Write solutions for below questions in scheme programming (.functional programming )

Write solutions for below questions in scheme programming (.functional programming )

1. Implement a function that returns the third element of a list.

2. Write a simple function that adds the first n integers. (e.g. (sum 5) returns 15).

3. Write a simple function that calculates the sum of a list of integers. e.g. (sum ‘(5 4 6)) returns 15. Implement a non-tail-recursive solution and a tail-recursive solution.

4. Write a Scheme max function that finds the largest number. The input should be a list of integers. The logic is discussed as follows.

boolean max(lst){

if (lst has only one element){

return the one element in lst

}

else if (car(lst) > max(cdr(lst))) {

return car(lst)

}

else {

return max(cdr(lst))

}

}

5. Arithmetic of Functions

We can define a higher-order function, i.e. functional form that accepts two functions as parameters and returns their sum,

As a running example, we consider two functions:

f(x) = x + 2

g(x) = 3x + 4

These are modeled, respectively, by the following Scheme functions:

(define (f x) (+ x 2))

(define (g x) (+ (* 3 x ) 4))

The higher-order function:

(define (plus func1 func2)

(lambda (x) (+ (func1 x) (func2 x))))

Note the use of lambda in order to return a nameless function. In essence, we are accepting two functions, func1 and func2, and returning a function that takes one parameter x and represents their sum. We can apply this functional form as follows:

((plus f g) 10) ; returns 46.

Or

(define (plus func1 func2 x)

(+ (func1 x) (func2 x))

)

(plus f g 10) ; returns 46.

Define a function (form) that computes the difference between two functions.

6. Imagine an accounting routine used in a bookshop. It works on a list with sublists, which look like this:

Order Number Book Title and Author Quantity Price per Item

34587 Learning Python, Mark Lutz 4 40.95

98762 Programming Python, Mark Lutz 5 56.80

77226 Head First Python, Paul Barry 3 32.95

Write a PURE Python function, which returns the grand sale total in dollar amount. The only parameter to the function is the list, and i/o should be in the main method. PLEASE DO NOT USE For loop except if list comprehension is used.