4. Write a function to find the factorial of a number. 4.1 Follow a recursive procedure to obtain (fact n). (There is a version you should have already seen in the slides-try first to piece it together from your memory and then look back at slides for a solution). 4.2 Use comments to indicate in the code the four steps of the fantastic approach: 1) The size-n problem 2) 3) 4) All the stopping conditions and the return values. All the size-m problems The lines of code that construct the size-n solution from the size-m solutions. Test cases: (fact 5) → 120 (fact 8)→40320 Test much a bigger input number too.
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- The goal is to rewrite the function, below, such that passes in a different list of parameters, particularly eliminating the need to pass low and high for each recursive call to binary_search. defbinary_search(nums,low,high,item): mid=(low+high)//2iflow>high:returnFalse #The item doesn't exist in the list!elifnums[mid]==item:returnTrue# The item exists in the list!elifitem<nums[mid]:returnbinary_search(nums,low,mid-1,item)else:returnbinary_search(nums,mid+1,high,item) The new function should be prototyped below. The number of changes between the given version, and the one requested is not significant. defbinary_search(nums,item):pass# Remove this and fill in with your code Tip: If you consider that high and low are used to create a smaller version of our problem to be processed recursively, the version requested will do the same thing, just through a different, more Pythonic technique.Consider the following recursive function: def rec1(aList,first,last): if first==last: return aList[first] else: return aList[last]*rec1(aList,first,last-1) Show the output of the following call (show your work and all recursive calls): print(rec1([1,2,3,4,5,6,7],3,5))? describe the task of the rec1 function.Consider the recursive function provided above. After the initial call to the function ham has been made with argument 26 then how many subsequent recursive calls will be made before a value a final result can be returned? This question is internally recognized as variant 235. Q11) 1 2 3 4 5 6 7 8 none of the above
- 12. Consider the recursive function int gcd( int a, int b) int gcd( int a, int b){ if (b > a) return gcd(b,a); if ( b == 0 ) return a; return gcd( b, a% b); } How many invocation (calls) of the gcd() function will be made by the call gcd(72, 30)?is it correct ? Write a recursive function that returns the nth number in a fibonacci sequence when n is passed to function. The fibonacci sequence is like 0,1,1,2,3,5,8,13...... Answer: #include <iostream> using namespace std; int getFibonacci(int n) { if (n == 0 || n == 1) return n; else return getFibonacci(n - 1) + getFibonacci(n - 2); } int main() { int n = 7; int result = getFibonacci(n); cout << result; }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…
- 1. Consider the following recursive function: def foo(n): if (n == 0): return 0 return n + foo(n - 1)a. What is foo(5) b. What is foo(10) c. Suppose that n + foo(n - 1) is changed to n * foo(n - 1). What is foo(5) now? d. What happens if foo(-1) is called?please code in python Write a recursive function power(x, n), where n is 0 or a postive integer. For example, power(2, 10) will return 1024. Write a suitable base case, and for the general case use the idea that x**n = x * (x**n-1).An arithmetic sequence is a sequence of values where successive values have a common difference. For example, 2,5,8,11,... is an arithmetic sequence starting at 2 with a common difference of 3. We call the starting point s and the difference d. Fill in the missing lines below to write a recursive Python function called arithmetic that takes values for s, d, and n, and returns the nth term of the arithmetic sequence. For example, given the main function: def main(): for i in range(1,6): print(arithmetic(2,3,i)) the output will be: 2 5 8 11 14 Note: No marks will be given for a non-recursive solution. Code with missing lines: # Line 1 # Line 2 # Line 3 # Line 4 # Line 5 Matching each line of code below to its proper line number (Line 1 to Line 5), indicated in the partial code above, to solve the problem. Some lines of code will not be used at all; for these you would select option 6 (i.e., Not Used) from the list of options - do not leave these blank. Question 8 options:…
- please code in python Write a recursive function to add a positive integer b to another number a, add(a, b), where only the unit 1 can be added, For example add(5, 9) will return 14. The pseudocode is: # Base case: if b is 1, you can just return a + 1 # General case: otherwise, return the sum of 1 and what is returned by adding a and b - 1.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…