The complexity of the following code is int i, j, k = 0; for (i = n / 2; i <= n; i++) { for (j k = k + n / 2; %3D 2; j <= n; j = j * 2) { %3D %3D %3D Select one: a. O(nlgn) b. O(n) c. O(n'Ign) d. O(n)
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- Assume that each of the expressions below gives the processing time T(n) spent by an algorithm for solving a problem of size n. Select the dominant term(s) having the steepest increase in n and specify the lowest Big-Oh complexity of each algorithm. For example, the dominant term in 0.1n + 10n4 is 10n4 and it is O(n4). Expression Dominant term(s) O(. . .) 5 + 0.001n3 + 0.025n 500n + 100n1.5 + 50n log10 n 0.3n + 5n1.5 + 2.5 · n1.75 n2 log2 n + n(log2 n)2 n log3 n + n log2 n 100n + 0.01n2 0.01n + 100n2 2n + n0.5 + 0.5n1.25 0.01n log2 n + n(log2 n)2 100n log3 n + n3 + 100n1. Input: G = (V, E)2. Output: MIS I of G3. I ← ∅4. V ← V5. while V = ∅6. assign a random number r(v) to each vertex v ∈ V7. for all v ∈ V in parallel8. if r(v) is minimum amongst all neighbors9. I ← I ∪ {v}10. V ← V \ {v ∪ N(v)}This algorithm terminates in O(log n)rounds with good probability. The stepsof the algorithm between lines 7–10 can be performed in parallel which will providea speedup.Make Python Implementation this algorithm in sequential formQuestion 1: Analyze the following codes for Time and space complexity. Determine Big O for the following code fragments in the average case. Assume that all variables are of type int. (d) for (i=0; i < n-1; i++) { for (j=i+1; j < n; j++) { tmp = A[i][j]; A[i][j] = A[j][i]; A[j][i] = tmp; } } (e) sum = 0; for (i=1; i<=n; i++) { for (j=1; j<=n; j*=2) { sum++; } } (f) sum = 0; for (i=1; i<=n; i/=2) { for (j=1; j<=n; j++) { sum++; } }
- 6.Coding-----""Euler's totient function, also known as phi-function ϕ(n),counts the number of integers between 1 and n inclusive,which are coprime to n.(Two numbers are coprime if their greatest common divisor (GCD) equals 1)."""def euler_totient(n): """Euler's totient function or Phi function. Time Complexity: O(sqrt(n)).""" result = n for i in range(2, int(n ** 0.5) + 1): if n % i == 0: while n % i == 0: n //= i.Question 1: Analyze the following codes for Time and space complexity. Determine Big O for the following code fragments in the average case. Assume that all variables are of type int. (j) sum1 = 0; for (k=1; k<=n; k*=2) { for (j=1; j<=n; j++) { sum1++; } } sum2 = 0; for (k=1; k<=n; k*=2) { for (j=1; j<=k; j++) { sum2++; } }Assume that each of the expressions in the following table has processing time T(n) to solve a problem of size n. Identify the dominant term(s) having the growing increase in n and specify the Big-Oh complexity. Expression Dominant term(s) Big-Oh A.1 8 + 0.081n2 + 0.040n A.2 100 + n log2 n A.3 100n + 0.081 log3 n + n3 A.4 0.081 log4 n + 81n
- 11.Code so on for_A pure full Implement c/c++ to evaluate round robin algorithm. You must use the job list given here: Job (1) arrive at CPU cycle1 Job (2) arrive at CPU cycle2 Job (3) arrive at CPU cycle36 I/O (32) CPU (54) I/O (45) CPU (20) I/O (40) CPU (48) CPU (39) CPU (48) I/O (55) Your job list must contain CPU bust and I/O bust as above. Quantum time = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60] The evaluation of the most suitable quantum time needs to consider the followingperformance metrics, but not limited to:(i) Turnaround time of the jobs;(ii) Waiting time of the jobs; and(iii) Number of interrupts incurred The code must able to read csv file format of the job list as input file. The code must able for user to input time quantum.. ..Given two sorted arrays nums1 and nums2 of size m and n respectively, return the median of the two sorted arrays. The overall run time complexity should be O(log (m+n)). Example 1: Input: nums1 = [1,3], nums2 = [2] Output: 2.00000 Explanation: merged array = [1,2,3] and median is 2. Example 2: Input: nums1 = [1,2], nums2 = [3,4] Output: 2.50000 Explanation: merged array = [1,2,3,4] and median is (2 + 3) / 2 = 2.5. Constraints: nums1.length == m nums2.length == n 0 <= m <= 1000 0 <= n <= 1000 1 <= m + n <= 2000 -106 <= nums1[i], nums2[i] <= 106 Write the whole code in python language Attach the code outputs also and explain the implementation.Given two sorted arrays nums1 and nums2 of size m and n respectively, return the median of the two sorted arrays. The overall run time complexity should be O(log (m+n)). Example 1: Input: nums1 = [1,3], nums2 = [2] Output: 2.00000 Explanation: merged array = [1,2,3] and median is 2. Example 2: Input: nums1 = [1,2], nums2 = [3,4] Output: 2.50000 Explanation: merged array = [1,2,3,4] and median is (2 + 3) / 2 = 2.5. Constraints: nums1.length == m nums2.length == n 0 <= m <= 1000 0 <= n <= 1000 1 <= m + n <= 2000 -106 <= nums1[i], nums2[i] <= 106
- Computer Science Given 2 arrays X[1...n] and Y[1...m], provide time analysis in term n and m successor (X[1...n]. Y[1...m]): set sucessor[1...m] to infinitive for each 1<= i <=n: for each 1<= j <=m: if Y[j] < X[i] and X[i] < successor[j]: successor[j] = X[i] return successorWrite a C++ code for the given problem: Given two arrays X and Y of positive integers, find the number of pairs such that xy > yx (raised to power of) where x is an element from X and y is an element from Y. Input: M = 4, X[] = [2 3 4 5] N = 3, Y[] = [1 2 3] Output: 5 Explanation: The pairs for the given input are 21 > 12 , 31 > 13 , 32 > 23 , 41 > 14 , 51 > 15 . Expected Time Complexity: O((N + M)log(N)) Constraints: 1 ≤ M, N ≤ 105 1 ≤ X[i], Y[i] ≤ 103Let, the time complexity of each of the following code snippets be T(n). Find out a tight bound for T(n) in Big-Theta () notation. for (i=n, i>=1; i=i/3) p=2 while(p<n) print(“hello”) p=p*p