Write an algorithm that generates the representation of N in base B.  2 2. Compute the time complexity of your algorithm

Q: Imagine a collection of nuts and bolts that are all together in one pile on a table. Describe, in…

A: Question a. Imagine a collection of nuts and bolts that are all together in one pile on a table.…

Q: Suppose we have positive integers a, b, and c, such that that a and b are not relatively prime, but…

A: Suppose we have positive integers a, b, and c, such that that a and b are not relatively prime, but…

Q: Let m be a randomly chosen non-negative integer having at most n decimal digits, i.e. an integer in…

A: Let m be randomly chosen non-negative integer having at most n digits, i.e.,an integer in the…

Q: Consider any two sets of integers strictly larger than 1, denoted by P and Q. The set P is said to…

A: Here is the detailed and simplified C++ code for the above listed problem statement:

Q: 'roof: given that f(0) exists, we must show that limx-o f(x)-f(0), or equivalently nat lim…

A: Please find the answer below:

Q: Use a software program or a graphing utility to solve the system of linear equations. (If there is…

A:

Q: Fibonacci numbers F1, F2, F3, . . . are defined by the rule: F1 = F2 = 1 and Fk = Fk−2 + Fk−1 for k…

A: In the question, it is given: Fk = Fk-2 + Fk-1 for k > 2 with F1=F2=1 ---(i) Lk = Lk-2 + Lk-1 for…

Q: ction that given integers j and k where j ≥ 2 that then j is not divisible by k or(∨) j is n

A: Proof by contradiction is a type of verification that builds up reality or the legitimacy of a…

Q: Let P(n):n and n+ 2 are primes. be an open sentence over the domain N. Find six positive integers n…

A: Given data is shown below:

Q: Let Σ = {a, b}. Indicate whether or not L is regular and prove your answer.   (i) L={w ∈ {a, b}* :…

A: Regular Expression: A regular expression is exists for all the regular languages. A regular…

Q: Given a real number x and a positive integer k, determine the number of multiplications used to find…

A:

Q: Given a set S of n planar points, construct an efficient algorithm to determine whether or not there…

A: The algorithm is shown below. Algorithm(S)//Algorithm to whether the set of points S has three or…

Q: log 2 (x +3) x2 +3x + 2 Find the domain of definition of f (x)=

A: Solution :-_

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 a function, f(x), which is a strictly increasing function, define an algorithm that finds the…

A: Unbounded Binary Search  Given a function ‘int f(unsigned int x)’ which takes a non-negative…

Q: In this exercise we will develop a dynamic programming algorithm for finding the maximum sum of…

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

Q: Find upper bound of running time of quadratic function f(n) = 3n2 + 2n + 4. To find upper bound of…

A:

Q: Asequencev(x,n)is bounded aboveif kER such that .A 2k V, EN .B X, Sk V, EN .C >k V EN

A: A sequence v( xn )is bounded above if k belongs to R such that ?

Q: Prove that the natural logarithm of (1 + x) for |x| < 1 is: x3 In(1 + x) = x - 3 n! Show that the…

A: Term  Xn / n!   in RHS seems irrelevant as Taylor or Maclaurin series for ln(1+x) does not have that…

Q: Consider the following functions: ● log2 x ● x.log₂ x • (3/2)* • x/log₂ x • 2x • √x • x² • (log₂ x)²…

A: Here is the order:

Q: 1. Big-O Notation Let fand g be functions from the set of integers or the set of real numbers to the…

A: Given that, f(x)= O(g(x)) that means f(x) is equal to big oh of g(x). Big-oh represents the tightest…

Q: We are now also given an array of integers A = {a;}"-1, and some random integer k. 1. Develop an…

A: I am solving this in Python language . I am giving you the code as well the screenshot of code and…

Q: You are given N sticks, where the length of each rod is a positive number. The cutting work is done…

A: APPROACH-: while stick array size is &gt;=1 do following operation print size of array initialize…

Q: Given a set S of n planar points, construct an efficient algorithm to determine whether or not there…

A: An algorithm is a limited arrangement of PC implementable directions, normally to tackle a class of…

Q: You are given a list of M positive numbers, Ao. A1. AM-1- You have to answer Q ... queries. Each…

