The prime factorization of a given positive number N is the set of prime numbers that when multiplied together give N. For instance, the prime factorization of N=8, is {2,2,2} since 2x2x2 = 8 and the prime factorization of 24 is {2,2,2,3} since 2x2x2x3 =24.
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A: The answer given as below:
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- Algorithm for Conversion from an Arabic number to a modern Roman number.in: decimal number n (0 ≤ n)out: sequence R = s0, s1,...,s12 representing the structure of the Roman number (Ri = number of primitives Vi in n for i ∈ [0, 12])Let P(n) be the statement “the number 2^2n -1 is divisible by 3”. Use mathematicalinduction to show that P(n) is true for all n >01. depends on pseudo code described algorithm below find primes up to N in java rogramming language. For all numbers a : from 2 to sqrt(N) IF a is unmarked THEN a is prime For all multiples of a (a < n) mark them as composite All unmarked numbers are prime Input N: 200 Primes up to 200: 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 Hint: Put 1 to n in a array. Mark composites with 0.
- The Longest Subsequence Problem is a well-studied problem in Computer Science, where given a sequence of distinct positive integers, the goal is to output the longest subsequence whose elements appear from smallest to largest, or from largest to smallest. For example, consider the sequence S = [9,7,4,10,6,8,2,1,3,5]. The longest increasing subsequence of S has length three ([4,6,8] or [2,3,5]), and the longest decreasing subsequence of S has length five([9,7,4,2,1] or [9,7,6,2,1]). And if we have the sequence S = [531,339,298,247,246,195,104,73,52,31], then the length of the longest increasing subsequence is 1 and the length of the longest decreasing subsequence is 10. Question: Let S be a sequence with ten distinct integers. Prove by Contradiction that there must exist an increasing subsequence of length 4 (or more) or a decreasing subsequence of length 4 (or more). Hint: for each integer k in the sequence you found in the first part, define the ordered pair (x(k), y(k)), where x(k)…In python, The Longest Subsequence Problem is a well-studied problem in Computer Science, where given a sequence of distinct positive integers, the goal is to output the longest subsequence whose elements appear from smallest to largest, or from largest to smallest. For example, consider the sequence S= [9,7,4,10,6,8,2,1,3,5]. The longest increasing subsequence of S has length three ([4,6,8] or [2,3,5]), and the longest decreasing subsequence of S has length five([9,7,4,2,1] or [9,7,6,2,1]). And if we have the sequence S = [531,339,298,247,246,195,104,73,52,31], then the length of the longest increasing subsequence is 1 and the length of the longest decreasing subsequence is 10. Question: Find a sequence with nine distinct integers for which the length of the longest increasing subsequence is 3, and the length of the longest decreasing subsequence is 3. Briefly explain how youconstructed your sequence.Below is an array of elements that can be traversed via Linear and Binary search. You will be given five elements for each searching algorithms. You need to list down the elements traversed until it reaches to the element we are looking for: 33 54 74 124 148 248 274 203 443 445 452 457 470 512 520 505 2 10 11 12 13 14 15 570 500 634 730 783 803 810 886 030 10 17 18 19 20 21 22 23 24 25 20 27 28 29 30 31 A. Linear Search 1. 763 2. 148 3. 476 4. 526 5. 74 B. Binary Search 1. 985 2. 590 3. 476 4. 887 5. 897
- Sudoku is a popular logic puzzle that uses a 9 by 9 array of squares that are organized into 3 by 3 subarrays. The puzzle solver must fill in the squares with the digits 1 to 9 such that no digit is repeated in any row, any column, or any of the nine 3 by 3 subgroups of squares. Initially, some squares are filled in already and cannot be changed. For example, the following might be a starting configuration for a Sudoku puzzle: Create a class SudokuPuzzle.java Download SudokuPuzzle.java that has the attributes • board—a 9 by 9 array of integers that represents the current state of the puzzle, where 0 indicates a blank square • start—a 9 by 9 array of boolean values that indicates which squares in board are given values that cannot be changed and the following methods: • SudokuPuzzle—a constructor that creates an empty puzzle • toString—returns a string representation of the puzzle that can be printed • addInitial(row, col, value)—sets the given square to the given value as an…Please do not give solution in image format thanku Implement the following recursively using sudo code: Suppose an elevator which is on a floor on n. For this elevator to go from the nth floor to the base(ground) floor, it should go to every floor under the nth floor. Let's consider an elevator on the 4th floor. This elevator 1st comes on the third(3rd) floor. 4th-> 3rd then 3rd-> 2nd then 2->1 and next 1->0(ground floor) The recursive equation defined is F(n)=1+F(n-1)Java Programming Some teams qualified for the 2014 World Cup. The score of the teams were stored in an array in sorted order and array index is the represents the team. Index O represents the Team 1; index 1 represents the Team 2 and so on. If a score is given, then should find out which team got that score with a O(log(n)) time. Since Ram wanted to solve this puzzle with binary search and he decided to write binary search himself. But he cannot remember the logic of binary search . Help Ram to write the program. Note: Create the main() inside the class BinarySearch' Function signature : public static int binarySearch(int] ar,int size,int key) Input and Output Format: Refer sample input and output for formatting specifications. Sample Input and Output 1: Enter the number of Teams: Enter the score: 12 16 23 45 67 Enter the score to be searched: 23 23 is the score of Team 3