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What is the order of each of the following functions?
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- Question 19. The following function f uses recursion: def f(n): if n 0 a <- a +i+ (1-1) return a c) def f(n): arr [0] <- 0 arr[1] <- 1 if n <= 1 return arr [n] else for i in 2..n arr [i] <- arr[i-1] + arr[i-2] return arr [n] d) def f(n): arr[0..n] <- [0, .., n) if n <= 1 return arr [n] else a <- 0 for i in 0..n a <- a + arr [i] return aarrow_forwardQ3 (Q5, Section 2.3 in the Textbook): Order the following functions according to their order of growth (from the lowest to the highest): (n – 2)!, 5 lg(n + 100)1º, 2²", 0.001n“, 3n³ + 1, ln²n, Vñ, 3".arrow_forwardFor each of the following function, indicate the class Q(n) the function belongs (use the simplest g(n) possible in your answer. a) (n2 + 1)10 b) 2nlog2(n+2)3 + (n+2)3log2(n/2) c) 8n+5 + 15n+1 d) n + 3n + n2 + 4narrow_forward
- Order the following functions by growth rate 250 N VN N1.5 N? NlogN NloglogN Nlog?N Nlog(N?) 2/N 2N 37 N²logN N3 Indicate which of the functions grow at the same rate.arrow_forwardOrder the following functions by asymptotic growth rate (number 1 is the best algorithm, and number 3 is the worst). 4nlog n+2n 2log n n³ + 2arrow_forwardWrite a function that given an integer N returns the maximum possible value obtained by deleting one 5 digit from the decimal representation of N it is guaranteed that N will contain at least one 5 digitarrow_forward
- List the following functions from increasing slower to faster order: n°, nlogn, n!, logn, n,,n², log(n!)arrow_forwardYihan recently learned the asymptotical analysis. The key idea is to evaluate the growth of a function. For example, she now knows that n² grows faster than n. She wants to know whether she really understands the idea, so she has created a little task. First of all, she found a lot of functions here: 91 3n log n² 92: n! log(n!) 93 911 √n 912 log log n 98 2n+1 913 (n+1)! 918 nlogn 99 ln ln n 914 Vlogn 919 5n² 13n+6 910: 10000 915 log √n 920 n/logn Note: log n = log₂ n; ln n = log n; log² n = = (log n)²; n! is the factorial of n, i.e., n! = 1 × 2 × · • × n. Reading the long list, Yihan realized that things were not as simple as she thought. Could you help her with the following problems? For all the questions in this problem, you only need to show your answer without explaining. The only exception is question (4), where you need to show proofs or explanations. (1) 94 : n³ 95 log² n (2) n² + n (3) 96 916 n 97 917 22 What does polylogarithmic mean (use O(.), N(.), w(.), ©(.), o(.) to…arrow_forwardWrite a program that computes the following: sigma summation i=0 to N (i^3 +2N)arrow_forward
- Which of the following is the time equation of the Hesap function? Hesap(n) if n==0 return 1 else return Hesap(n/2)*Hesap(n/2) end end A.T(n) = 2T(n/2) + θ (n) B.T(n) = T(n/2) + θ(n) C=T(n) = 2T(n/2) + θ(1) D. T(n) = T(n/2) + θ(1)arrow_forwardSIC ty.com/player/ ster A O O Consider the following code which will print the nth term of a Fibonacci sequence. def fibonacci(n): if n English SAVE Sign out Kinl Section 5 of 5 SUBMI ©2016 Glynlyon, Inc. All rights reserve Mar 27 2arrow_forwardThe following function f uses recursion: def f(n): if n <= 1 return n else return f(n-1) + f(n-2) Let n be a valid input, i.e., a natural number. Which of the following functions returns the same result but without recursion? a) def f(n): a <- 0 b <- 1 if n = 0 return a elsif n = 1 return b else for i in 1..n c <- a + b a <- b b <- c return b b) def f(n): a <- 0 i <- n while i > 0 a <- a + i + (i-1) return a c) def f(n): arr[0] <- 0 arr[1] <- 1 if n <= 1 return arr[n] else for i in 2..n arr[i] <- arr[i-1] + arr[i-2] return arr[n] d) def f(n): arr[0..n] <- [0, ..., n] if n <= 1 return arr[n] else a <- 0 for i in 0..n a <- a + arr[i] return aarrow_forward
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