Old MM2 hw #

Write a recursive Racket function “sum-alternate” that takes a positive integer x as a parameter. The function should return the sum of all the integers x, x-2, x-4, x-6, etc, as long as the numbers are positive. For example, (sum-alternate 5) should evaluate to 5+3+1, and (sum-alternate 6) should evaluate to 6+4+2.

(define (sum-acc sum acc)
    (if (<= sum 0)
        acc
        (sum-acc (- sum 2) (+ sum acc))))

(define (sum-alternate sum)
        (sum-acc sum 0))

Write a recursive Racket function “sum” that takes two integers as parameters, each greater or equal to zero, and evaluates to their sum. In this problem, you must use the built-in functions add1 and sub1 and may not use the built-in functions “+” or “-”. For example, (sum 2 3) should evaluate to 5. Note: (add1 5) evaluates to 6 and (sub1 4) evaluates to 3. Hint: like you saw in the “append” lecture, treat one of the parameters as the size of the problem and recurse until it reaches your base case.

(define (sum-acc a b acc)
    (cond ((> a 0) (sum-acc (sub1 a) b (add1 acc)))
          ((> b 0) (sum-acc a (sub1 b) (add1 acc)))
          (else acc)))

(define (sum a b)
        (sum-acc a b 0))

Write a recursive Racket function “remove-char” that takes two string parameters, s and c, and evaluates to string s with all occurrences of c removed. The string c is guaranteed to be a length-1 string; in other words a single character string. For example (remove-char "abc" "b") should evaluate to “ac”. Here is pseudocode that you could implement.

if s is empty
   return s
else if (c = first char of s)
   return remove-char(all but first char of s)
else
   return first char of s concatenated with remove-char(all but first char of s)

(define (remove-char s c)
    (cond ((string=? s "") s)
          ((string=? c (substring s 0 1)) (remove-char (substring s 1) c))
          (else (string-append (substring s 0 1) (remove-char (substring s 1) c)))))

Write a recursive Racket function “all-same” that takes a string as a parameter and evaluates to true iff every character in the string is the same. Note: A string of length 0 or 1 should also evaluate to true.

(define (all-same s)
    (cond ((<= (string-length s) 1) #t)
          ((string=? (substring s 0 1) (substring s 1 2)) (all-same (substring s 1)))
          (else #f)))