The formal approach to determining the big-O complexity of an algorithm is to set up recurrence relations and solve them. The recurrence relation for the Linear Search algorithm is defined by: I. T(n)=T(n-1)+1 II. T(n) = 2T(n/2)+1 III. T(n)=T(n-1)+Theta(n) IV. T(n)=2T(n/2)+Theta(n) V. None of the other answers

Q: Given that EuV k=1 to n k = n(n+1)/2, evaluate Euu k=1 to n (k+1)

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Q: In each of the following show whether f(n) = O(g(n)) and/or f(n) = Ω(g(n)): (a) f(n) = 20n + logn,…

A: Defined the given function

Q: Based on the master theorem, what is the solution to T (n) = 16 (4) +n o e (n² log n) o e (n*) e…

A: - We have to get the complexity according to master's theorem.

Q: 1 g(n) = 4 · g(n/3) + log(n)

A: The solution for the above given question is given below:

Q: ++i) { A. for (i = 0; i < 5n + 1; for (j = 0; j < 2*i + 1; ++j) sum += i + j; { } k

A: Here we can see the use of nested for loop. What is for loop? For loop is a programming language…

Q: and h(n) = 0(n). Then %3D

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Q: O(1) if n = 1 , T(n) = 8T (п/2) + Ө(n?) if n > 1.

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Q: = 4T(√n) + (log [n) =

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Q: If f(n)=(h(n)) and g(n)=(h(n)) then (select all that applies): a) f(n)+g(n)=(h(n)) b)…

A: Given that: f(n) = theta(h(h)) and g(n) = Θ(h(n)) Note: Θ(h(n)) means both O(h(n)) and Ω(h(n)) means…

Q: Prove that 0(n -1) +0(n)= 0(n). Does it follow that 0(n)= 0(n)-0(n -1)? Justify your answer

A: Given that, O(n)=O(n-1)+O(n) and O(n)=O(n)-O(n-1) Big O represents the worst case time complexity…

Q: Solve the recurrence: T(n) = 3T()+n° – lg n %3D

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Q: Use induction to verify that T(n)=O(n^3) where T(n) ≤ 3T(n/2) + 4T(n/3) + n^3

A: The recurrence relation is a formula that describes a series based on a rule that determines the…

Q: T(n) = 4T(n/2) +n is (n²)

A: The Master Theorem is a tool used to solve recurrence relations that arise in the analysis of…

Q: Consider the sequence a(n) given by a(1) = a(2) = 1, and for n ≥ 1, the next term a(n + 1) = a(a(n))…

A: In mathematics and programming, recursion is the idea that a function can call itself while it is…

Q: Prove the following by using induction: 1(1!) + 2(2!) + 3(3!) +...... + n(n!) = (n + 1)! - 1, for n…

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Q: (n) and

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Q: Prove or disprove the following statements: 1)Suppose that  f(n) = Θ(nlogn) and g(n) = Θ(n2/logn).…

A: 1. The given statement can be prove f(n) = Θ(nlogn) and g(n) = Θ(n2/logn). Then, h(n) = f(n) x g(n)…

Q: ?(?)=3n+100 × log n is Ω(n) (A) True (B) False Explain why as well

A: An Ω(n) is the set of functions.  f(n) = Ω (g(n))  Positive constants c and k, such that 0 ≤ cg(n) ≤…

Q: • Given f(n) E 0(n), prove that f(n) E O(n²). • Given f(n) E O(n) and g(n) E O(n²), prove that…

A: Task :- Prove given statements about time complexity notations.   Big-Oh notation definition :-…

Q: SHOW YOUR SOLUTION  Find the exact running time T(n) then explain of how you solve or get the…

A: Question : What is the value of sum after the code below is executed?#include&lt;stdio.h&gt;int…

Q: for ( i = 1 ; i < n ; i * 2 ){         for ( j = 0 ; j < min( i , k ) ; j++){             sum++…

A: Time complexity = O(n^2)

Q: Show that if f(n) is O(g(n)) and g(n) is e(h(n)) then f(n) is O(h(n))

A: θ-notation denotes tight bound. O-notation denotes upper bound. For a given function g(n), we denote…

Q: T(n) = T(n – 1) +1 T(1) = 1 0 (n²) O(log n) O(n) 0 (n²)

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Q: Algorithm P(n)// Input: A positive integer n if n=1 return 1 else return P(n-1) non n

A: Algorithm: The algorithm is a set of steps that should be followed to complete a specific task.

Q: f(n) = n/ log n and g(n) = n(log n)? Select one: O a. f=Ø(g) O b. f=N(g) O .f=O(g) O d. None of…

A: Actually, algorithm is an step by step process.

Q: T(n) = T(n - 1) + 3n and T(0)=0. Then T(n) is e (n³1 e (n) e (n lg n) e (2")

A: Given question about  Recursive relation Find time complexity

Q: Show that T(n) has the same order as S(n) where T(n) = 3nª – 5n? S(n) = nº

A: Defined the asymptomatic order of the  given functions

Q: olve the following recurrence by method of backwards substitution   A(n)=2A(n-1)+1 for n>1 , with…

A: Answer : The complexity will be n.

Q: (n + 1)! - 1 + (n + 1)(n + 1)! = (n + 2)! -1

A: n!  =  n*(n-1)*(n-2)*........*1 (n+1)! = (n+1)*n*(n-1)*(n-2)*........*1 (n+2)! =…

Q: Using whatever method you want, find and prove the answers to the following- a) T(n) = 3T(n /3) +…

A: If we compare given recurrence relations with T(n) = aT(n/b)+f(n) we can see that in each case…

Q: Can someone explain how the ouput is, 642211431136     def Q3(n):                  if (n <= 0):…

A: I have  fixed to print desired  output--------- After  fixing ,  I have  provided  PYTHON  CODE…

Q: ndicate the run time compl For (int i = 1; i < 999; i++) y++; O O(n) O O(n lg n) O O(n) O 0(1)

A: answer is option d :-  O( 1 )

Q: Use substitution to show T(n) = 4T(n/4)+n is T(n) is both in O(n?) and O(n log n)- note for O(n?)…

A: ANS:

Q: Function f grows no faster than function g O f (n) = O(g(n)) O f (n) = w(g(n)) O f (n) = O(g(n)) %3D…

A: Solution:

Q: tion that d. In a proof by formula holds for every integer n ≥ 1, wh must be shown in the inductive…

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Q: Given the runtime, (n) = n° + n +n+1 show that a. f(n) = 0(n*) b. f(n) = e(n³) c. f(n) = (n²)

A: The given Function       f(n) = n3 + n2 + n + 1  The higest power in the given function is n3  So ,…

Randomized Select Algorithm

A randomized algorithm is defined as one that uses a certain amount of randomization in its logic or operation. It is said to be an algorithm that depends on the random number to perform its operation. It is used for reducing the overall time complexity, space complexity in the standard algorithm. The randomized algorithm uses the concept of random numbers to find the solutions to the different kinds of problems and also to improve the problem solutions.