Problem 1: The Mysterious FunctionWe have come through an old interesting function whose pseudo-code was defined asfollows:Algorithm 1 MYSTERIOUS-FUNCTION(n)Require: n E Z An< 350if n > 350 thenreturn n – 47elsereturn MYSTERIOUS-FUNCTION(MYSTERIOUS-FUNCTION(n + 48))end ifa) Implement the an or.chm in Pythonb) Try various inpi ts, with the valid range n < 350, what have you noticed of theoutput?Prove your thoughts, hypothesis, in part (b)[Hint: use your implementation to prove a property of the output at a particularinput along with inductive scheme]d) Empirically, show the performance curve of the algorithm using time measurements

Prove your thoughts, hypothesis, in part (b) [Hint: use your implementation to prove a property of the output at a particular input along with inductive scheme] d) Empirically, show the performance curve of the algorithm using time measurements

Prove your thoughts, hypothesis, in part (b) [Hint: use your implementation to prove a property of the output at a particular input along with inductive scheme] d) Empirically, show the performance curve of the algorithm using time measurements

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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The Lucas numbers are a series of numbers where the first two Lucas numbers (i.e., at indices 0 and 1) are 2 and 1 (respectively) and the kth Lucas number L_k (where k>1) is L_(k-1) + L_(k-2). Consider the following recursive definition for a function that is supposed to find the nth element of the Lucas numbers. Select the best option that identifies the line of code that prevents this function from running recursively and provides the correct code. Question options: line 5 should be return recursive_function(n-1) + recursive_function(n-2) line 3 should be return [2,1][n-1][n-2] line 3 should be return [2,1][n-1] line 2 should be if n <= 2: line 5 should be return recursive_function(n-1 + n-2) None of these options
MAKE A FLOWCHART PLEASE clc;clear; function [] = Bisection(xl,xu,es,imax)ea = 100xr = (xu+xl)/2;x=xrfr=evstr(f)while (ea>es)a=fl-fu;if (a==0) thenmprintf("Error: Division by Zero")abortendtest = fl * fr;mprintf(" %d %10f %10f %10f %12.7f %12f %12.f %10.7f\n",iter,xl,xu,xr,fl,fu,fr,ea);if (test<0) thenxu=xr;elseif (test>0) thenxl=xr;elseif (test==0) thenmprintf("\n\nThe root of the equation is %f",xr)abortendx=xlfl=evstr(f)x=xufu=evstr(f)xrold=xrxr=(xu+xl)/2;x=xrfr=evstr(f)ea=abs((xr-xrold)/xr)*100;iter=iter+1;test=fl*frif ea < es thenmprintf(" %d %10f %10f %10f %12.7f %12.f %12.f %10.7f\n",iter,xl,xu,xr,fl,fu,fr,ea);mprintf("\n\nThe approximate root for the given function is %f",xr)abortendif iter > imaxmprintf("The approximate root for the given function is %f",xrold)mprintf("\nSlowly converges. It is suggested that the initial values should be change");abortendendendfunction //main disp("This program will solve/give the approximate root of any given nonlinear…
Use the Fibonacci search method for optimization and code a program in C to determine the maximum or minimum of a given function. The user must specify the function, the intervals, if the search is for a maximum or minimum and the number of iterations. The Fibonacci number and the new interval of each iteration needs to be displayed
a) Write a non-recursive function in C++/ to multiply all even numbers from 2 to n, where n is an input to the function, and n>=2. (reminder: An even number is divisible by 2 and generates a remainder of 0. for example 2,4,6,... are even numbers). b) Analyze your algorithm in part (a) in the worst-case. Show all your work. Then express the time as Big-O().
In programming, a recursive function calls itself. The classical example is factorial(n), which can be defined recursively as n*factorial(n-1). Nonethessless, it is important to take note that a recursive function should have a terminating condition (or base case), in the case of factorial, factorial(0)=1. Hence, the full definition is: factorial(n) = 1, for n = 0 factorial(n) = n * factorial(n-1), for all n > 1 For example, suppose n = 5: // Recursive call factorial(5) = 5 * factorial(4) factorial(4) = 4 * factorial(3) factorial(3) = 3 * factorial(2) factorial(2) = 2 * factorial(1) factorial(1) = 1 * factorial(0) factorial(0) = 1 // Base case // Unwinding factorial(1) = 1 * 1 = 1 factorial(2) = 2 * 1 = 2 factorial(3) = 3 * 2 = 6 factorial(4) = 4 * 6 = 24 factorial(5) = 5 * 24 = 120 (DONE) Exercise (Factorial) (Recursive): Write a recursive method called factorial() to compute the factorial of the given integer. public static int factorial(int n) The recursive algorithm is:…
I need help problem: A two dimensional random walk simulates the behavior of a particle moving in a grid of points. At each step, the random walker moves north, South, east, or West with probability 1/4, independent of previous moves. Compose a program that takes a command line argument n and estimates how long it will take a random walker to hit the boundary of a 2n-by-2n square centered at the starting point.
Question 1: Tracing Recursive functions The solution can be handwrittena) Trace the following recursive method for the function call “multiplyDigits(58746)” and show the output result.
Problem 5: Functions and Sets Let Σ denote a finite alphabet, Σ* denote all words over that alphabet, and L denote the function that maps a string to its length, i.e. L : Σ* → N (where N denotes the natural numbers) [a] Is L partial, total, or both? [b] Is L one-to-one? onto? a bijection? [c] How many words in Σ* have length n? [d] How many words in Σ* have length ≤ n [e] Explain whether Σ* is finite, countable, or uncountable. [f] Explain whether P(Σ*) - the set of all subsets over Σ* - is finite, countable, or uncountable. Hint: how is this related to the real numbers in [0, 1).
The solution can be handwritten b) Trace the following recursive method for the function call “isPalindrome(rotator)” and show the output result.
Note: Solve using c++ Write a recursive function to get count of a specific character in given string or array ofcharacters.Prototype of Function: int getCharCount(const char* ptr, char c)Input: const char* ptr=” wavelength”, char c=’e’Output: 2 (as ‘e’ occurs two times in the “wavelength”)
The first few numbers in the series of Lucasnumbers are:{1; 3; 4; 7; 11; 18; ... ; LN}The Lucas-numbers are determined by:(?1 = 1, ?2 = 3, ??+2 = ??+1 + ??)That is, a Lucas number is calculated as the sumof its two immediate previous terms in the Lucasseries.Using this information, write a C/C++ program thatdefines a function Lucas() that calculates the nthnumber in a Lucas number sequence, where theuser enters n into the program interactively. Forexample, if n=6, the program should display thevalue 18.The function accepts one integer parameter for thevalue of n and returns the result to the callingstatement in main().See the example output in Figure 2.2.
Redo problem 2 where you have to define and use the following functions: (a) isTriangle - takes 3 sides of a triangle and returns true if they form a triangle, false otherwise. (b) isIsosceles - takes 3 sides of a triangle and returns true if they form an isosceles triangle, false otherwise. (c) isEquilateral - takes 3 sides of a triangle and returns true if they form anequilateral triangle, false otherwise. (d) isRight - takes 3 sides of a triangle and returns true if they form a right triangle, false otherwise. (e) your program should run continuous until the user wants to quit this is my problem 2: #include <iostream> #include <cmath> using namespace std; // Constant Declarations const double E = .0001; int main() { double side1, side2, side3; bool isTriangle, isRight, isEquilateral, isIsosceles; cout << "Enter the lengths of the 3 sides of a triangle -- "; cin >> side1 >> side2 >> side3; isTriangle = side1 + side2 > side3 &&side1 +…