CS 30 Homework 3

Reading assignment: Chapters 7-8 of The Little Schemer.

Finish the following recursive functions from the last two labs. Don't hesitate to use helping functions if that would make solving the problem easier. Make sure to test your programs on a variety of input data to verify that they work correctly in all cases.

These functions work with flat lists:

1. (odd-or-even nums) takes a flat list of numbers and returns a new list with odd numbers replaced by the symbol odd and even numbers replaced by the symbol even. Remember that the built-in Scheme functions odd? and even? are available. Example:
   (odd-or-even '(1 2 3 5 4)) => (odd even odd odd even)

2. (count-nums lat) takes a flat list of atoms and tells how many numbers are in the list. The built-in Scheme function number? will come in handy here, which returns true given a number, or false otherwise. Examples:
   (count-nums '(a b c 42 d 13 e f 8)) => 3
(count-nums '(x y z)) => 0

3. (all-nums? lat) takes a flat list of atoms and returns true if the list contains only numbers, or false otherwise. The built-in Scheme function number? will come in handy here. Examples:
   (all-nums? '(1 2 3 4)) => #t
(all-nums? '(2 b or not 2 b)) => #f

4. (index sym lat) takes a symbol sym and a flat list of symbols lat and returns the index number of the first occurrence of sym in lat, counting from zero. If sym does not appear in the list, then index returns -1. Examples:
   (index 'cs30 '(this class is cs30)) => 3
(index 'mango '(apple banana cherry)) => -1
(index 'hello '(hello goodbye)) => 0

5. (insert n nums) takes a number n and a flat list of numbers in ascending order, and returns a new list with n inserted into nums at the correct position. Examples:
   (insert 5 '(1 3 4 8 9)) => (1 3 4 5 8 9)
(insert 5 '(1 3 5 5 9)) => (1 3 5 5 5 9)
(insert 2 '(6 7 8)) => (2 6 7 8)
(insert 10 '(6 7 8)) => (6 7 8 10)

6. (sort nums) takes an unsorted list of numbers and returns a new list with the numbers sorted into ascending order. Example:
   (sort '(8 4 5 1 4 2 7)) => (1 2 4 4 5 7 8)
HINT: To sort a list of numbers, first sort the rest of the numbers, then insert the first number into the rest at the appropriate location. Think recursively!

These functions work with arbitrarily-nested lists:

7. (odd-or-even* nums) takes a nested list of numbers and returns a new list with the same nested structure, with odd numbers replaced by the symbol odd and even numbers replaced by the symbol even. Example:
   (odd-or-even* '((1 2) ((3)) 5 4)) => ((odd even) ((odd)) odd even)
(odd-or-even* '(7 (2 (3 8) 5))) => (odd (even (odd even) odd))

8. (count-all* ls) takes an arbitrary nested list and tells how many items are in the list. Examples:
   (count-all* '((3 apple) ((peach 8 6) 9) pie)) => 7
(count-all* '(ginger fred)) => 2

9. (count-nums* ls) takes a nested list of atoms and tells how many numbers are in the list. Examples:
   (count-nums* '((3 apple) ((peach 8 6) 9) pie)) => 4
(count-nums* '((apple banana) cherry)) => 0

10. (addup-nums* ls) takes a nested list of atoms and adds up all of the numbers in the list. Examples:
    (addup-nums* '((3 apple) ((peach 8 6) 9) pie)) => 26
(addup-nums* '((apple banana) cherry)) => 0

11. (swap* s1 s2 ls) takes two symbols s1 and s2 and a nested list, and returns a new nested list with all occurrences of the s1 symbol replaced by the s2 symbol, and vice versa. Examples:
    (swap* 'red 'blue '(red (yellow (blue) red)))
   => (blue (yellow (red) blue))
(swap* 'orange 'blue '(((red yellow)) blue red))
   => (((red yellow)) orange red)

12. (reverse* ls) takes a nested list and returns a "mirror image" of the list, with all of its internal structure preserved. Examples:
    (reverse* '(a (b (c (d e))))) => ((((e d) c) b) a)
(reverse* '((a b c d) e f g)) => (g f e (d c b a))

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