The Fibonacci algorithm is a famous mathematical function that allows us to create a sequence of numbers by adding together the two previous values. For example, we have the sequence: 1, 1, 2, 3, 5, 8, 13, 21... Write your own recursive code to calculate the nth term in the sequence. You should accept a positive integer as an input, and output the nth term of the sequence. Once you have created your code, add comments describing how the code works, and the complexity of any code you have created.

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...

K + edgenuity.com/player/ s Semester A 7 1 2 3 4 5 05 return 1 else: return n* factorial(n-1) Which line of code includes a recursive function call? 0 3 04 01 Consider the Python code for finding the factorial of an integer n using recursion. Line numbers have been added to the left of each line of code. def factorial(n): if n == 1: Mark this and return c C O M 31 0 DELL O FIXIXI A Save and Exit G < Next English Sign out V 4 19 Kinley Heat TIME REMAINING 59:14 Submit Mar 27 0 2:38

Suppose you are given a vector x. Write first a pseudo-code or algorithm that would print out the sum of all the entries in x. You will probably want to use a some kind of for loop construction to achieve this. 1: for i = start : finish do 2: statements 3: end for Now use the start:increment:finish notation, and modify your procedure slightly, to print out the sum of the odd elements in the array (that is, the elements in entries 1, 3, 5, and so on). Implement and test your algorithm with an arbitrary array of real numbers using Python.

Make a code using Recursion The countSubstring function will take two strings as parameters and will return an integer that is the count of how many times the substring (the second parameter) appears in the first string without overlapping with itself. This method will be case insensitive. For example: countSubstring("catwoman loves cats", "cat") would return 2 countSubstring("aaa nice", "aa") would return 1 because "aa" only appears once without overlapping itself. public static int countSubstring(String s, String x) { if (s.length() == 0 || x.length() == 0) return 1; if (s.length() == 1 || x.length() == 1){ if (s.substring(0,1).equals(x.substring(0,1))){ s.replaceFirst((x), " "); return 1 + countSubstring(s.substring(1), x); } else { return 0 + countSubstring(s.substring(1), x); } } return countSubstring(s.substring(0,1), x) + countSubstring(s.substring(1), x); } public class Main { public static void main(String[] args) {...

1. a) Given a recursive algorithm as below: int F(int n) { if (n <= 1) return 1; else if (n % 2 == 0) return F(n-1) + n; else return F(n/2) - 1; } Illustrate how you will find out the value of F(10) using the above algorithm. You need to show all the steps. b) Given a function as below: int recFx(int a, int b) { If (a < b) return a +b; else return recFx(a - b, b + 1); } Determine the values of: recFx(-10, 8) recFx(148, 78) (11) Must show all the steps.

The Tower of Hanoi is a puzzle where n disks of different sizes arestacked in ascending order on one rod and there are two other rods with nodisks on them. The objective is to move all disks from the first rod to thethird, such that:- only one disk is moved at a time- a larger disk can never be placed on top of a smaller oneWrite a recursive function that outputs the sequence of steps needed tosolve the puzzle with n disks.Write a test program in C++ that allows the user to input number of disks andthen uses your function to output the steps needed to solve the puzzle.Hint: If you could move up n−1 of the disks from the first post to thethird post using the second post as a spare, the last disk could be moved fromthe first post to the second post. Then by using the same technique you canmove the n−1 disks from the third post to the second post, using the firstdisk as a spare. There! You have the puzzle solved. You only have to decidewhat the nonrecursive case is, what the recursive...

Python

Using recursion, write a function sum that takes a single argument n and computes the sum of all integers between 0 and n inclusive. Do not write this function using a while or for loop. Assume n is non-negative. def sum(n): """Using recursion, computes the sum of all integers between 1 and n, inclusive. Assume n is positive.>>> sum(1) 1>>> sum(5) # 1 + 2 + 3+ 4+ 5 15 "*** YOUR CODE HERE ***"

python 3 Write a program that lists all ways people can line up for a photo (all permutations of a list of strings). The program will read a list of one word names, then use a recursive method to create and output all possible orderings of those names, one ordering per line. When the input is: Julia Lucas Mia then the output is (must match the below ordering): Julia Lucas Mia Julia Mia Lucas Lucas Julia Mia Lucas Mia Julia Mia Julia Lucas Mia Lucas Julia question: is it any way that i can use ('if' statement as base case, and 'else' statement as recursive case) in the code below? thanks. code: def all_permutations(permList, nameList):# TODO: Implement method to create and output all permutations of the list of names.def createPermutationsList(nameList):f = len(nameList) if f == 0:return [] if f == 1:return [nameList] permList = [] for i in range(f):newList = nameList[i]remaining = nameList[:i] + nameList[i+1:]for p in createPermutationsList(remaining):permList.append([newList] + p)...

Python language only Suppose you are working in the pizza company named Dominoes. Dominoes provides the best in class pizza in the world so While dealing with the coustomer you got a number on every billed amount. SO here your task is to identifiy that the billing amount is a magic number or not. A number is said to be a magic number, if the sum of its digits are calculated till a single digit recursively by adding the sum of the digits after every addition. If the single digit comes out to be 1,then the number is a magic number. Input : 1234Output : Yes it isInput : 12345Output : No it is not

Finish the splitOdd10 using recursion to determine if the elements of an array can be split into two groups such that the sum of one group is a non-zero multiple of 10 and the sum of the other group is odd

IN PYTHON, Using recursion: ask the user for the length of a square and the character they want to use. Draw the square (similar to mini assignment #15 in functions part 3). Once the user creates the square with their specification, ask them if they want it to be smaller or larger and how many times. Draw all the squares growing in size to the specified range.