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Question2 0/5 pts If exact running time of an algorithm is T(n)-5n3+ n2 + 3n -5...
a) Prove that running time T(n)=n3+30n+1 is O(n3) [1 mark] b) Prove that running time T(n)=(n+30)(n+5)...
a) Prove that running time T(n)=n3+30n+1 is O(n3) [1 mark] b) Prove that running time T(n)=(n+30)(n+5) is O(n2) [1 mark] c) Count the number of primitive operation of algorithm unique1 on page 174 of textbook, give a big-Oh of this algorithm and prove it. [2 mark] d) Order the following function by asymptotic growth rate [2 mark] a. 4nlogn+2n b. 210 c. 3n+100logn d. n2+10n e. n3 f. nlogn
3. (20 pts.) You are given two sorted lists of numbers with size m and n....
3. (20 pts.) You are given two sorted lists of numbers with size m and n. Give an O(logn+ logm) time algorithm for computing the k-th smallest element in the union of the two lists. 4. (20 pts.) Solve the following recurrence relations and give a bound for each of them. CMPSC 465, Fall 2019, HW 2 (a) T(n) = 117(n/5)+13n!.3 (b) T(n) = 2T (n/4)+nlogn (c) T(n) = 5T (n/3) +log-n (d) T(n) = T(n/2) +1.5" (e) T(n) =...
1. (10 points) Write an efficient iterative (i.e., loop-based) function Fibonnaci(n) that returns the nth Fibonnaci...
1. (10 points) Write an efficient iterative (i.e., loop-based) function Fibonnaci(n) that returns the nth Fibonnaci number. By definition Fibonnaci(0) is 1, Fibonnaci(1) is 1, Fibonnaci(2) is 2, Fibonnaci(3) is 3, Fibonnaci(4) is 5, and so on. Your function may only use a constant amount of memory (i.e. no auxiliary array). Argue that the running time of the function is Θ(n), i.e. the function is linear in n. 2. (10 points) Order the following functions by growth rate: N, \N,...
EC2 (5 Points): The running time of Algorithm Ais (1) n? + 1300, and the running...
EC2 (5 Points): The running time of Algorithm Ais (1) n? + 1300, and the running time of another Algorithm B for solving the same problem is 112n - 8. Assuming all other factors equal, at what input sizes) would we prefer one algorithm to the other? 7.5 EC3 (2.5 Points): What is the recurrence relation (an equation that recursively defines) of the Towers of Hanoi problem? Remember, the base case is T(1) = 1 BIVAAI EE11
1 question) Arrange the following in the order of their growth rates, from least to greatest:...
1 question) Arrange the following in the order of their growth rates, from least to greatest: (5 pts) n3 n2 nn lg n n! n lg n 2n n 2 question)Show that 3n3 + n2 is big-Oh of n3. You can use either the definition of big-Oh (formal) or the limit approach. Show your work! (5 pts.) 3 question)Show that 6n2 + 20n is big-Oh of n3, but not big-Omega of n3. You can use either the definition of big-Omega...
d. (4 pts) Fill in the asymptotic complexity (not the exact solution) of the work represented...
d. (4 pts) Fill in the asymptotic complexity (not the exact solution) of the work represented by the following summations for an input of size n. Write complexities in simplest form. ) (1) Ź 2' = 01 — (3) Z(64) = 01_ (2) (Si +5) = 01 - (4) I"3n =01_ logn ) ) e. (5 points) Consider the recurrence T(n) = 4T(n/2) +n , T(2) = 8. and a proposed closed-form solution T(n) = n² + 2n Suppose we...
0/10 pts Question 10 The next question is about estimating the clock time for instances of...
0/10 pts Question 10 The next question is about estimating the clock time for instances of different sizes for for a given algorithm. Assume that a certain algorithm with the running time 22 uses 3 sec to solve an instance of size 100. How long will it take this algorithm to solve an instance of size n 1200? Choose the closest estimate: the running time is about... none of the listed You Answered 1 minute 15 minutes Correct Answer 7...
Let T(n) denote the worst case running time of an algorithm when its input has size...
Let T(n) denote the worst case running time of an algorithm when its input has size n. In divide and conquer algorithms, T(n) is often expressed using a recursion. Hence, expressing T(n) in terms of the big-Oh notation requires a bit of work. There are many ways of determining the growth rate of T(n). In class, I’ve shown you how to do it by drawing the recursion tree. Here are the steps: (1) draw the recursion tree out, (2) determine...
