# Lab: Insertion sort

Assigned
Wednesday, Dec 5, 2018
Due
Lab writeups are due at 10:30pm on the day of the next class meeting. For example, a Wednesday lab is due at 10:30pm on Friday. Each lab writeup will be announced at the end of class on a lab day.
Summary
In this lab, we explore a variety of issues related to the insertion sort algorithm.

## Preparation

a. Update the csc151 package.

b. Make a copy of insertion-sort-lab.rkt, the code for this lab.

## Exercises

### Exercise 1: Inserting strings

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.

### Exercise 2: Counting steps in insertion sort

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

a. The procedures counter-new, counter-increment!, counter-reset!, and counter-print are in the new csc151/counters package. Remind yourself of what they do.

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

(define insert-number-counter (counter-new "insert-number"))


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

  (counter-increment! 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.

### Exercise 3: Generalized insertion sort

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

### Exercise 4: Observing insert!

(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.

### Exercise 5: Keyed insertion sort

a. You will note that the file for this lab includes a list called grinnell-directory. Review the structure of grinnell-directory. Then write a call to the generalized list-keyed-insertion-sort to sort by username.

b. Write a call to the generalized list-keyed-insertion-sort to sort the list ("clementine" "starfruit" "apple" "kumquat" "pineapple" "pomegranate" "cantelope") alphabetically. Note, for example, that the key of "clementine" is "clementine".

c. Write a call to the generalized list-keyed-insertion-sort to sort alphabetically by last name and first name. Note, for example, that the key of ("Rebelsky" "Essay" "muser" "4410") would be "Rebelsky, Essay".

## For those with extra time

### Extra 1: Sorting vectors of strings

Write a procedure, (string-vector-insertion-sort vec), that sorts a vector of strings. You may not call the generalized vector-insertion-sort. However, you may use that procedure (and the corresponding generalized vector-insert!) as a template for your procedure.

### Extra 2: Keyed insertion sort for vectors

Write a procedure, (vector-keyed-insertion-sort vec get-key may-precede?), that sorts a vector of lists 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 so that it calls vector-insertion-sort!` appropriately.