Suppose a list of integers is [5, 7, 2, 9, 11, 10, 12].Suppose we conduct the bubble sort algorithm on this list.def BubbleSort(a):n = len(a)for i in (0, n):for j in range(0, n - i - 1):return aif a[j] > a [j+1] :temp = a[j]a[j] = a[j+1]a[j+1] = tempWhat are the values of the following (where n is the length of the list)?n =||a[1] =a[5] ===When i = 1 and j = 1 enter the correct values for the following variable:a[1] =a[5] =When i = 2 and j = 1 enter the correct values for the following variable:a[2] =a[6]=2.

If n is the length of the list:n: The length of the list is 7, so n = 7.a[1]: This refers to the…

Answered: Suppose a list of integers is [5, 7, 2,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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]
Let x be a natural number with a binary representation where the difference between the number of 1 bits with an even index and the number of 1 bits with an odd index is a multiple of 3. Prove that x is a multiple of 3.
According to the Master Theorem, what is the run time of the algorithm described by the function T(n) - 4T () +e(nº")
4. Consider the set of all strings of a's, b's, c's and d's. (a) Make a list of all of these strings of length zero, one, and two that do not contain the pattern bb. (b) For each integer n > 0, let sn = the number of strings of a's, b's, c's and d's of length n that do not contain the pattern bb. Find so, s1, and s2. (c) Find a recurrence relation for the sequence s0, S1, S2, . ..
Let S be the set of all bit strings (strings of 0's and I's) Select one: O A. f(s) = the string obtained by moving the first bit of s to the end of the string. (For example, f(1001101) = 0011011) O B. f(s) = the string obtained from s by interchanging 0's and I's. (For example, f(11000) = 00111) O c. f(s) the string & with a 1 bit appended at the end. (For example, f(1101) = 11011) O D. f(s) the reversal of s. (For example, f(110) = 011) length at least 2. Which of the following functions f : S → S is not onto S?
12. A parking lot has visitor spaces, numbered from 0 to 30. Visitors are assigned parking spaces using the Hashing function h(k) = k mod 31, where k is the number formed from the license plate. Which spaces are assigned by the Hashing function to cars that have the following license plates: 317, 007, 102, 111, 918 ? (x2 + 1) mod 15, show how the data 5, 8, 20, 32 and 13. For the Hashing function h(x) 40 would be inserted in the order given in initially empty cells indexed 0 to 14.
Express efficient algorithms clearly for the below problem. Also, explain the asymptotic behavior of the algorithm. Assume a list of building blocks. Each block is a cube with a given size, and has ontop, a list of all the other blocks that can be placed directly on top of it. You are also given a number k. Determine whether or not you can build a tower with block 0 at the bottom and block 1 at the top using no more than k blocks. If so, we want to know the height of the shortest such tower. Example: given 0: 8, ontop=2,3 1: 15, ontop=0 2: 11, ontop=1,3,4 3: 10, ontop=0,1,2 4: 7 ontop=1 if k were 2 the answer would be no. if k were 4 the answer would be yes, with height 33 (block0 then block3 then block1)
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.
Prove that multiplication on N preserves order: (a) If a = b,then ac = bc. (b) If a < b,then ac < bc.
(a) For integers a, b, q, r, prove that if a = bq + r then (a, b) = (b, r). (b) Determine (1000, 2025) by using the Euclidean algorithm. Then express the answer as a linear combination of 1000 and 2025. Show all your working. (c) Suppose that G = (a), a ‡e, and a5 : = e. Construct a Cayley table for the group (G,.). (d) Determine the right cosets of ((1 2), [1]) € S3 × Zi₂. (e) Find the subgroups of Z24.
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
Sort 6, 2, 5, 4, 3 in increasing order using the following algorithm sort(a(1),..., a(n): real numbers with n ≥ 2) for i:=1 to n-1 for j:=1 to n-i if a(j) > a(j+1) then interchange a(j) and a(j+1) {a(1),...,a(n) is in increasing order} Which of the following steps do not attained during the procedure? 1. 2, 5, 6, 4, 3 II. 2, 6, 4, 5, 3 III. 2, 4, 3, 5, 6 IV. 2, 6, 5, 4, 3 V. 2, 4, 5, 6, 3 II and V I and II III and IV only V

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