Demonstrate that the following issue falls within the NP class: A set S of integers and an integer number t are provided to us. Exists a subset of S such tha the product of its components equals t? Note: Problem with Data Structures and Algorithms

A problem called S reduces to a problem called T if a T solver can be used as a subroutine to solve S. In pseudocode: Solves(...): ... SolveT(...) ... Assuming that this reduction is correct, answer the following questions regarding what the reduction tells us. If we know that an algorithm exists for solving Problem S, what does that tell us about Problem T? [ Select] If we know that an algorithm cannot exist for solving Problem S, what does that tell us about Problem T? [ Select] If we know that an algorithm exists for solving Problem T, what does that tell us about Problem S? [ Select ] [ Select ] An algorithm cannot exist for solving Problem S,r solving Problem T, what does that tell us about Nothing An algorithm exists for solving Problem S

applied disreet maths  if |A| = n and f:  A--->B is injective, what is |f(A)|?

Select all that apply. Which are the following properties of the Rosenblatt's Perceptron cause it to be difficult to use in the real world? □ It is never guaranteed to converge It only converges for data that is linearly separable It only works for binary classifcation tasks It only works for data that contains more than 2 classes

[Introduction to the Design and Analysis of Algorithms, 3rd Edition] Maxima search. A point (xi, yi) in the Cartesian plane is said to be dominated by point (xj , yj ) if xi ≤ xj and yi ≤ yj with at least one of the two inequalities being strict. Given a set of n points, one of them is said to be a maximum of the set if it is not dominated by any other point in the set. For example, in the figure below, all the maximum points of the set are circled. Design an efficient algorithm for finding all the maximum points of a given set of n points in the Cartesian plane. What is the time efficiency class of your algorithm?

Refer to image: (Computation and Automata) Provide new and correct solution for positive feedback!

Long chain of friends: You are given a list of people, and statements of the form “x knows y”. You are asked to find, is there a chain of k distinct people, such as x1 knows x2, x2 knows x3, and xk-1 knows xk. Prove that this problem is NP-complete by using one of the known NP-complete problems (CLIQUE, 3-SAT, Hamiltonian Path, Hamiltonian Cycle, Independent Set, etc.)

Recall a set A is countable if |N| ≥ |A|. Recall that Cantor’s theorem shows that P(N) = {X ⊆ N}is uncountable. We will show that F = {X ⊆ N | |X| < ∞} is countable, with an onto functiong : N → F that is computable.Write a program/function (e.g., in Python) that runs forever and prints every element of F,e.g., if run it would print something like{0}{1}{0,2}{3}{0,2}{0,5,7}{1}{0,1}{}{2}...(Note that you must prove that the program works, i.e., it prints every element of F, and onlyelements of F.)

Prove this issue is NP-complete:   S and t are integer integers. Does S have a subset with a t-sum?   Data Structures and Algorithm issue

In this group of problems, you are given the predicate P(x), where the domain of x is the set of natural numbers.