Given f(n) and g(n). Is f(n) = O(g(n))? Select one: a. Yes b. No c. None d. May

Q: The graph below is strongly connected b. O True O False

A: In a directed graph is said to be strongly connected, when there is a path between each pair of…

Q: d. y=0; for (i=0; im; j++) x--; } e. for(i=1; isn; i++) { for(j=1; jj; k--) x=x+5; y /= 3; } x =…

A: d. The time complexity of the program mainly depends on the loops and the number of times each loop…

Q: Fill in the blanks for the big-theta. if n 4. n, T(n) Big-theta: 0(

A: Answer:--------n^2

Q: What are the running times of the following four loops? Briefly justify your answers. (in all cases,…

A: According to the Question below the Solution:

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A: Given data: M=1 L=0   Given Expression: ~((M∨L)·~(M·L))

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: 6. Let a @b= max {a, b} = a if b ≤ a, otherwise a @ b = max {a, b} = b. Give a proof by cases that…

A:

Q: Consider the set of integers. 1. Use a direct proof to show that the sum of two even integers is…

A: 1. Use a direct proof to show that the sum of two even integers is even. Solution: let assume x and…

Q: For each of the statements below, determine for yourself if the statement is true or false. If it is…

A: Given the two statements below to  determine for yourself if the statement is true or false. If it…

Q: Use direct proof to show, "If  m+n and n+p are even integers (s and t), where m, n and p are…

A: Here m+n Ana n+p are even integers.

Q: se you are provided with a random number generator that outputs numbers between 0 and 1. Describe a…

A: Suppose you are provided with a random number generator that outputs numbers between 0 and 1.…

Q: The binomial coefficients are the integers Prove the recursion k(n) k! n! n! (kn)! k (k+ (* + 1) =…

A: Define function factorial to return the factorial of the number. Input k and n values. Print the…

Q: Cody has a circle of friends of 5 people To show his appreciation of them, Cody wants to be able to…

A: EXPLANATION: Include the necessary header files. Create an array that will contain the height of…

Q: . Suppose H = {cat, dog, rabbit, mouse}, F= {dog, cow, duck, pig, rabbit} J = {duck, rabbit, deer,…

A: We are given 3 sets H,F,W and we are going to apply union and intersection operations on them which…

Q: 3. Prove that (P =Q) = R has the same truth with (P = R) ^ (Q=R). We write (P=Q)=R= (P=R) ^ (Q=R).

A: Given:   Prove that (P⇒Q) ⇒ R has the same truth with (P⇒ R) ^ (Q⇒R).

Q: 1. Let x ∈ Z. Use a direct proof to show that if 5x2 + 8 is odd then x is odd. 2. Show by…

A: 1) Given 5x2+8 is odd which implies 5x2 is odd as the sum of any odd and even is odd.  so 5x2 is…

Q: Given f(n) and g(n). Is f(n)+g(n)=Θ(min(f(n), g(n)))? Select one: a. None b. No c. Yes d. Maybe

A: Case1: Consider f(n)=n2, g(n)=n2+2n f(n)+g(n)=n2+2n θ(min(f(n), g(n))) =θ(min(n2, n2+2n)) =θ(n2)…

Q: 'Let positive integer n be given. Of the following randomized algorithm, what is the expected value…

A: - The given algorithm represented in terms of a code :  import randomn = 10p = 0t = 0while p < n:…

Q: P1 P1 P1 R D U P2 P2 P2 F M H T T P1 5,4 -1,1 7,0 2,6 7,4 2,1 7,3 K 4,1 2,1 a)Find the subgame…

A: a) Subgame Perfect EquilibriumIn sport theory, a subgame best equilibrium (or subgame best Nash…

Q: 3. Prove that (P = Q) = R has the same truth with (P = R) ^ (Q = R). We write (P=Q)=R= (P=R) ^ (Q =…

A: We need to prove the given statement.

Q: Let P(n) be the statement n(n+1)(2n+1) 12 + 22 + ... + n2 = 6. for the positive integer n. What is…

A: Option d is correct.

