Consider the following problem: given a list of integers N and an individual integer n, is there any element of N that is a factor of n? (1) There is a semi-decision procedure for the problem. If your answer is true, try to describe the procedure in English or pseudocode for learning purposes. Group of answer choices True False
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Consider the following problem: given a list of integers N and an individual integer n, is there any element of N that is a factor of n?
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- Consider the following problem: given a list of integers N and an individual integer n, is there any element of N that is a factor of n? (2) There is a decision procedure for the problem. If your answer is true, try to describe the procedure in English or pseudocode for learning purposes. Group of answer choices True FalseAlgorithm of Preis in AlgebraThe following steps make up the algorithm.A weighted graph G = as the first input (V, E, w)A maximum weighted matching M of G as the output.While E =, choose any v V at random, let e E be the largest edge incident to v, and then perform the following calculations: 3. M e; 4. E e; 5. V V; 6.11. Two different Python implementations of this algorithm are shown by E, E, and all edges that are adjacent to e.Based on the given adjacency lists and the figure below for the graph search, which of the following statements are correct? (Select all that applies.) adj(s) = [a, c, d], adj(a) = [ ], adj(c) = [e, b], adj(b) = [d], adj(d) = [c], adj(e) = [s]. see the picture sent Group of answer choices Breadth-First Search: s a c d e b Breadth-First Search: s a c d b e Depth-First Search: s a c b d e Depth-First Search: s a c e b d
- For any program P that takes as input a string, can P ever solve a language other than Y(P)? If your answer is yes, give an example. If your answer is no, briefly justify your answerWrite an algorithm that inputs a number n followed by an array of n numbers and outputs the number of values of i, with i between 1 and n-1 such that ai < ai +1. {i| i is a natural number and 1 <= i <= n-1 and ai < ai +1} *The output is the cardinality of the set Can be written in pseudocodeFor relatively small values of n, algorithms with larger orders can be more efficient than algorithms with smaller orders. Use a graphing calculator or computer to answer this question. For what values of n is an algorithm that requires n operations more efficient than an algorithm that requires [50 log2(n)] operations? (Assume n is an integer such that n > 1.) n?
- Given is a strictly increasing function, f(x). Strictly increasing meaning: f(x)< f(x+1). (Refer to the example graph of functions for a visualization.) Now, define an algorithm that finds the smallest positive integer, n, at which the function, f(n), becomes positive. The things left to do is to: Describe the algorithm you came up with and make it O(log n).Assume that you were given N cents (N is an integer) and you were asked to break up the N cents into coins consisting of 1 cent, 2 cents and 5 cents. Write a dynamic programming-based recursive algorithm, which returns the smallest (optimal) number of coins needed to solve this problem. For example, if your algorithm is called A, and N = 13, then A(N) = A(13) returns 4, since 5+5+2+1 = 13 used the smallest (optimal) number of coins. In contrast, 5+5+1+1+1 is not an optimal answer. Draw the recursion tree for the algorithm where N = 7. Derive the complexity bound of the algorithm. Do not need to prove the complexity bound formally, just derive it by analyzing each component in your algorithm.Please written by computer source Let x be a binary string. The minimal description of x, written d(x), is the shortest string ⟨M, w⟩ where TM M on input w halts with x on its tape. If several such strings exist, select the lexicographically first among them. The descriptive complexity, or Kolmogorov complexity, of x, written K(x), is K(x) = |d(x)|. Show that the function K(x) is not a computable function. HINTS: If K is a computable function, there is some TM which computes it. That TM can be used to find strings of large complexity. Try to design a program which outputs “complex” strings but which contradicts their supposed complexity, and even contradicting the supposed complexity of a single string suffices.
- 2. Let n be a positive integer, and let A be a list of positive integers. We say that the integer n can be factorized by A if there exists a sequence of integers 11, 12,..., ik (with 0 ≤i; < len (A), for j = 1,..., k) such that n is the product of the integers A[i], A[i2],..., A[ik]. Write an efficient algorithm factorizable (n, A) that returns True if n can be factorized by A, and False otherwise. Prove that your algorithm is correct, and bound its running time. Larger scores will be awarded to faster solutions. Example 1: if n = 6 and A [4,2,3], then factorizable (n, A) should return True, L[1] * L[2]. since n == Example 2: if n = 8 and A = L[0] * L[0] * L[0]. [2,5], then factorizable (n, A) should return True, since ,2,3,5,7], then factorizable (n, A) should return Example 3: if n = 13 and A = False since n cannot be factorized by A.On the Island of Knights and Knaves we have two people A and B. A says: Exactly one of us is a knight if and only if B is a knight. B says: A is a knight if I’m a knight. determine if A and B are each a knight or a knave. (The problem might have no solutions, one solution, or many solutions.)consider a jewler who shows a collection of diamonds to a person. all diamonds have different integer ounce weights and are laid out in a single row on the table. what is the largest weight amount of diamonds that the person can take, provided that the person cannot select adjacent diamonds? use standard pseudocode notation similar to python to write a dynamic programming bottom up algorithm that solves this problem for any n number of diamonds.