Algorithm Analysis: estimate the time complexity of the following methods using Big O notation. (highlight final answer)| (a) public static void mA(int n) { for (int i = 0; i < n; i++) { System.out.print (i) (b) public static void mB (int n) { for (int i = 0; i < n; i++) { for (int j = 0; j

Algorithm Analysis: estimate the time complexity of the following methods using Big O notation. (highlight final answer)| (a) public static void mA(int n) { for (int i = 0; i < n; i++) { System.out.print (i) (b) public static void mB (int n) { for (int i = 0; i < n; i++) { for (int j = 0; j

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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case #5 int i , p =1; for(i=1;i<=n;i++) p = p*i case #6 int rec(int r) { if(r==0) return 1; else return r*(rec(r-1); } Compare the two methods (#5 and #6 above) and answer the following: What is the “stopping” case for each (what causes the methods to “end”)? How do you guarantee that the methods will “stop” (infinite loop, infinite recursion)? Which method one is “better”? Why?
explain how to get correct answer for the following question Given that (n!=1 if n=0, n!=n x (n-1) x (n-2) x ... x 1) The order of growth for the depth of recursion associated with the recursive factorial (returns N!) method is: A. O(N) B. O(N^2) C. O(log2N). D. O(1). Given the following code, what are the constraints on the input argument? int mystery(int num){ if (num == 0) return 0; else if (num > 100) return -1; else return num + mystery(num – 1); } A. It must be between 0 and 100 inclusive. B. It must be greater than 0. C. It must be less than 0 or greater than 100. D. It must be greater than or equal to 0. The number of recursive calls that a method goes through before returning is called: A. order of growth efficiency. B. the depth of recursion. C. combinatorial recursive count. D. activation stack frame. The following code is supposed to return the sum of the numbers between 1 and n inclusive, for positive n. An analysis of the code using the…
Pseudo-random numbers Randomly generating numbers is a crucial subroutine of many algorithms in computer sci- ence. Because computers execute deterministic code, it is not possible (without external influence) to generate truly random numbers. Hence, computers actually generate psuedo- random numbers. The linear congruential method is a simple method for generating pseudo-random numbers. Let m be a positive integer and a be an integer 2 < a <m, and c be an integer 0 ≤ c<m. A linear congruential method uses the following recurrence relation to define a sequence of pseudo-random numbers: In+1=a+c mod m (a) Use the linear congruence method with a = 8, c=5, and m = 14, to compute the first 15 pseudo-random numbers when co= 1. That is, compute zo,X1, X 14- (b) From part (a) we should notice that, with m = 14, the sequence does not contain all 14 numbers in the set Z14. In particular because the sequence is periodic. Using m = 8, determine the value of a which does give all 8…
You are advised to refer to the recommended textbook “Introduction to Algorithms (3rdedition) by Thomas H. Corman, Charles E. Leiserson, Ronald L. Rivest and Clifford Stein”. Have areading through Chapter 04 and answer the following questions as a follow up exercise 1) Compute big-oh of the given T(n) using the iteration methods
Draw the recursion trace for the following algorithm, which is written in a pseudocode style: method6(int x, int y) { // returns integer if y=0, then return 1; else { int w = method6(x, y/3); // y/3 is integer division int z = w * x; if y is even, then z = z * 2 + 1; y = y + 1; end of if return z } // end of else
Tiling: The precondition to the problem is that you are given threeintegers n, i, j, where i and j are in the range 1 to 2n. You have a 2n by 2n squareboard of squares. You have a sufficient number of tiles each with the shape . Your goalis to place nonoverlapping tiles on the board to cover each of the 2n × 2n tiles except forthe single square at location i, j. Give a recursive algorithm for this problem in whichyou place one tile yourself and then have four friends help you. What is your base case?
Information is present in the screenshot and below. Based on that need help in solving the code for this problem in python. The time complexity has to be as less as possible (nlogn or n at best, no n^2). Apply dynamic programming. Do not use recursion. Make sure ALL test cases return expected outputs. Sample Input 0:5 20011014 Sample Output 0:1 1 Explanation 0:The best way to jump from square 1 to square 5 is by jumping 4 squares. That requires only 1 jump.In fact, that is the only solution, thus the second output is 1. Sample Input 1:6 3010100123 Sample Output 1:2 2 Explanation 1The best sequence is to jump 2 squares to square 3 then 3 squares to end in square 6.This is one solution. The other solution is to jump from 1 -> 3 -> 5 -> 6. These are the only two solutions, therefore the second output is 2. Sample Input 2:7 2000110037 Sample Output 2:-1 0 Explanation 2:It is impossible to reach square 7 with the specified jump values. The actual…
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///.
Information is present in the screenshot and below. Based on that need help in solving the code for this problem in python. The time complexity has to be as less as possible (nlogn or n at best, no n^2). Apply dynamic programming. Do not use recursion/memoization. Make sure ALL test cases return expected outputs. Sample Input 04 412340123 Sample Output 013715 Explanation 0You are given the sequence 1,2,3,4.F0 = A0 = 1F1 = A1 + F0 = 2 + 1 = 3F2 = A2 + F1 + F0 = 3 + 3 + 1 = 7F3 = A3 + F2 + F1 + F0 = 4 + 7 + 3 + 1 = 15 The actual code def solve(k,a): MOD = 1000000007 # compute and return answer here q, n = list(map(int,input().rstrip().split(" ")))a = [int(input().rstrip()) for i in range(n)]outs = []for i in range(q): k = int(input().rstrip()) outs.append(solve(k,a))print("{}".format("\n".join(list(map(str,outs)))))
Trace the execution of the call mystery(4) for the following recursive method using the technique shown in slide#15. What does this method do? public static mystery(int n) { if (n == 0) return 0; else return n*n + mystery(n-1); } Answer the above exercise using activation frames.
Consider the Java program bellow. What is the worst-case notation for the algorithm implemented in the solve method assuming the n value passed as an argument is equalto 90?
Subject: Design and Analysis of Algorithms Prove or disprove the following statements: (See attached photo for the problem) PLEASE SHOW YOUR SOLUTION