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 is 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 28? For each integer n 2 1, let s, be the number of operations the algorithm executes when it is run with an input of size n. Then s, = 7 v and for each integer k 2 1. Therefore, s,, s,, S2, is a geometric sequence V with constant final value x which is 2 . So, for S = every integern2 0, s, = 7 It follows that for an input of size 28, the number of operations executed by the algorithm is s27 which equals 939524096

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 is 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 28? For each integer n 2 1, let s, be the number of operations the algorithm executes when it is run with an input of size n. Then s, = 7 v and for each integer k 2 1. Therefore, s,, s,, S2, is a geometric sequence V with constant final value x which is 2 . So, for S = every integern2 0, s, = 7 It follows that for an input of size 28, the number of operations executed by the algorithm is s27 which equals 939524096

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

For the list [44, 18, 74, 61, 42, 31], how will the array elements look like after second pass (after i-2 but before i=3) of the Insertion sort algorithm? def insertionSort(a): for i in range(1,len(a)): currentvalue = a[i] position = i while position>0 and a[position-1]>currentvalue: a[position]=a[position-1] position = position-1 a[position]=currentvalue return a [18, 44, 74, 61, 42, 31] [18, 44, 61, 74, 42, 31] [18, 42, 44, 61, 74, 31] [18, 31, 42, 44, 61, 74]
Solve the following Integer Programming problem using the graphical or branch and bound algorithm, where n=5, s=13.
According to the Master Theorem, what is the run time of the algorithm described by the function T(n) - 4T () +e(nº")
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.
The extended Euclidean algorithm computes the gcd of two integers ro and r₁ as a linear combination of the inputs. gcd(ro, r₁) = s.ro + t •rı Here s and t are integers known as the Bezout coefficients. They are not unique. The algorithm works like the standard Euclidean algorithm, except that at each stage the current remainder ri is expressed as a linear combination of the inputs. ri = siro + tir₁. This produces a sequence of numbers To, T1, Tn-1, Tn where r = 0 and gcd(ro, r₁) = Tn-1. Suppose that ro = 420 and T1 = 382. Give the sequence ro, T1,..., Tn-1, în in the blank below. Enter your answer as a comma separated list of numbers. What is GCD(420,382)? What is s? What is t?
1. For each pair of integers m and n, use the division algorithm to divide m by n. Write the result in the form m = q⋅n + r where 0 < r < n. a. m = 32 and n = 9 b. m 62 and n = 7 = c. m -45 and n = 11 d. m 3 and n = 8 2. For each pair of integers a and b, use the Euclidean Algorithm to find the GCD(a, b). Then use Theorem 92 to find the LCM(a, b) a. a = 48 and b = 54 b. a = 330 and b = 156 c. a=1188 and b = 385 3. For each pair of integers m and d, calculate m mod d. Show your work! a. m 43 and d = 9 b. m 50 and d = 7 c. m 28 and d = 5 d. m = 30 and d = 2