CS 210   December 2007

Some of these questions will be on the final exam.  (perhaps with slight modifications)

SORTING

fill in the table.

name of alg.
 simple | adv?
 approx. big-O
fast if alrdy inorder?
 recursive?
 needs xtra space
 key term    
i__





s__





m__





S__





q__






a "key term" would be something like:  "variant of xxx sort", "partition", "similar to binary search", "find minimum"
Does the sort have a worst case situation?  (think about binary search:  does it have a worst case scenario?)

Chose one simple sort and one advanced sort:  Describe how to move ahead one step in the operation of the sort.  (This is like explaining the algorithm in pseudo-code).   For instance,
                ^ j

"find the smallest element to the right of "j";  swap it with element at j. 
  move j one position to right.  Repeat until done (j==N-1)

(this is supposed to be easier than actually writing the program.)
Note that we've spent more time on some sorts than on others ... clearly, you should know more about those.

LISTS

Create a class List<E> which is a simple linked-list class to hold objects of any reference type.   Provide two routines, add() and remove().  If the list is empty, remove() should return null.
  Let's create a full program.  Here's a little bit to get you started.

class List<E> {
   void add(...
   ....  remove(...
}
class ListElt....
}

class ListTest {
  public static void main(String args[]) {
      List .... L = new List ....;
      L.add("world");
      L.add("hello");
      System.out.println(L.remove());
      System.out.println(L.remove());
      System.out.println(L.remove());
  }
}

What will this print when run?  (What other kind of data structure behaves like this?)

BINARY [SEARCH] TREES

What is the invariant for a binary tree?
          |
          10
         /  \
        5    20
            /'x'
What is the immediate (primary) invariant describing nodes on arc "x"?
What is the full (derived) invariant condition for nodes on "x" and below?  (hint: could 7 be placed there?)

Place (insert) the following values in order:  7   11  6

Here's another tree
          |
          18
         /  \
        /    \
      13      36
     /  \    /  \
    7       35  38
     \
     12
Remove the node containing 13.   Then remove the one containing 18.
  (you don't need to write the Java program.  Show which nodes move where and why)

Write a Java program to traverse a binary search tree and count how many nodes have 2 children.

         |
         E
        / \
       B   L
      / \
     J   M
          \
           U

Indicate the following components:  root;  root of subtree;  leaves.    How many nodes are there?  How many edges?
Show the result of doing a "postorder" walk of the tree.
What kind of helper data structure would be needed to do a breadth-first walk of the tree?


HASH TABLES

Consider a hash table with "separate chaining", table size 7.  We'll be storing data of type "int", and the hash function is %tablesize.
  Show the table after the insertion of 10, 9, 36, 23

  Do the same, but for an open addressing table with linear probing (the simplest overflow scheme).

(note: you are not required to know all about the various overflow schemes)

What is the "load factor"?  How high can it reasonably be for open addressing?  For separate chaining?

Given a hash table with array HTA[], and hash function htfunc()..  What three main steps need to occur in order to find the entry corresponding to a key value "kv"?
  Which of these need to be repeated in the event of a collision?