Q: Give a direct proof of: "If x is an odd integer and y is an Question 4. even integer, then x + y is…

A: I will explain it in details,

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: • 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: An electrician has wired n lights, all initially on, so that: 1) light 1 can always be turned…

A: IMPLEMENTATION: The algorithm works from left to right implementing individual bits. First bit can…

Q: Given f(n) ∈ Θ(n),  prove that f(n) ∈ O(n²). Given f(n) ∈ O(n) and g(n) ∈ O(n²), prove that…

A: Asymptotic notations (Θ, O, Ω) compares a time complexity function with another standard function…

Q: A. Prove the following: 1. n(n – 1) = 0(n²) 2. 10 log, n+ 4 = ®(log, n) 3. 3n + 5 = 0(n²) 4. 100n =…

A:

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

A:

Q: Lao Wang sold apples in n days (n < = 5). For example, n is five days. On the first day, he sold…

A: Code: #include &lt;iostream&gt;#include &lt;string&gt;using namespace std;int main (){char Apples =…

Q: Let the statement be "If n is not an odd integer then square of n is not odd.", then if P(n) is "n…

A: Contrapositive statement: It is an indirect proof technique. If the statement is said as A -&gt;B…

Q: f(n) ∈ Θ(n),  prove that f(n) ∈ O(n²).

A: Given f(n) ∈ Θ(n),  prove that f(n) ∈ O(n²

Q: (b) Prove: max(f(n), g(n)) E O(f(n)g(n)), i.e., s(n) E O(f(n)g(n)). Assume for all natural n, f(n) >…

A: Given that, f(n)&gt;=1 and g(n)&gt;=1 s(n)= max(f(n), g(n))

Q: Heuristics Prove or disprove: If h1(n), ..., hk(n) are admissible, so is h(n) = h1(n) + ... + hk(n)

A: It is generally understood that the pointwise maximum of any set of admissible heuristics h1,...,hk…

Q: length n is known as a palindrome if the uniformity t[i]=t[n−i+1] is valid for all I (1≤i≤n).…

A: Here have to determine about the palindrome if the uniformity programming problem statement.

Q: 4. Consider f(n) = 3n2 + 4n – 3, mathematically show that f(n) is O(n?), 2(n²), and O(n2).

A:

Q: A string of colored lights contains 15 orange, 25 blue, 22 red, 18 yellow, and 20 green lights.…

A:

Q: Q1/ Let p:e N q: Thi-Qar is not in Iraq r:3 is a prime number are three propositions. Find the truth…

A:

Q: Prove that if n is an integer, then ⌊n/2⌋ = n/2 if n is even and (n − 1)/2 if n is odd.

A: Actually, the answer has given below;

Q: Consider the following: [Int]$N1 = 2.7 [Int]$N2 = 2.7 What is the answer for $N1 + $N2 Group of…

A: Given code is : [Int]$N1 = 2.7[Int]$N2 = 2.7

Q: Let p(n) 3+3-5+3 5++3-5-3(5+1-1)/4 a) What is the statement P(1)? b) Complete the inductive step of…

A: a)  P(1) = 18 b) The statement is true for all natural numbers.

Q: Let p(n) 3+3 5+3 5++3-5=3(5″+¹ − 1)/4 a) What is the statement P(1)? b) Complete the inductive step…

A:

Q: Prove that if x∈R and x >−1, then(1 +x)n≥1 +nx for all n∈N

A: since 10&gt;4+1 I will use this theory  Let P(n):(1+x)^n&gt;=(1+nx), for x&gt;-1 Let n=1,…

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

A: Prove the given asymptotic

Q: Let f(n) and g(n) be positive functions over the natural numbers. For each of the following claims…

A: Asymptotic notation of the given functions correct or disprove

Q: Consider the following uniformly distributed random numbers. Generate an exponentially distributed…

A: Lets see the solution.

Q: Show that for f(n) = 2n2 and g(n) = 20n + 3n2 , f(n) is θ(g(n)). How many ways can it be shown?…

A: We have to show that the following asymptotic notation .

Q: Prove that (n + a)^b = Θ( n^b), b > 0

A: Proof: The proof of the statement is explained in the below steps: n + ab ≤ n + ab, where n &gt; 0≤…

Q: 12. Give a Divide and Conquer algorithm for calculating xn wheren is a positive integer. [Note: If n…

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Q: Let n be an integer, use the definition of even to prove that 18n + 2 is even. 18n+2= Since X is an…

A: A number is said to be even if that number is a multiple of 2 and A number is said to be odd if a…

Counting sort

The counting sort algorithm sorts an array’s contents by counting the repetition of each element that occurs in the array. A counting sort algorithm is a stable algorithm that works the best when the range of elements in the array is small, say for example from 0 to 9. The count which is the number of repetitions of an element in the array is mapped to an index of an auxiliary array, which is then saved in an auxiliary array. The counting sort algorithm has a stable time complexity of the order of O(size of array + size of auxiliary array). Let’s discuss the algorithm in detail as follows.