15 marks A CPSC 121 student who was feeling bored during the three days between midterm 1 and the release of assignment 3 wrote a program to generate all sequences of n bits that do not contain two consecutive O's The student found that there were 2 such sequences for n 1 (the sequences are 0 and 1 ), 3 for n 2 (the sequences 01 , 10 and 11 ), and 5 for n 3 He then hypothesized that the number S(n) of these sequences satisfies the equation S(n) n 1 if n 3 One of the student's friends (a MATH major) then confirmed this, and told him that S(n) is approx imately equal to 1 (1 75 152 a 3 marks The student's program generates 50 sequences per seconds Fill in the following table with the largest value of n for which his program terminates for each duration indicated Duration Largest value of n Duration Largest value of n 1 second 1 minute 1 hour 1 day 1 month 1 year 10 years 100 years b 2 marks One of the CPSC 121 TAs then tells the student a C version of the program would run 50 times faster than the Dr Racket version the student wrote Will the C version help the student solve the problem for a much larger value of n than the Dr Racket version, when the program is allowed to run for 100 years Why or why not 15 marks A CPSC 121 student who was feeling bored during the three days between midterm 1 and the release of assignment 3 wrote a program to generate all sequences of n bits that do not contain two consecutive O's The student found that there were 2 such sequences for n 1 (the sequences are 0 and 1 ), 3 for n 2 (the sequences 01 , 10 and 11 ), and 5 for n 3 He then hypothesized that the number S(n) of these sequences satisfies the equation S(n) n 1 if n 3 One of the student's friends (a MATH major) then confirmed this, and told him that S(n) is approx imately equal to 1 (1 75 152 a 3 marks The student's program generates 50 sequences per seconds Fill in the following table with the largest value of n for which his program terminates for each duration indicated Duration Largest value of n Duration Largest value of n 1 second 1 minute 1 hour 1 day 1 month 1 year 10 years 100 years b 2 marks One of the CPSC 121 TAs then tells the student a C version of the program would run 50 times faster than the Dr Racket version the student wrote Will the C version help the student solve the problem for a much larger value of n than the Dr Racket version, when the program is allowed to run for 100 years Why or why not

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15 marks A CPSC 121 student who was feeling bored during the three days between midterm  1 and the release of assignment  3 wrote a program to generate all sequences of n bits that do not contain two consecutive O's  The student found that there were 2 such sequences for n 1 (the sequences are  0  and  1 ), 3 for n   2 (the sequences  01 ,  10  and  11 ), and 5 for n   3  He then hypothesized that the number S(n) of these sequences satisfies the equation  S(n)  n  1 if n 3 One of the student's friends (a MATH major) then confirmed this, and told him that S(n) is approx  imately equal to 1 (1 75  152 a   3 marks  The student's program generates 50 sequences per seconds  Fill in the following table with the largest value of n for which his program terminates for each duration indicated  Duration Largest value of n   Duration Largest value of n 1 second 1 minute 1 hour 1 day 1 month 1 year 10 years 100 years b   2 marks One of the CPSC 121 TAs then tells the student a C version of the program would run 50 times faster than the Dr  Racket version the student wrote  Will the C version help the student solve the problem for a much larger value of n than the Dr  Racket version, when the program is allowed to run for 100 years  Why or why not  15 marks A CPSC 121 student who was feeling bored during the three days between midterm  1 and the release of assignment  3 wrote a program to generate all sequences of n bits that do not contain two consecutive O's  The student found that there were 2 such sequences for n 1 (the sequences are  0  and  1 ), 3 for n   2 (the sequences  01 ,  10  and  11 ), and 5 for n   3  He then hypothesized that the number S(n) of these sequences satisfies the equation  S(n)  n  1 if n 3 One of the student's friends (a MATH major) then confirmed this, and told him that S(n) is approx  imately equal to 1 (1 75  152 a   3 marks  The student's program generates 50 sequences per seconds  Fill in the following table with the largest value of n for which his program terminates for each duration indicated  Duration Largest value of n   Duration Largest value of n 1 second 1 minute 1 hour 1 day 1 month 1 year 10 years 100 years b   2 marks One of the CPSC 121 TAs then tells the student a C version of the program would run 50 times faster than the Dr  Racket version the student wrote  Will the C version help the student solve the problem for a much larger value of n than the Dr  Racket version, when the program is allowed to run for 100 years  Why or why not

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15 marks A CPSC 121 student who was feeling bored during the three days between midterm #1 and the release of assignment #3 wrote a

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