Comp 271-400 Week 3
Lewis Tower 410, 4:15-8:15
Bailey chapter 6, on sorting
Bailey chapter 9, on lists (and, in particular, linked
Bailey chapter 15.4.2: (chained) hashing
Morin chapter 1, sections 1.1 and 1.2
One slight peculiarity of Morin is
that he refers to the array-based List implementation of chapter 2 as an
Primary text: Bailey, online, and maybe Morin, also online.
Information about MSDNAA is in the Intro to C++
See also linkedlistij.zip.
Class both.java in linkedlistij.zip: change from ArrayList to LinkedList.
Table of Factors
This is the example on Bailey page 88. Let us construct a table of all the
k<=n and a list of all the factors (prime or not) of k, and ask how much
space is needed. This turns out to
be n log n. The running time to construct the table varies with how clever
the algorithm is, it can be O(n2) [check all i<k for
divisibility], O(n3/2) [check all i<sqrt(k)], or O(n log n)
[Sieve of Eratosthenes].
Space in a string
The answer depends on whether we're concerned with the worst case or the
average case (we are almost never interested in the best case). If the
average case, then the answer typically depends on the probability
distribution of the data.
A function is said to be polynomial
if it is O(nk) for some fixed k; quadratic growth is a special
So far we've been looking mainly at running
time. We can also consider space needs.
in-class lab: GetHashCode() values of strings from hashij.zip's
classes hashCodes.java and hashStats.java.
Chapter 6: Sorting
Recursion starts at Bailey page 94
- Factorial (done)
- Fibonacci (mostly done)
- Postage (currently first-class is 49¢, and post cards are 34¢)
in-class lab 2
The gcd() method on Bailey page 9 is recursive. How does this work?
In analyzing a recursive method, there are two specific issues: does the
method, when it returns, return the correct value? And does the method ever
return? Then there's the issue of how recursion can work at all. Internally,
the runtime system handles this by creating a separate set of local
variables for each call to gcd(). This is done on the so-called runtime
stack. This means that different calls to gcd(), with different
parameter values, don't interact or interfere.
For the return value, note that gcd(a,b) = gcd(a,b%a), always; any divisor
of a and b is a divisor of b%a (which has the form b-ka), and any divisor of
a and b%a is a divisor of b.
Finally, there's the question of whether rgcd() ever returns. One
way to prove this is to argue that the first parameter to rgcd() keeps
getting smaller. We stop when it reaches 0, as it must (why can't rgcd()
terminate with first parameter > 0?). The atomic case
in the recursion is the case that involves no further recursive calls; in
the gcd() example it is the case when a==0.
insertion and search