Test #1 questions.

Two questions from the following ones will be given on the test, 
plus 5 - 6 practical problems (such as, define the efficiency of 
a program fragment, trace a data structure, etc.)

1. Explain why it is important to know the run time efficiency of 
algorithms, and how this knowledge helps us decide which algorithm
is the best for a given application. Define the big-O notation and
explain how well it allows us to classify algorithms from a real-
world perspective. Give some peculiar examples to show the potential
problems.

2. Explain and compare selection, insertion and bubble sorts. Assume
that your application (say a data base application) deals with 
large records where comparisons are performed by means of integer keys. 
Assume also that your application requires a stable sorting method,
i.e. a method that does not change the relative ordering of elements 
that are equal. Which of these sorting methods would you choose, 
and why? (Hint: consider sorting based on the following integer keys
19, 14(1), 7, 12, 14(2), 10)

3. Describe the divide-and-conquer search algorithm and explain its 
efficiency. Consider two different Split functions: Split = Lo, and
Split = (Lo + Hi) / 2. Draw the trees of recursive calls. Assume that 
we are searching a large data base with 4 million items represented 
as an ordered array. How many probes into the list will the binary 
search require before finding the target or concluding that it cannot 
be found? Assume that it takes 1 microsecond to access an item, 
estimate the execution time of the binary search.

4. Explain how the efficiency of recursive algorithms is defined.
Consider two examples: the recursive binary search, and the tower of
Hanoi problem. Draw the tree of recursive calls for both problems,
and compare their efficiencies. 

5. Describe Shell sort (example is always helpful). What advantage 
do the relatively prime values of the increments have over other values?
Provide examples of best case and worst case data sets for Shell sort,
and compare its efficiency in these cases to the best case and worst
case efficiency of Quick sort.

6. Describe and compare Quick sort and Merge sort. How important is
the choice of the pivot in Quick sort? Using trees of recursive calls,
analyze and compare best and worst case efficiencies of Quick and Merge
sorts.  

7. What is an Abstract Data Type and what is a data structure? 
Explain the levels of abstraction in the data specification. Consider
the Matrix ADT example to illustrate your explanation.

8. Describe the Queue ADT (give a definition, set of operations).
Explain and compare array and linked list implementations of
the Queue ADT. Explain how queues are used in the Radix sort, and 
explain the Radix sort itself. Discuss the efficiency of the Radix
sort.

9. Describe the Stack ADT (give a definition, set of operations).
Explain and compare array and linked list implementations of
the Stack ADT.Describe one stack application -- your choice.Suggestions: 
converting expressions from infix to postfix form, evaluation of 
arithmetic or logical expressions, using stacks in Java Virtual Machine.

10. Describe the List ADT (give a definition, set of operations).
Describe different versions of the List ADT (ordered, unordered)
and their implementations (array implementation, linked list
implementation and doubly linked list implementation). Define
the Double-Ended Queue ADT.

11. Describe the Ranked Sequence ADT (give a definition, set of 
operations). Compare the array-based and the doubly linked list
implementation of the Ranked Sequence ADT (in details for each
operation).

12. Describe the Positional Sequence ADT (give a definition, set 
of operations). Explain the notion of a position. Explain how 
Positional Sequence ADT is different from Ranked Sequence ADT.

NOTE: Your answer must be specific, detailed, include example, 
pseudocode where appropriate.