1. A sequence of numbers can be defined recursively, that is the next number can be defined as a function of one or more of the previous numbers (the Fibonacci Sequence is a well known example of this). A recursive sequence is given by the recursive formula Xn = 3xn-1+ 2x,n–2 where 11 = 1 and x2 = 1. (a) Write a small program, using a loop, to calculate and display the first 10 terms, a1,..., x10- If we do not need to store past results for (say) plotting purposes we do not need to save past values. In your code do not create a vector of these values, that is do not use subscripts( ie x(1), x(2) etc) in your code. The calculation that is repeated, ie xn = 3xn-1+2xn-2, has the form c= 36 + 2a. You should update the values in a and b (as the relevant older values) each time through the loop after c has been calculated. (b) Now create a version where you do create a vector saving the values of xn and then plot these values against n using a semi-log axis (log in the "y-axis"). Give the plot a title and tight axis and use '.-r' dictates that we join the dots with lines and use the colour read.

1. A sequence of numbers can be defined recursively, that is the next number can be defined as a function of one or more of the previous numbers (the Fibonacci Sequence is a well known example of this). A recursive sequence is given by the recursive formula Xn = 3xn-1+ 2x,n–2 where 11 = 1 and x2 = 1. (a) Write a small program, using a loop, to calculate and display the first 10 terms, a1,..., x10- If we do not need to store past results for (say) plotting purposes we do not need to save past values. In your code do not create a vector of these values, that is do not use subscripts( ie x(1), x(2) etc) in your code. The calculation that is repeated, ie xn = 3xn-1+2xn-2, has the form c= 36 + 2a. You should update the values in a and b (as the relevant older values) each time through the loop after c has been calculated. (b) Now create a version where you do create a vector saving the values of xn and then plot these values against n using a semi-log axis (log in the "y-axis"). Give the plot a title and tight axis and use '.-r' dictates that we join the dots with lines and use the colour read.

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter15: Recursion

Section: Chapter Questions

Problem 1TF

See similar textbooks

Similar questions

4. The Fibonacci series: 0, 1, 1, 2,3,5,8,13,21... begins with terms 0 and 1 and has the property that each succeeding term is the sum of the two previous terms. Write a program containing a recursive function that computes and displays the nh Fibonacci number, given the value for n.
An arithmetic sequence starts 2, 5, . . . Write a recursive definition for this sequence using function notation.
Question
2. Consider a rectangle whose side lengths are two consecutive Fibonacci numbers. (Of course, neither of them is 0.) Such a rectangle could be, for example, 3 by 5, or 8 by 13, or 21 by 34, etc. (a) Give a recursive algorithm to dissect such a rectangle into squares such that no more than two of the resulting squares are the same size. (For example, if you had two 3 by 3 squares, you could have at most one 4 by 4 square.) Here's a specification for your algorithm: // Input: Two consecutive Fibonacci numbers f0, f1, representing an f0 by f1 rectangle, such that f0 <= f1. (Neither f0 nor f1 will be 0.) // Output: A list of integers representing side lengths of squares, such that the input rectangle can be dissected into squares of those sizes. No more than two of the squares can be the same size. Please be sure to give an English description of the algorithm along with pseu- docode, explaining the main points of its design, and a concise inductive argument for its correctness (i.e., say…
A recursive sequence is defined by - d k = 6 d k − 1 + 3 , for all integers k ≥ 2 and d1 = 2 Use iteration to guess an explicit formula for the above sequence.
Write a recursive function to implement the recursive algorithm (determining the number of ways to select a set of things from a given set of things). Also, write a program to test your function.
Consider the sequence -3 4 11 18 1.write a recursive definition for the sequence 2.write a actual formula for the sequence (not recursive) convert the binary number 1100 0101 1010 1001 to hexadecimal
Consider a network of streets laid out in a rectangular grid, In a northeast path from one point in the grid to another, one may walk only to the north (up) and to the east (right). Write a program that must use a recursive function to count the number of northeast paths from one point to another in a rectangular grid. Your program should prompt the user to input the numbers of points to the north and to east respectively, and then output the total number of paths. Notes: 1. Here is a file (timer.h download and timer.cpp download) which should be included in your program to measure time in Window or Unix (includes Mac OS and Linux) systems (use start() for the beginning of the algorithm, stop() for the ending, and show() for printing). 2. The computing times of this algorithm is very high, and the number of paths may be overflow, don't try input numbers even over 16. 3. Name your recursive function prototype as calcPath(int north, int east) to ease grading. 4. Paste your output
A 5-digit positive integer is entered through the keyboard, write a function to calculate multiplication of digits of the 5-digit number: (1) Without using recursion (2) Using recursion
Using recursive functions in Python, given three letters in the alphabet, get their permutations together with the combinations of any two letters from it.
Write a recursive algorithm to calculate the factorial function of a given number. Implement the below algorithm in c programming language using a recursive function. Save and print a copy of your c program.
31