f (n) = cos n + 12 O 0(1) O Olg n) O None of the choices O O(n) O O(n lg n)

Q: Show that T(n) = O(n³) where T(n) = 1 + 2 + 3+...+n

A: If we move according to your question the sum of n natural numbers is given by n*(n+1)/2  And thus…

Q: Indicate the run time complexity: for(int i = 1; i < n; i= i*2) y++; O O(lg n) O O(n) O O(n lg n) O…

A: The theta notation is used to describe the complexity of an algorithm. It bounds a function from…

Q: Let T(n) = T(n-2)+2T([])+n, for all n and T(n) E N(n²). 2 3. T(1) = T(2) 1. Prove that T(n) E O(2")…

A: Explanation given in step 2

Q: Use the substitution method to show that T(n) = 8T(n/2) + n² is N(n³) Use the substitution method to…

A: Here, first we will solve given recurrence relation using substitution method. And then we will show…

Q: Indicate the run time complexity: for(int i = 1; i 0) { k++; j--; } } O O(n) O O(n°) O(n°) None of…

A: Explanation: The outer for loop running n times and inner while loop also running n times but it…

Q: Indicate the run time complexity: for (int i = 1; i < n; i++) { x++; y += I; } O(n lg n) O(lg n)…

A: Solution:   Given,

Q: What does it mean to say that f(n) is in O(g(n))?

A: To say that f(n) is in O(g(n)) means that there exists a positive constant K such that f(n)= kg(n)…

Q: Solve the recurrence using repeated substitution. (a) T(n) = T(n-1) + n (b) T(n) = 2T(n-1) + 1 (c)…

A: Part (a): T(n) = T(n-1) + n   PROGRAM STRUCTURE: Write the definition of the recursive function.…

Q: 18. What is the running time of the following algorithm? Input: The number n is a power of 2. 1: i =…

A: The running time of an algorithm or a data structure method typically grows with the input size,…

Q: ndicate the run time con or i = 1 + n*n: x++; For i = 1 e n: x++; O O(n² lg n) Oln3)

A: The first for loop will run for O(n2)times. The second for loop will run for O(n) times . Therefore…

Q: Indicate the run time complexity: for (int i = 1; i < n; i++) for (int j=0; j < i; j+=2) k++; O O(n…

A: Given lines of code is, for(int i=1;i&lt;n;i++)     for(int j=0;j&lt;i;j+=2)        k++; The outer…

Q: Sort the following in order of asymptotic order: f1(n) = n" f2(n) = nvn f3(n) = 2" fa(n) = f4(n/2) +…

A: The fourth equation needs to be converted to an asymptomatic notation. Using Master's theorem:…

Q: What is the running time of the following algorithm. f(n){ for(int j = 1; j<=7; j++) f(n/7): for(int…

A: I'm providing the answer of the above question. I hope this will be helpful for you...

Q: complete the following pseudo coded algorithm for computing the factorial of n if n equals 0 n! is…

A: Factorial of a non-negative number, is increase of all whole numbers less than or equivalent to n.…

Q: Let A(n) = 8 A(n/2)+ n³ the time of this recurrence equation is Select one: O a. O(n*) O b.O (2") c.…

A: If T(n) = aT(n/b) + f(n) where a &gt;= 1 and b &gt; 1 The theorem consists of the following three…

Q: Indicate the run time complexity: for(inti = 1; i < 555; i++) for(int j = 1; j< n; j*=2) y++; O None…

A:

Q: if n = 0, 1, 2 or 3 otherwise t(n) = n t(n-1) + t(n-3) + t(n-4) Express your answer as simple as…

A: Given recurrence relation is, t(n)=t(n-1)+t(n-3)+t(n-4) t(0)=0, t(1)=1, t(2)=2 and t(3)=3

Q: nction isPrime(n) { if (n < 2 || n % 1 ! return false; } for (let i = 2; i < %3D

A: Ans. ) YES, it's program to find prime number. Explanation:- Following program to find prime number…

Q: Consider the following statements, choose all that are incorrect. O 1. 3n +7 is O(n^2) (i.e., n…

A:

Q: Accepting n calculate the following expression : 1/2 + 2! + 3/4 + 4! + 5/6 + 6! + 7/8 + 8! + ... +…

A: #include &lt;iostream&gt;using namespace std; double factorial(int n){    double fact = 1.0;    for…

Q: from math import sqrt def prime_factorization (n): # verify that the input is an integer > 2 if not…

A: prime_factorization function: - This function first verifies input parameter n. If n is not an…

Q: O Make the program that finds the standard deviation (o) for (1- n) x values by using iteration and…

A: Note- since programming language is not specified we are providing answer in python programming

Q: = 0; int b = n/2; b >= 1; b /= 2) while (k+b <n && array[k+b] <= x) k += b; rray[k] =x) // x found…

A:

Q: (j) for i+1. n do jj do j<j+1 (1) for i+ 1 .. n do j<n while i<j*j do j<jdiv 2

