a) AlgorithmX(n) 1. xfl 2. for i 1 to n² 3. x←max(x,i) 4. for j1 to n² 5. x←max(x.j) 6. return x b) Algorithm Y(n) 1. xl 2. for i 1 to n³ 3. 4. 5. 6. 7. j←I while j
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- 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 dynamicprogramming 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.Check these two codes and then answer these questions please: 1) Empirically, show the performance curve of the algorithm using time measurements 2) Using the basics of the theoretical analysis, write the complexity of its worst-casetime. 1. Approach: Non recursive: //include necessary header files#include <iostream>using namespace std;//main functionint main(){ int days,buy_on_this_day ,sell_on_this_day; //get number of days as input from user cout<<"Enter number of days: "; cin>>days; int stock_price[days]; for(int i=0;i<days;i++) { cout<<"Enter stock_price"; cin>>stock_price[i]; } int i=0; for(int i=0;i<days-1;i++) { //comparing current price with next day price and finding the minima while(i<days-1 && stock_price[i+1]<=stock_price[i]) i++; if(i==days-1) break; buy_on_this_day =i++; while(i<days && stock_price[i]>=…a) Consider a recursive function to return the Number of Binary Digits in the Binary Representation of a Positive Decimal Integer (n) using a recursive algorithm. int Process (int n) { if (n == 1) return 1; else return (Extra() + Process (n/4) + Process (n/4)); } Given that Extra(n) is a function of O(n)1) Find T(n) = number of arithmetic operations. 2) Calculate the complexity of this algorithm using Back Substitution.
- #4. Euler's totient function, also known as phi-function ϕ(n),counts the number of integers between 1 and n inclusive,which are coprime to n.(Two numbers are coprime if their greatest common divisor (GCD) equals 1)."""def euler_totient(n): """Euler's totient function or Phi function. Time Complexity: O(sqrt(n)).""" result = n for i in range(2, int(n ** 0.5) + 1): if n % i == 0: while n % i == 0: n //= i.1. a.An algorithm can be specified in various ways. Identify and explain four ways in which an algorithm can be specified. b. (b). Two algorithms A, B sort the same problem. When you go through each algorithm and break them down into their primitive operations, each can be represented as follows:A = 2n7 + 100n4 + 26n + 50 B = 7n4 + 22n2 + nlogn + 200For very large values of n, which of the algorithms A or B will runin the shortest time to solve the problem and why? (c). Two Computer Science students, Priscilla and Julius, are discussing how to compare two algorithms for solving a given problem. Priscilla suggests that they should use the execution times of the algorithms as criterion; but Julius insists that they should use the number of statements the algorithms execute as criterion. (i). Discuss the reasons why both criteria they are considering are not good for comparing algorithms.(ii). Recommend an ideal solution/criterion that they should rather use for comparing algorithmsUsing recursion, write a Java program that takes an input ‘n’ (a number) from a user to calculate and print out the Fibonacci using the following modified definition: F(N) = 1 if n = 1 or n = 2 = F((n+1)/2)2 + F((n-1/2)2 if n is odd = F(n/2 + 1)2 – F(n/2 – 1)2 if n is even Your solution must implement recursion to receive points for this question.
- calculate number of operations in this algorithm void my_dgemv(int n, double* A, double* x, double* y) { double alpha=1.0, beta=1.0; int lda=n, incx=1, incy=1; cblas_dgemv(CblasRowMajor, CblasNoTrans, n, n, alpha, A, lda, x, incx, beta, y, incy); }Construct a memoized algorithm for this algorithm and and derive its time complexity: 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 dynamicprogramming 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. You do not need to prove the complexity bound formally, just derive it by analyzing each component in your algorithm.Given a positive integer 'n', find and return the minimum number of steps that 'n' has to take to get reduced to 1. You can perform any one of the following 3 steps:1.) Subtract 1 from it. (n = n - 1) ,2.) If its divisible by 2, divide by 2.( if n % 2 == 0, then n = n / 2 ) ,3.) If its divisible by 3, divide by 3. (if n % 3 == 0, then n = n / 3 ). Write brute-force recursive solution for this.Input format :The first and the only line of input contains an integer value, 'n'.Output format :Print the minimum number of steps.Constraints :1 <= n <= 200 Time Limit: 1 secSample Input 1 :4Sample Output 1 :2 Explanation of Sample Output 1 :For n = 4Step 1 : n = 4 / 2 = 2Step 2 : n = 2 / 2 = 1 Sample Input 2 :7Sample Output 2 :3Explanation of Sample Output 2 :For n = 7Step 1 : n = 7 - 1 = 6Step 2 : n = 6 / 3 = 2 Step 3 : n = 2 / 2 = 1 SolutionDp///.
- Discuss another algorithm under Divide and Conquer. In your discussion, include the following: 1. Introduction about the algorithm. 2. The pseudocode 3. Explanation of its complexityCorrect answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. Ridbit begins with an integer n. In one action, he can perform one of the accompanying tasks: partition n by one of its appropriate divisors, or take away 1 from n in case n is more prominent than 1. An appropriate divisor is a divisor of a number, barring itself. For instance, 1, 2, 4, 5, and 10 are appropriate divisors of 20, however 20 itself isn't. What is the base number of moves Ridbit is needed to make to decrease n to 1? Input The principal line contains a solitary integer t (1≤t≤1000) — the number of experiments. The main line of each experiment contains a solitary integer n (1≤n≤109). Output For each experiment, output the base number of moves needed to lessen n to 1.Analyze another algorithm under Divide and Conquer. In your discussion, include the following: 1. Introduction about the algorithm. 2. The pseudocode 3. Explanation of its complexity