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- 4.6.1: Recursive function: Writing the base case. Add an if branch to complete double_pennies()'s base case.Sample output with inputs: 1 10Number of pennies after 10 days: 1024 Note: If the submitted code has an infinite loop, the system will stop running the code after a few seconds, and report "Program end never reached." The system doesn't print the test case that caused the reported message # Returns number of pennies if pennies are doubled num_days timesdef double_pennies(num_pennies, num_days):total_pennies = 0 ''' Your solution goes here ''' else:total_pennies = double_pennies((num_pennies * 2), (num_days - 1)) return total_pennies # Program computes pennies if you have 1 penny today,# 2 pennies after one day, 4 after two days, and so onstarting_pennies = int(input())user_days = int(input()) print('Number of pennies after', user_days, 'days: ', end="")print(double_pennies(starting_pennies, user_days))Define a function is_prime that recieves an integer arguement and returns true if the arguement is a prime number and otherwise returns false. This function may be written with a for loop, while loop or using a recursion.4.7.1: Writing a recursive math function. Write code to complete raise_to_power(). Note: This example is for practicing recursion; a non-recursive function, or using the built-in function math.pow(), would be more common.Sample output with inputs: 4 24^2 = 16
- Artificial Intelligence (Part - 2) ==================== The Towers of Hanoi is a famous problem for studying recursion incomputer science and searching in artificial intelligence. We start with N discs of varying sizes on a peg (stacked in order according to size), and two empty pegs. We are allowed to move a disc from one peg to another, but we are never allowed to move a larger disc on top of a smaller disc. The goal is to move all the discs to the rightmost peg (see figure). To solve the problem by using search methods, we need first formulate the problem. Supposing there are K pegs and N disk. (2) What is the size of the state space?Computer Science A) If the values of c and d are given and the function Euclid(c,d) below is executed, multiple recursive calls (Bolded at function) are performed to obtain gcd(c,d) and terminate. Give examples of c and d that make exactly 7 recursive calls, and show the process. However, c>d>=1. Euclid(c,d) if d=0 then return c else return Euclid(d,c mod d)Use Sage to program Exercise 5.In 1202 AD, Leonardo Pisano asked the following famous problem:A certain man had a pair of rabbits together in a certain enclosedplace, and one wishes to know how many are created from the pair inone year when it is the nature for of them in a single month to bearanother pair, and in the second month those born bear also. Becausethe abovewritten pair in the first month bore, you will double it. therewill be two pairs in one month. One of these, namely the first, bears inthe second month, and thus there are in the second month three pairs;of these in one month two are pregnant, and in the third month 2pairs of rabbits are born, and thus there are 5 pairs in the month;...Explain how the rabbits reproduce. Create a list F where F[x] is the number ofrabbits in month x. (so F[0]=1, F[1]=2) Find F[12]. Find F[100].
- Artificial Intelligence (Part - 1) ==================== The Towers of Hanoi is a famous problem for studying recursion in computer science and searching in artificial intelligence. We start with N discs of varying sizes on a peg (stacked in order according to size), and two empty pegs. We are allowed to move a disc from one peg to another, but we are never allowed to move a larger disc on top of a smaller disc. The goal is to move all the discs to the rightmost peg (see figure). To solve the problem by using search methods, we need first formulate the problem. Supposing there are K pegs and N disk. (1) Propose a state representation for the problem?10.25 LAB: Quadratic formula Implement the quadratic_formula() function. The function takes 3 arguments, a, b, and c, and computes the two results of the quadratic formula: x1=−b+b2−4ac2a x2=−b−b2−4ac2a The quadratic_formula() function returns the tuple (x1, x2). Ex: When a = 1, b = -5, and c = 6, quadratic_formula() returns (3, 2). Code provided in main.py reads a single input line containing values for a, b, and c, separated by spaces. Each input is converted to a float and passed to the quadratic_formula() function. Ex: If the input is: 2 -3 -77 the output is: Solutions to 2x^2 + -3x + -77 = 0 x1 = 7 x2 = -5.50A self-avoiding walk in a lattice is a path from one point to another that does not visit the same point twice. Self-avoiding walks have applications in physics, chemistry, and mathematics. They can be used to model chainlike entities such as solvents and polymers. Write a Turtle program that displays a random path that starts from the center and ends ata point on the boundary, as shown in Figure 11.11a, or ends at a dead-end point (i.e., surrounded by four points that have already been visited), as shown in Figure 11.11b. Assume the size of the lattice is 16 * 16.
- 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…What is the data type of pointer variables? Suppose that we don‘t know the name of a variable but we do know its address. Can we access the contents of that variable? Explain briefly. Subject: C++Create a recursive function that checks if a word is a palindrome. A palindrome is a word, phrase, number, or other sequences of characters that reads the same forward and backward (ignoring spaces, punctuation, and capitalization). For example, "radar" is a palindrome.