A: (1)   for 1 &lt;-- .. n do   j &lt;- 2      while j &lt;= n do j &lt;-- j*j   Answer:O(n*√n)…

Q: n2 Example 1 Find O bound for f (n) n %D 2 2

A: Answer: Here is the theta bound condition: c1*g(n)&lt;=f(n)&lt;=c2*g(n) we will apply this condition…

Q: Indicate the run time complexity: for(int i = 1; i < n; i= i*2) y++; O None of the choices O (1) O…

A: Here we have given the time complexity with explanation for the loop

Q: Debug the following program: 1- def factorial (n): if(n<0): 2 - 3 return 1 result!=n 0: result =…

A: To do : Debug the given program and to fix it

Q: Suppose, T(n) = 12+22+32+…..+n2. Show that, T(n) is in Θ(n3 ).

A: Given  T(n) = 12+22+32+…..+n2

Q: Indicate the run time complexity: for(int i = 1; i < n; i = i*2) y++; for(int i = 1; i < n; i = i*2)…

A: if we are using two loops which re not nested then complexity will be O(2n) where 2 will be consider…

Q: (a) T(n) = 2T (n/3) + 1. (b) T(n) = 7T(n/7) + n. (c) T(n) = 9T(n/3) + n². (d) T(n) = T(n-1) +2.

A:

Q: Indicate the run time complexity: for (int i = n; i > 1 ; i=i/2) k++; O O(n Ig n) O O(n²) O None of…

A: Runtime complexity is way to describes the performance of an algorithm, or how much more processing…

Q: True False Given a sorted array of n integers, we can find the median of them in O(1) time. True…

A: We can sort n integers between 0 and 2n in O(n) time.   True   False   Given a sorted array of n…

Q: 4. fun(n) if (n <= 1) return 1 for i=n it=2 f(n-1) + f(n-2) +f (n-3)... i/=n

A: fun(n)      if(n&lt;=1)           return 1 for(i=1;i&lt;=n;i=i+2)      return(f(n-i)+f(n-i-1))

Q: | T(n – 1) + 7 for n 2 2 for n=1

A: Hey there, I am writing the required solution of the questin mentioned above. Please do find the…

Q: Show that T(n) = 0(n°) 3 where T(n) = n?

A: Here in this question we have asked to show that  T(n) = O (n^3)  Where T(n) = n^2

Q: for ( int i= 1; i<n*n*n;i *=n) { for ( int j= 0; j<n;j+=2){ for ( int k = 1; k<n; k *= 3 ) {…

A: Big-O Complexity Analysis: It is a time analysis of an algorithm, program code block, and…

Q: The complexity of the following code is int i, j, k = 0; for (i = n / 2; i <= n; i++) { for (j k = k…

A: EXPLANATION: For the outer for loop, the value of the loop variable starts from n/2 and goes up to…

Q: Order the following: O(n2), O(12 + 7n), O(n log(n) + 300 n2 + 1/125 n3)

A: Ordering based on Big-O notationAccording to Big-O notation, f (n) = O (g (n)) if there exist a…

Q: The solution of the following recurrence T(n) = T(n/2) + n is: %3D Select one: O a. O(log n) O b.…

A: Big-O notation: The time complexity of an algorithm can be measured by the Big-o notation. The…

Q: Find the space complexity of the following code fib(int n) {   if (n <= 1) return n; return…

A: The amount of space required is the same for fib(6) and fib(20). i.e. as N changes the space used…

Q: 2 T(n) = 3T (n) + 0(1).

A: The given equation is a recurrence relation. This is one way of determining run time of a program.…

Q: 11. Show that lower order terms don't matter in the O() notation by showing that if g(n) = O(f(n))…

A: We need to prove that, if g(n)=O(f(n), then, g(n) +f(n)=O(f(n)).

Q: Indicate the run time complexity: for (int i = 0; i < 8n; i=i+2) k++; O O(n) O O(4n) O (8n) O O(n lg…

A: In this question, we are going to find out the time complexity of given piece of code. For loop will…

Q: The following Prefix_Average algorithm needs O(n-logn).

A: THE ANSWER IS false.

Q: Consider the following code where n can be any number of more than 20. Select the correct time…

A: Answer 8: for the question 8 the time complexity will be option B. O(nm) because outer loop is…

Q: e complexity of the following code is void f(int n) { if (n > 0) { DoSomething (n); // O(n) f(n-1);

A: Here we will discuss the complexity of he code

Q: Show that T(n) = 0(n²) where T(n) = 1+ 2 + 3+. .. +n

A: We have to show that T(n) = O(n2)  Where T(n) = 1+2+3+.......+n

Q: if ns if -4 Sn 4/n if 1<n %3D "lot g[n] Plot mran nart VI

A: Following is the Matlab code for the given problem : g[n] function : function y=g(n)if n&lt;=-4…