Question

Objective To program using the functional programming paradigm Assignment: Write the following functions using Scheme (or LISP if you prefer) . A function (binomial N k) that returns the binomial coefficients C(N, k), defined recursively as: C(NO) = 1, C(N, N) = 1, and, for 0<k < N E(N, k) = C(N-1, k) + C(N-1, k-1) 2. A function (mod N M) that returns the modulus remainder when dividing N by M 3. A function (binaryToDecimal b) that takes a binary number and returns its decimal value (binaryToDecimal 1101) returns 13 . A function (addBinary binaryList) that takes a list of binary numbers and returns their 101)) returns 27 value in a simple list of integers s. A function (min list) that returns the smallest 6. A function (myRemove atm list) that removes all occurrences of the atom atm from a simple list, returning list with atm removed. myRemove should return the original list if atm is not found 7. A function (selectionSort list) that returns a simple list of integers in ascending order using a recursive selection sort algorithm. Hint: use your min function All the functions must be written in a functional style and must use only the basic LISP functions car, cdr, cons, null, atom, the equality functions, the arithmetic functions, and the append function

Answer 1

1.

(define (binomial N k)

(if (= k 0)

1

(if (= k N)

1

(+ (binomial (- N 1) k) (binomial (- N 1) (- k 1))))))

Output:

>(define (binonial N k) (k e) if (k N) (binontal N 1) k) (binontal (- N 1) (- k 1)))>) > (binonia1 8 3) Value: 56 (binonial 10 4) Value: 210 value: 21 1 (binonial 6 4) Value: 15
2.

(define (mod N M)

(remainder N M))

Output:

(define (mod N M) (remainder N M)) Value: mod 1 J-> (nod s 3) Value: J(nod 98 22) Value: 10
3.

(define (binaryToDecimal b)

(if (= b 0)     

0

(+ (remainder b 10) (* 2 (binaryToDecimal (quotient b 10))))))

Output:

(define (binaryToDectal b) Value: binarytodecimal 1 1 (binaryToDecimal 101) Value: 5 -(binaryToDecimal 1011) Value: 11 1 (binaryToDecimal 110101) Value: 53
4.

(define (binaryToDecimal b)

(if (= b 0)

0

(+ (remainder b 10) (* 2 (binaryToDecimal (quotient b 10))))))

(define (addBinary binaryList)

(if (null? binaryList)

0

(+ (binaryToDecimal (car binaryList)) (addBinary (cdr binaryList)))))

Output:

(define (addBinary binaryList) (if (null? binaryList) (binaryToDecimal (car binaryList)) (addBinary (cdr binaryList)) Value: addbinary ;value: 27 (addBinary '(101 1011 11000011)) Value: 211