Question

A. Write an algorithm in pseudocode, which prints all strings of length 6 where the first three characters are any symbol from X={!,@,#,$,%,^}, the 4^th and 5^th characters are any digit 0,1,…9, and the last character is any digit 1,2,…9.

How many times will the print command be called (e.g. how many 6-character strings will be printed)?

B. Let g(n)=n³ + 2n² - 5. Determine the big-theta estimate of f. A complete response will include analysis of: , and .

C. How many compares of the form    will the following algorithm perform on a list of length n? Express your answer as a rational expression in terms of n.

for $4Pi0+1u0xuwAAAAASUVORK5CYII=$ do

         for do

                 if then swap $8GYbT8mpCzFa4AAAAASUVORK5CYII=$ and $0AZF9BIt7GBqkAAAAASUVORK5CYII=$

Answer 1

Sol. Given! prints all strings of length 6. first three characters are any synd for x=!,@,#,#2:1.,1}.. y = {0, 1, 2} Z ={1,2,3,4,5,6,7,8,93 All strings of length it when ist of ith character are the forum X". Second charactose from "y" tised thired charactor towns "2"

@ o 2 r for it to length (2) for jki length lyn lr for kal length (3) 6 [print (x(i), y(), alk), x(e)] Given P sendood the print command will be called 942 (Flul xfylxle1x1x13. Given, gin) = n3+ anzus. ş for all ry, I} a glini cn3+an +5. < n² + Zn²+5n3 ' =sms - And also be gin = n3tants {for all ny,2} >n²+zn2 - zn3 Equation ③ & ne g(n) < sn} & {n>,2} n3 ginssn² {n7,23 . olg) = n3 2(g) = n3 ; 0(g) = n3 * Rebloce f by g to the problem is place. Olf), (f), off). © Givent it {1,2,...n-ię do it {1+1, 2, -gn-izdo af ne>x; then swap x; & dy i=1 J =250 nolana i-a > J=ano -nal n-a

üsn-2 → j =net til i=n-1 ;=$} in total = 0+1+---+(n-3)+(n-2) In-2)(n-2+1) 2 Total = ln-1 (n-3)