Python Programming Exercises1. Modify the recursive Fibonacci program given in the chapter so that it printstracing information. Specifically, have the function print a message when it iscalled and when it returns. For example, the output should contain lines likethese:Computing fib(4)Leaving fib(4) returning 3Use your modified version of fib to compute fib(10) and count how manytimes fib(3) is computed in the process.# fib.pydef loopFib(n):# pre: n > 0# returns the nth Fibonacci numbercurr = 1prev = 1for i in range (n-2):curr, prev = curr+prev, currreturn curr# fib.pydef recFib(n):if n < 3:return 1else:return recFib(n-1) + recFib(n-2)

count3 = 0def recFib(n): global count3 if n == 3: count3 += 1 print(f"Computing fib({n})") if n…

1. Modify the recursive Fibonacci program given in the chapter so that it prints tracing information. Specifically, have the function print a message when it is called and when it returns. For example, the output should contain lines like these:

1. Modify the recursive Fibonacci program given in the chapter so that it prints tracing information. Specifically, have the function print a message when it is called and when it returns. For example, the output should contain lines like these:

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 17PE

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Modify the recursive Fibonacci program given in this chapter so that itprints tracing information. Specifically, have the function print a messagewhen it is called and when it returns. For example, the output shouldcontain lines like these: Computing fib(4)0 0 0Leaving fib(4) returning 3 Use your modified version of fib to compute fib(10) and count howmany times fib(3) is computed in the process.
For function log, write the missing base case condition and the recursive call. This function computes the log of n to the base b. As an example: log 8 to the base 2 equals 3 since 8 = 2*2*2. We can find this by dividing 8 by 2 until we reach 1, and we count the number of divisions we make. You should assume that n is exactly b to some integer power. Examples: log(2, 4) -> 2 and log(10, 100) -> 2 public int log(int b, int n ) { if <<Missing base case condition>> { return 0; } else { return <<Missing a Recursive case action>> }}
A palindrome is a sentence that contains the same sequence of letters reading it either forwards or backwards. A classic example is '1\.ble was I, ereI saw Elba." Write a recursive function that detects whether a string is apalindrome. The basic idea is to check that the first and last letters of thestring are the same letter; if they are, then the entire string is a palindromeif everything between those letters is a palindrome.There are a couple of special cases to check for. If either the first orlast character of the string is not a letter, you can check to see if the restof the string is a palindrome with that character removed. Also, when youcompare letters, make sure that you do it in a case-insensitive way.Use your function in a program that prompts a user for a phrase andthen tells whether or not it is a palindrome. Here's another classic fortesting: '1\. man, a plan, a canal, Panama!"
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…
Recursion 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…
Write a recursive fibonacci (n) function with an expression body. The function should return an Int; it will be too slow to deal with inputs whose fibonacci numbers are too large anyway. You do *not* need to use memoization. Note that: fibonacci(0) = 0 fibonacci(1) = 1 fibonacci(n, where n is greater than 1) = fibonacci(n-2) + fibonacci(n - 1)
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.
Write a recursive function to implement the recursive algorithm (multiplying two positive integers using repeated addition). Also, write a program to test your function.
Write a recursive function called print_num_pattern() to output the following number pattern. Given a positive integer as input (Ex: 12), subtract another positive integer (Ex: 3) continually until 0 or a negative value is reached, and then continually add the second integer until the first integer is again reached. For coding simplicity, output a space after every integer, including the last. Do not end output with a newline. Ex. If the input is: 12 3 the output is: 12 9 6 3 0 3 6 9 12 # TODO: Write recursive print_num_pattern() function if __name__ == "__main__": num1 = int(input()) num2 = int(input()) print_num_pattern(num1, num2)if (num1<=0): print(num1,end= '')
Recursion efficiency in Julia can be improved using memorization technique to store the values of previously computed functions. The following Fibonacci function below does not employ memorization, please change into a recursive function with memorization: function fib(n) if n==1 return 1 elseif n==2 return 1 elseif n<=0 printstyled("Invalid input",color=:red) return else return fib(n-1)+fib(n-2) end end
A recursive function is a function defined in terms of itself via self-referential expressions. This means that the function will continue to call itself and repeat its behavior until some condition is met to return a result. a- Write a python recursive function prod that takes x as an argument, and returns the result where, result=1*1/2*1/3*….*1/n b- Include a screenshot that shows a python program that uses the above function and prints the rounded result to three decimal places after prompting the user to enter a number, x. Use x=3. N.B: The code should be included in your answer.
Write a recursive function in f#, named specialSum, that has the followeing signature: int * int -> int, where sum(m,n) = m + (m +1) + (m+2) + ... + (m + (n-1)) + (m+n) for m >= 0 and n >= 0: (Hint use two clauses with (m,0) and (m,n) A PATTERNS.) start code with let rec specialSum (m,n) match m,n with | m,0 -> | m,n - >