey) { t a; 4 f (lstfull(l)) lsterror("full", LINE ); 4 al->cout++; 7 whle(a> && strcmp(ey,l->l[a-])<) { strcpy(l->l[a],l->l[a-]); 8 a--; 3 } l->l[a]maed(ey); } 93 7

8 Programmg II Key 3 Revso COMSC 63 Summer 8. (73 pots) Employ the defto of T()O(f()) to fd the upper boud o the rate of growth for fucto f8. a. (8 pots) Complete Table 3 ad fd T(). b. (3 pots) Express T() ope form usg summato symbols ( Σ ). Place your aswer the space provded. c. ( pots) Fd T() closed form wthout summato symbols. Place your aswer the space provded. d. (4 pots)fd c m ad c. Place your aswer for c m ad c the space provded. e. (33 pots) Solve T ( ) cf ( ). Fd the smallest postve teger value for. vod f8(t ) { t a,b,sum; for (a;a<*;a++) for (b;b<a;b++) sum++; } Table 3. Tmg aalyss for fucto f8. Le Code Cost Value vod f8(t ) { t a,b,sum; 3 a; 4 whle (a<*) { 8 5 b; same as le 4 6 whle (b<a) { a a a b 7 sum++; same as le 6 8 b++; same as le 6 9 } same as le 4 a++; same as le 4 } } Ope Form T ( ) 3 a a b + 4 a + 3 Closed Form T ( ) f() 4 f ( ) c m 3 c m c 5 c solve T ( ) cf ( ) Let x x 5x (5 pots) Complete Tables 5 ad 6 that trace the executo of fucto bs. Fucto bs mplemets a bary search. Each row represets oe terato of the loop fucto bs. Values 3 8

9 Programmg II Key 3 Revso COMSC 63 Summer array A are gve Table 4. The ey o whch to search Table 5 s ad the ey o whch to search Table 6 s 4. Table 4. Values array A dex value Table 5. Bary search, lo h lo<h m A[m] A[m] A[m]> A[m]< 3 yes 6 7 o yes o 5 yes 5 o o yes 3 5 yes 4 yes o o Table 6. Bary search, 4 lo h lo<h m A[m] A[m] A[m]> A[m]< 3 yes 6 7 o yes o 5 yes 5 o yes o yes o o yes yes 3 o o yes o t bs(t A[], t, t ) { t lo,h-; whle (lo<h) { t m(lo+h)/; f (A[m]) retur m; f (A[m]>) hm-; else lom+; } retur -; } 9

10 Programmg II Key 3 Revso COMSC 63 Summer. (55 pots) Descrbe a algorthm that serts a ey to a led lst. The ey s a detfer composed of a strg of characters. Idetfers o the lst appear lexcographc (alphabetc) order. Each ode o the lst has a poter to the ode referecg the ext larger detfer ad a poter to the ode referecg the ext smaller detfer. The lst s ot crcular. The ode referecg the smallest detfer has a ull poter to the ode referecg a detfer smaller tha the smallest detfer. Smlarly, the ode referecg the largest detfer has a ull poter to a ode referecg a detfer larger tha the largest detfer. The lst s achored by a structure cotag members that pot to odes referecg the smallest ad largest detfers. Storage for the achor ad odes s allocated dyamcally. a) (6 pots) Draw a pcture of the lst. l lst_t * lst_t smallest largest lst_e* lst_e* lst_e smaller d larger lst_e* char* lst_e* a d a lst_e smaller d larger lst_e* char* lst_e* e v e lst_e smaller d larger lst_e* char* lst_e* lst_e* l s e lst_e smaller d larger lst_e* char* lst_e* e lst_e* s u e lst_e smaller d larger lst_e* char* lst_e* z o e Fgure 3. Aswer to problem a.

11 Programmg II Key 3 Revso COMSC 63 Summer b) (3 pots) Idetfy ad descrbe boudary codtos. Idetfy those odes that requre specal maagemet.. Determe whe the lst s empty. Isert the frst ode ad assg both poters the achor to the frst ode. Both members the frst ode to the ext larger ode ad the ext smaller ode are ull.. Determe whe the ey s the smallest ey o the lst. Isert the ode before ay ode o the lst. Assg the referece to the ew ode to member smallest the achor. 3. Determe whe the ey s the largest ey o the lst. Isert the ode after ay ode o the lst. Assg the referece to the ew ode to member largest the achor. c) (5 pots) Idetfy ad descrbe those odes that do ot requre specal hadlg.. The lst caot be empty.. The ey caot be the smallest ey. 3. The ey caot be the largest ey. d) (5 pots) Wrte a step-by-step descrpto of your algorthm.. Determe whe the lst s empty. Isert the frst ode ad assg both poters the achor to the frst ode. Both members the frst ode to the ext larger ode ad the ext smaller ode are ull.. Determe whe the ey s the smallest ey o the lst. Isert the ode before ay ode o the lst. Assg the referece to the ew ode to member smallest the achor. 3. Determe whe the ey s the largest ey o the lst. Isert the ode after ay ode o the lst. Assg the referece to the ew ode to member largest the achor. 4. Assg local varable e to pot to the ode referecg the smallest ey. 5. Traverse the lst, gog to the ext larger ode, as log as the put ey s larger tha the ey the curret ode refereced by local varable e. 6. Stop o the ode referecg a ey that s just larger tha the put ey. The ode may referece a ey equal to the put ey. 7. If the put ey ad the ey the ode refereced by local varable e are detcal stop. Do ot sert duplcate eys. 8. Allocate storage for the ew ode usg local varable. 9. Bd the ew ode to the lst.. Bd the lst to the ew ode.