A: Code Flow: In the main question, the solution is 4 * 5 * 4 * 6, because we only need to select one…

Q: The coordinates of a polygon can be represented as a list of tuples: [(x1, y1), (x2, y2), ..., (xn,…

A: required: given a list of vertices of the polygon, write a python program to find it are.   all the…

Q: In this group of problems, you are given the predicate P(x), where the domain of x is the set of…

A:

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

A:

Q: A well-known problem in computer science is called the knapsack problem. A variation is as follows:…

A: Using recursion For the recursive approach, we will consider two cases.  Consider the first element…

Q: Consider the function f:N×N¬N defined recursively by: 1) Base case: Let meN and define 0,m) = 0 2)…

A: ANSWER: Leave the assertion alone P(n): f(n,3*m)= 3*f(n,m) given f(0,m)=0 and f(x,m)= f(x-1,m)+m.…

Q: numerous bouquet combinations, including two 5-rose bouquets (total profit of $70), and a 4-rose…

A: Roses 1 2 3 4 5 Profit $5 $15 $24 $30…

Q: You are given a sequence of integers A1, A2, ..., AN and an integer M. For any valid integers p, q,…

A: As per the specification given in the question , this will be the required python Read the commented…

Q: Consider a sequence of integers defined by the following recurrence: f(0) = 0, f(1) = 1, and f(i) =…

A: Given the sequence of integers defined the following recurrence.

Q: Let f(n) = n2 and g(n) = 3n2 - 6n +4. Show that g(n) = 0(f(n)) by showing that there exist positive…

A:

Q: You are given an integer A. Let's define an infinite sequence S(A) = A%P, A²%P, A³%P,..., where P =…

A: Required: Write the Java code following the instructions provided for the total D (S (A)).…

Q: Given an array A of n distinct positive integers and an integer B, find the number of unordered…

A: Here i write the code in c :   #include &lt;stdio.h&gt; int main() {    int n,i,j,B=20;    int…

Q: S De a set of n numbers, and let k De a natura less than equal n. Let X Be the set of all subsets of…

A: The objective is to define a one-to-one and onto function . , A function f from set X to set Y…

Q: You are given N sticks, where the length of each rod is a positive number. The cutting work is done…

A: Input-Output Explanation The first line contains a single integer N.The next line contains N…

Q: Prove the following problem is NPC: Given n sets S1,...,Sn, can we find a set A with size at most k,…

A: Before entering into problem we have to understand the following : Hitting set : Let C be a…

Q: (Basic) Consider a sequence of integers defined by the following recurrence: f(0) = 0, f(1) = 1, and…

A: Dynamic programming is an approach to enhancing recursion. Sometimes a problem contains an…

Q: According to the rule of sums: Suppose $$ g_{1} \in O(f_{1}),  \space{} and \space{} g_{2} \in…

A: Given data: If g1∈O(f1) and g2∈O(f2) then g1+g2 ∈O(max(f1,f2))   h∈O(n log n) and g∈O(n)

Q: Let S be a sequence with ten distinct integers. Prove by Contradiction that there must exist an…

A: By Contradiction that there must exist an increasing subsequence of length 4 (or more) or a…

Q: We consider certain strings of length 6 over the alphabet S = {A,B,C}.  We require that the string…

A: we need to form 6 letter string using A,A,B,B,C,C //exactly two A's,B's,C's lets start with placing…

Q: What are the complexities of the following code segments in terms of n? Give an upper bound. a) int…

A: Let's understand step by step :   Answer (a) : int i=1;while (i&lt;= n) {    int j = i;   while (j…

Q: Let a M be a finite set of messages, and let S(M) denote the set of all permutations of M (all…

A: Answer: I have given answered in the handwritten format.

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…

Q: nd A[0] > A[N-1] (0 indexed), devise an efficient algorithm to find a pair of adjacent elements A[il…

A: Algorithm - there should be two loops- one for row and second for column - for(int…

Q: Write the following as proposition: For every integer n, there exists an integer m such that m > n2

A: Here in this question we have given a english sentence and we have asked to convert it into…

Q: Let f(n) = 2n and g(n) = n. a) Show that f is O(g) using specific values of C and no. b) Show that g…

A: Big-O Notation O(n): Let f(n) and g(n) be the two functions described and the function f is said to…

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.