Insertion Sort

Write a new insert-string procedure that inserts a string into a list of strings that are in alphabetical order:

> (insert-string (list "ape" "bear" "cat" "emu" "frog") "dog")
("ape" "bear" "cat" "dog" "emu" "frog")

In case you've forgotten, string<=? and string-ci<=? are useful predicates for comparing strings for order.

Your goal in this problem is to follow (and therefore better understand) the pattern of the insert-number procedure. Hence, you may not use the generalized insert procedure in writing insert-string.

Let's see how many times the insert-number method is called. We'll use the techniques from the lab on analyzing procedures.

a. Note the definitions of counter-new, counter-count!, counter-reset!, and counter-print! already in your definitions pane and remind yourself how they work if you need to.

b. Define a counter named insert-number-counter.

c. Add the following line to the beginning of the insert-number procedure:

  (counter-count! insert-number-counter)

We can count the number of calls to insert-number for a particular list as follows:

> (counter-reset! insert-number-counter)
> (numbers-insertion-sort list)
> (counter-print! insert-number-counter)

d. Determine how many calls to insert-number are involved in sorting each of the following lists.

i. (iota 5)

ii. (iota 10)

iii. (iota 20)

iv. (iota 40)

v. (reverse (iota 5))

vi. (reverse (iota 10))

vii. (reverse (iota 20))

viii. (reverse (iota 40))

e. Explain, to the best of your ability, what the numbers you got say about the number of function calls the insertion sort algorithm makes. Your answer should take the length of the list into account.

Write a call to the generalized list-insertion-sort to sort the list ("clementine" "starfruit" "apple" "kumquat" "pineapple" "pomegranate") alphabetically.

a. Add the following definition to your definitions pane.

(define numbers (vector 1 5 6 7 2 8 0 3))

b. Check that vector-insert! works by using it to move the 2 into the correct place in the first five spaces in numbers.

Note: Solving this step requires that you understand the parameters to vector-insert!.

c. Extend vector-insert! so that it displays the vector and the position at every step. That is, add calls to display and newline in the kernel, before the cond.

d. Re-create the numbers vector from step a, and observe what happens when we insert the 2, then the 8, then the 0, then the 3.

e. Observe the insertion steps in a vector of about eight randomly-generated numbers.

> (define nums (vector (random 10) (random 10) (random 10) (random 10)
               (random 10) (random 10) (random 10) (random 10)))
> (vector-insertion-sort! nums _____)

f. Explain, in your own words, how vector-insertion-sort! works.

a. Write a call to the generalized list-keyed-insertion-sort to sort the list ("clementine" "starfruit" "apple" "kumquat" "pineapple" "pomegranate") alphabetically.

b. Review the structure of drawing (a list of named objects). Then write a call to the generalized list-keyed-insertion-sort to sort drawing by object name.

c. Write a call to the generalized list-insertion-sort to sort drawing alphabetically by color name.

d. Write a call to the generalized list-keyed-insertion-sort to sort drawing by object width.

Write a procedure, (vector-keyed-insertion-sort vec get-key may-precede?) that sorts a vector of compound objects by key.

While it is possible to write this procedure by converting the vector to a list, using list-keyed-insertion-sort!, and then converting the result back to a vector, you should not use this strategy. Rather, write this procedure directly. (You may want to use vector-insertion-sort! as a template.)