Computer Science Foundation Exam. August 12, Computer Science. Section 1A. No Calculators! KEY. Solutions and Grading Criteria.

Transcription

1 Computer Sciece Foudatio Exam August, 005 Computer Sciece Sectio A No Calculators! Name: SSN: KEY Solutios ad Gradig Criteria Score: 50 I this sectio of the exam, there are four (4) problems. You must do all of them. The weight of each problem i this sectio is idicated with the problem. Partial credit caot be give uless all work is show ad is readable. Be complete, yet cocise, ad above all be eat.

2 . [5 poits 5 pts each] Aswer each of the followig timig questios cocerig a algorithm of a particular order ad a data set of a particular size. Assume that the ru time is affected oly by the size of the data set ad ot its compositio ad that is a arbitrary iteger. Show your work ad place your fial aswer i the box. (a) For a O( log ) algorithm, oe data set with 3 takes 6 secods. How log will the same algorithm take if the size of the data set is icreased to 56? Deduct poit for each simple math/algebra error. Deduct 3-5 poits for improper techique depedig o mistake sec 3log 3 3(5) 56 log T 048 0T 56(8) T 0.48sec 0 (b) For a O( ) algorithm, oe data set with 6 takes 4 secods. What is the largest size data set that ca be executed by this algorithm i 60 secods? Deduct poit for each simple math/algebra error. Deduct 3-5 poits for improper techique depedig o mistake (c) Suppose you have two differet algorithms that both correctly solve a particular problem. Oe of the algorithms is O(!) ad the other algorithm is O( 3 ). Which of the algorithms takes loger to execute whe 5? The O( 3 ) 5! algorithm takes the loger time > 0 so the O( 3 ) algorithm takes loger whe 5 Deduct poit for each simple math/algebra error. Deduct 3-5 poits for improper coclusio depedig o how/why they aswered icorrectly.

3 For parts (a)-(c).. [5 poits 5 pts each] Show all work ad Deduct place your poit fial for aswer each simple i the box math/algebra provided. error. (a) Give the followig pseudocode segmet, Deduct determie 3-5 poits the for value improper of x whe techique the for depedig loops ed i terms of. o mistake (icludig use of wrog closed form). x 0; for i to 3* do 3 5 for j to - do x x + j; ( )( ) j 3 j ( 3 + ) ( )( 3 + ) (b) Give the followig pseudocode segmet, determie the value of x whe the for loops ed i terms of. x 0; for i to * do for j to do if (j < i) the x x + ; 3 j k k ( + ) 4 3 (c) Fid the closed form for the followig sequece. S (-) + (-) S ( ( ) + ( )) ) ( )() i ( )() 3

4 3. [0 poits] Show the results of each pass of the sortig algorithm of your choice o the followig usorted array. You may choose from (a) the bubble sort, (b) the selectio sort, ad (c) the isertio sort. Choose oe () of these sortig techiques oly ad show the effect o the array after each pass of the sortig techique of your choice. Clearly idicate i the box provided the sortig algorithm you have selected. Assume the elemets are to be sorted ito ascedig order. You may stop illustratig passes whe the array becomes sorted. The usorted array I have chose the Bubble Sort smallest to largest Iitial Deduct 3-4 poits if they do ot specify which sortig techique they utilized. Deduct 4-5 poits if they specified oe techique but actually used aother (mixed up the ames of the sorts). Deduct - poits for improper positioig of values i the array after a pass has bee made. Ofte i CS whe a questio such as this appears o a exam, there will be several studets who develop very creative sorts, so be sure that they are applyig oe of the specified sortig techiques. 4

5 I have chose the Bubble Sort largest to smallest Iitial I have chose the Isertio Sort Iitial

6 I have chose the Selectio Sort smallest to largest Iitial I have chose the Selectio Sort largest to smallest Iitial

7 4. [0 poits] Give the sequece of operatios show below o their respective data structures, clearly show the fial state (i.e., the cotets) of each of the data structures. Assume that the data structures ivolved are dyamic (ot arrays). Draw your data structures carefully ad label them appropriately. Poits will be deducted if the data structures are ot properly labled! push(4) push(5) push(6) equeue(pop( )) equeue(pop( )) equeue(pop( )) push(dequeue( )) push(dequeue( )) push(dequeue( )) Deduct 4-5 poits if the data structures are ot properly labeled as to type ad where the top, frot, ad rear are located. I ve had a questio like this o CS exams before ad sometimes the studet will attempt to solve this problem with a sigle data structure rather tha usig push ad pop o a stack ad equeue ad dequeue o a queue. 6 top frot rear 5 4 ull ull ull stack after first 3 push operatios, queue empty at this poit frot rear ull ull top queue after first 3 equeue operatios, stack is ow empty after 3 pops stack fial state: top frot rear ull ull ull Code reversed cotets of the stack usig a queue. 7