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Ch4 HW1

Read pages 99-101 in the book and write complement and find-all, possibly copying them from the book.

(ball)
- Make a structure ball that holds the kind of ball (a symbol) and the circ-umference of the ball (in inches, a number).
- Create a softball with a circumference of 12.
- Modify the circumference to be 13.
- Write a function that takes in anything (even lists and numbers) and returns true if the item is a ball of circumference greater than 10.
The function pos+ takes in a list and returns a list of each element plus its position.
```
 (pos+ '(7 5 1 4))
 => (7 6 3 7)
```
Write the pos+ function using (i) recursion; (ii) iteration (like loop); and (iii) mapcar.
Write a function rle that takes in a list and outputs a list of pairs (item repeats), where repeats tells how many times in a row the item is repeated.
```
 (rle '(7 7 7 7 7 4 1 4 4 4))
 => ((7 5) (4 1) (1 1) (4 3))
```
(div2) You will write the function div2, divides a number by two. It has a keyword argument :skip-odd which defaults to false (nil).
```
 (div2 5) => 2.5
 (div2 8) => 4
 (div2 5 :skip-odd T) => 5
 (div2 8 :skip-odd T) => 4
```
(add2len) Use &rest to make a function that returns the first number added to the number of arguments it receives.
```
 (add2len 5 10 20 30 40 50 60) => 5 + 7 = 12        
```

Fixit

A classmate is trying to write a function that reteurns the sum of all of the non-nil elements in a list. Neither version below works. Explain why and fix each (in the style it is written):

(defun summit (lst)
  (remove nil lst)
  (apply #'+ lst))

(defun summit (lst)
  (let ((x (car lst)))
    (if (null x)
      (summit (cdr lst))
      (+ x (summit (cdr lst))))))

Utility Functions

Make a file called “utility.lisp” and write the functions below, all recommended by Paul Graham. Make sure to test them! We will keep adding to our utility functions file every week.

(last1 lst): The last item in a list.
(single lst): True if the argument is a length 1 list. (Do not use length it is slow.) Test your function on: '(a) and '(a b). We will discuss the weird case of '() in class.
(append1 lst item): Append a single item to the end of a list.
(mklist obj): If the object is not already a list, put it in one.
(longer x y): Give true if the list x is longer than y, but do not traverse the whole list - once you know enough to deduce x is longer (or not), stop and give the answer.

The last function is a little more complex than the other ones, I am thinking of a recursive solution that goes through both lists at the same time.