A certain computer algorithm executes twice as many operations when it is run with an input of size k as when it is run with an input of size k - 1 (where k s an integer that is greater than 1). When the algorithm is run with an input of size 1, it executes seven operations. How many operations does it execute when it is run with an input of size 23? For each integer n ≥ 1, let s-1 be the number of operations the algorithm executes when it is run with an input of size n. Then so = 7 Therefore, S0, S₁, S₂,... is a geometric sequence ✔✔, which is 2 which equals 29360128 size 23, the number of operations executed by the algorithm is S 22 ✔✔with constant multiplier ✓ and Sk = ✔. So, for every integer n ≥ 0, Sn= 2sk-1 ✓ for each integer k ≥ 1. X. It follows that for an input of

Start Fill in the missing numbers of the sequence generated by Euclid's algorithm on inputs 70 and 15. gcd(70, 15) yields sequence: 70 15 Ex: 5 Ex: 5 0 Check cative inverse mod n 1 Next 2

Solve the following Integer Programming problem using the graphical or branch and bound algorithm, where n=5, s=13.

Jump to level 1 Fill in the missing numbers of the sequence generated by Euclid's algorithm on inputs 58 and 10. gcd(58, 10) yields sequence: 58 10 Ex: 5 Ex: 5

A student is tracing the following algorithm. The function INT gives the integer part of any number, eg INT(2.3) = 2 and INT (6.7) = 6. Line 10 Input A, B Line 20 Let C = INT(A ÷ B) Line 30 Let D = B × C Line 40 Let E = A – D Line 50 If E = 0 then go to line 90 Line 60 Let A = B Line 70 Let B = E Line 80 Go to line 20 Line 90 Print B Line 100 Stop Trace the algorithm in the case where the input values are: (a) (i) A = 36 and B = 16; (ii) A = 11 and B = 7. (b) State the purpose of the algorithm.