# Lab: Insertion sort

Held
Wednesday, 1 May 2019
Writeup due
Friday, 3 May 2019
Summary
In this lab, we explore a variety of issues related to the insertion sort algorithm.

## Preparation

a. Update the loudhum 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. Define an counter.

b. Add a line to insert-number to count each call.

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

i. (range 5)

ii. (range 10)

iii. (range 20)

iv. (range 40)

v. (reverse (range 5))

vi. (reverse (range 10))

vii. (reverse (range 20))

viii. (reverse (range 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".

### Exercise 6: Index of largest

Write a procedure, (index-of-largest ints boundary), that takes a vector of integers and a boundary as parameters and finds the index of the largest integer between 0 (inclusive) and boundary (exclusive).

### Exercise 7: Selection sort

Write a procedure, (selection-sort ints), that takes a vector of integers as a parameter and sorts the vector by repeatedly finding the largest remaining element, swapping it to the boundary, and decreasing the boundary. The following diagram may help.

+-------------------+-----------------+
| unsorted, smaller | sorted, larger  |
+-------------------+-----------------+
|
boundary


## 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.