(Research Project: 1m proving the Recursive Fibonacci Implementation) In Section 5.15, the recursive
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- Please help. I don’t understandarrow_forwardOne-friend recursion vs iteration. 1. Your objective is to receive the tuple a1, a2,..., a and return the tuple an, an1,..., a1 that has been inverted. You will only take an element off of one end or put an element back on one end because you are being lazy. But you have friends in recursion who can assist you.Please provide the recursive code as well as a paragraph with the friend's description of the algorithm.2. Now imagine that you lack friends but have a stack. Quickly design an iterative programme to address this issue. Include loop invariants and other crucial stages that are necessary to describe an iterative method.3. Trace both of these scripts separately. On a computer, step by step compare and contrast their calculations.arrow_forwardPlease help Report - I/II. Do not copy other solutions. Please write your own words to avoid doing same with others.arrow_forward
- please code in python Here is another recursion example, but with less guidance. Write a function log2(x), which gives an integer approximation of the log base 2 of a positive number x, but it does so using recursion. Use a base case where you return 0 if x is 1 or less. In the general case, add 1 to the answer and divide x by 2. (This is purposely vague so you can figure it out yourself.)arrow_forwardRecursion can be direct or indirect. It is direct when a function calls itself and it is indirect recursion when a function calls another function that then calls the first function. To illustrate solving a problem using recursion, consider the Fibonacci series: - 1,1,2,3,5,8,13,21,34...The way to solve this problem is to examine the series carefully. The first two numbers are 1. Each subsequent number is the sum of the previous two numbers. Thus, the seventh number is the sum of the sixth and fifth numbers. More generally, the nth number is the sum of n - 2 and n - 1, as long as n > 2.Recursive functions need a stop condition. Something must happen to cause the program to stop recursing, or it will never end. In the Fibonacci series, n < 3 is a stop condition. The algorithm to use is this: 1. Ask the user for a position in the series.2. Call the fib () function with that position, passing in the value the user entered.3. The fib () function examines the argument (n). If n < 3…arrow_forwardProvide JAVA source code with proper comments for attached assginment.arrow_forward
- Only typing answers please.arrow_forwardQuestion 1: Implement programs that run and give running time for the two Fibonacci sequence functions based on recursion and iteration.arrow_forwardRecursion is a technique that calls the function by itself. Demonstrate and write a program to find the GCD of two numbers using recursion and mention the advantages of recursion.arrow_forward
- Write a recursive function for int powerOfTwo (int k). The function determines the value of 2k. (Note: k is a positive integer). Example, when k=0 the function returns 1 and when k-3 the function returns 8. To show that your code is correct, give the recursive trace for powerOfTwo (2) that returns 4.arrow_forwardIteration versus one-friend recursion. 1. Your job is to accept the tuple a1, a2,..., a and return the tuple an, an1,..., a1 that has been reversed. You will only take an element off of one end or put an element back on one end because you are being indolent. But you have allies in recursion who can assist you.Please include the recursive code as well as a paragraph with the friend's description of the algorithm. 2. Now imagine that you lack pals but have a stack. (Refer to Chapter 3. Quickly design an incremental programme to address this issue. Include loop invariants and other crucial stages that are necessary to describe an iterative algorithm. 3. Trace both of these scripts separately. Compare and contrast their computerised calculations step by step.arrow_forwardNeed python help. For problems 1 and 2, add your code to the file Lab2.java. Add your tests in the main function of Lab2.java. Do not use static variables in class Lab2 to implement recursive methods. Problem 1: Implement a recursive method min that accepts an array and returns the minimum element in the array. The recursive step should divide the array into two halves and find the minimum in each half. The program should run in O(n) time and consume O(logn) memory. Demonstrate the output of min on the array int [] a = { 2, 3, 5, 7, 11, 13, 17, 19, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 23, 29, 31, 37, 41, 43 } Problem 2 You have been offered a job that pays as follows: On the first day, you are paid 1 cent, on the second day, 2 cents, on the third day, 4 cents and so on. In other words, your pay doubles every day. Write a recursive method computePay that for a given day number computes the pay in cents. Assume that you accumulate all the money that you are paid. Write a…arrow_forward
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