Question: Given a set T of numbers (represented in an array A[1..n]), a sum s, and a non-negative integer k, our task is to design an

Given a set T of numbers (represented in an array A[1..n]), a sum s, and a non-negative integer k, our task is to design an algorithm to identify a subset of numbers in T, with size k, such that the sum of the numbers in the subset equals s, or report that such a subset does not exist.

(a) Design a recursive algorithm to enumerate all subsets of T with size k and analyze its time complexity. If T = {4, -2, 3} and k = 2, the output would be the list as follows (can be in any order):

-2

4, -2

4, 3

-2, 3

(b) Based on your algorithm in (a), design an algorithm to solve the above problem and analyze the time complexity of your algorithm.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Databases Questions!

Question 2 . You are given a sorted array A of n distinct integers, drawn from 1 to m where A 1 , 2 , dots,mOAA 2 , 3 , 5 , 7 , 8 , 1 0 O ( n ) S n k n k S S n . That i s , A i s a subset o f 1 , 2 ,...

2. For this problem, you need to base your answer on the definitions of the asymptotic notations. 1. (10 points) Show 8n3logn+14n2=(n3logn) 2. (10 points) If f(n)=O(g(n)), can we conclude If...

In this question you will be asked to reflect on a project you have been involved in or observed, in which a design evolved, or could have evolved, through applying a theory of user behaviour. You...

In a Hopfield neural network configured as an associative memory, with all of its weights trained and fixed, what three possible behaviours may occur over time in configuration space as the net...

Consider the trigonometric series a0 2 + X r=1 (ar cos rx + br sin rx) where a0, a1, a2, . . . and b1, b2, . . . are constants and suppose that f(x) is a periodic function of x with period 2. (a)...

Let r and s be solutions to the quadratic equation x 2 b x + c = 0. For n N, define d0 = 0 d1 = r s dn = b dn1 c dn2 (n 2) Prove that dn = r n s n for all n N. [4 marks] (b) Recall that a commutative...

For each of the problems in the easy section it is enough to describe in English the idea of your algorithm, define the memo table, write the base case and the recursive step to fill the table, and...

1 Easy Questions. 5 points each. For each of the problems in the easy section it is enough to describe in English the idea of your algorithm, define the memo table, write the base case and the...

(iii) Now express your decision rule instead using only the quantities p(Ck), p(Cj ), p(x|Ck), p(x|Cj ), and relate it to the diagram above. [2 marks] (iv) If the classifier decision rule assigns...

Let i and j be positive integers. (i) Prove that there exist natural numbers a and b such that ai = bj+gcd(i, j). You may use standard results provided that you state them clearly. [4 marks] (ii) Let...

A company currently manufactures 9,600 units per month of its only product and sells them at Rs.120 per unit. Recently the company agreed to a union demand for 15% increase in wages. This will come...

Suppose a country bans trade with other countries, so net exports are always zero. How would this affect the slope of the AE curve? Explain.

By default, Jupyter Notebook is stored online, not on the local device. Question 1 options: True False

Which of the following are problems with identifying users of ABC? Multiple select question. ABC means different things to different organizations. Organizations will announce the discontinuance of...

6. Are my sources reliable?

How do you feel about the fact that even unintentionally using someone elses words, ideas, or intellectual property is still plagiarism? Does it seem unfair that you might suffer severe consequences...

5. Are my sources compelling?