What does a run-time analysis usually countS pts a. The number of arithmetic and other operations...
What does a run-time analysis usually countS pts a. The number of arithmetic and other operations required fot the b. The number of megabytes required for the program to run c. The number of seconds required for the program to run. d. The number of seconds plus the number of megabytes Total 100 points, 30 ins and other operations required for the program to rn 2. What do we call an input that results in the longest execution timet a....
Subject: Algorithm solve only part 4 and 5 please. need urgent. 1 Part I Mathematical Tools and Definitions- 20 points, 4 points each 1. Compare f(n) 4n log n + n and g(n)-n-n. Is f E Ω(g),fe 0(g)...
Subject: Algorithm
solve only part 4 and 5 please.
need urgent.
1 Part I Mathematical Tools and Definitions- 20 points, 4 points each 1. Compare f(n) 4n log n + n and g(n)-n-n. Is f E Ω(g),fe 0(g), or f E (9)? Prove your answer. 2. Draw the first 3 levels of a recursion tree for the recurrence T(n) 4T(+ n. How many levels does it have? Find a summation for the running time. (Extra Credit: Solve it) 3. Use...
3. (20 pts.) You are given two sorted lists of numbers with size m and n. Give an O(logn+ logm) time algorithm for computing the k-th smallest element in the union of the two lists. 4. (20 pts.) Solve the following recurrence relations and give a bound for each of them. CMPSC 465, Fall 2019, HW 2 (a) T(n) = 117(n/5)+13n!.3 (b) T(n) = 2T (n/4)+nlogn (c) T(n) = 5T (n/3) +log-n (d) T(n) = T(n/2) +1.5" (e) T(n) =...
1. (10 points) Write an efficient iterative (i.e., loop-based) function Fibonnaci(n) that returns the nth Fibonnaci number. By definition Fibonnaci(0) is 1, Fibonnaci(1) is 1, Fibonnaci(2) is 2, Fibonnaci(3) is 3, Fibonnaci(4) is 5, and so on. Your function may only use a constant amount of memory (i.e. no auxiliary array). Argue that the running time of the function is Θ(n), i.e. the function is linear in n. 2. (10 points) Order the following functions by growth rate: N, \N,...
EC2 (5 Points): The running time of Algorithm Ais (1) n? + 1300, and the running time of another Algorithm B for solving the same problem is 112n - 8. Assuming all other factors equal, at what input sizes) would we prefer one algorithm to the other? 7.5 EC3 (2.5 Points): What is the recurrence relation (an equation that recursively defines) of the Towers of Hanoi problem? Remember, the base case is T(1) = 1 BIVAAI EE11
d. (4 pts) Fill in the asymptotic complexity (not the exact solution) of the work represented by the following summations for an input of size n. Write complexities in simplest form. ) (1) Ź 2' = 01 — (3) Z(64) = 01_ (2) (Si +5) = 01 - (4) I"3n =01_ logn ) ) e. (5 points) Consider the recurrence T(n) = 4T(n/2) +n , T(2) = 8. and a proposed closed-form solution T(n) = n² + 2n Suppose we...
0/10 pts Question 10 The next question is about estimating the clock time for instances of different sizes for for a given algorithm. Assume that a certain algorithm with the running time 22 uses 3 sec to solve an instance of size 100. How long will it take this algorithm to solve an instance of size n 1200? Choose the closest estimate: the running time is about... none of the listed You Answered 1 minute 15 minutes Correct Answer 7...
What does a run-time analysis usually countS pts a. The number of arithmetic and other operations required fot the b. The number of megabytes required for the program to run c. The number of seconds required for the program to run. d. The number of seconds plus the number of megabytes Total 100 points, 30 ins and other operations required for the program to rn 2. What do we call an input that results in the longest execution timet a....
Subject: Algorithm
solve only part 4 and 5 please.
need urgent.
1 Part I Mathematical Tools and Definitions- 20 points, 4 points each 1. Compare f(n) 4n log n + n and g(n)-n-n. Is f E Ω(g),fe 0(g), or f E (9)? Prove your answer. 2. Draw the first 3 levels of a recursion tree for the recurrence T(n) 4T(+ n. How many levels does it have? Find a summation for the running time. (Extra Credit: Solve it) 3. Use...
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