Summary:
We consider a more efficient way to sort values.
Contents:
a. Make a copy of mergesort.scm,
my implementation of merge sort. Scan through the code and make
sure that you understand all the procedures.
b. Start DrScheme.
a. Write an expresssion to merge the lists (1 2 3) and
(1 1.5 2.3).
b. Write an expression to merge two lists that contain the same values.
c. Write an expression to merge two lists of strings. (You may choose the
strings yourself. Each list should have at least three elements.)
d. Assume that we represent names as lists of the form
(last-name first-name).
Write an expression to merge the following two lists
(define cs-faculty
(list (list "Bishop" "David")
(list "Gum" "Ben")
(list "Rebelsky" "Samuel")
(list "Stone" "John")
(list "Walker" "Henry")))
(define young-cs-kids
(list (list "Rebelsky" "Daniel")
(list "Rebelsky" "Jonathan")
(list "Rebelsky" "William")))
a. What will happen if you call merge with unsorted
lists as the first two parameters?
b. Verify your answer by experimentation.
c. What will happen if you call merge with sorted lists
of very different lengths as the first two parameters?
d. Verify your answer by experimentation.
Use split to split:
a. A list of numbers of length 6
b. A list of numbers of length 5
c. A list of strings of length 6
a. Run merge-sort on a list you design of fifteen integers.
b. Run new-merge-sort on a list you design of twenty strings.
c. Uncomment the lines in new-merge-sort that print out
the current list of lists. Rerun new-merge-sort on a list
you design of twenty strings. Is the output what you expect?
a. Run both versions of merge sort on the empty list.
b. Run both versions of merge sort on a one-element list.
c. Run both versions of merge sort on a list with duplicate elements.
a. Using DrScheme's built-in timing mechanism (you may have to look through the
online help to find information about that mechanism), make a table of the
running time of insertion sort, merge-sort and
new-merge-sort on inputs of size 0, 10,
100, 1000, 10000, 20000, and 50000.
b. Graph your data.
c. Based on your data, what can you say about the relative speeds of the
three sorting methods?
One of my colleagues prefers to define split something
like the following
(define split
(lambda (ls)
(let kernel ((rest ls)
(left null)
(right null))
(if (null? rest)
(list left right)
(kernel (cdr rest) (cons (car rest) right) left)))))
a. How does this procedure split the list?
b. Why might you prefer one version of split over the other?
;
Check with Bobby