EECS2040 Data Structure Hw #2

EECS2040 Data Structure Hw #2 (Chapter 3 Stack/Queue)

Format: Use a text editor to type your answers to the homework problem. You need
to submit your HW in an HTML file or a DOCX, pdf file named as Hw2-SNo.docx,
Hw2-SNo.pdf or Hw2-SNo.html, where SNo is your student number. Send the
Hw2-SNo.doc or Hw2-SNo.html file in eLearn. Inside the file, you need to put the
header and your student number, name (e.g., EE2410 Data Structure Hw #2
(Chapter 3 of textbook) due date 4/17/2021 by SNo, name) first, and then the
problem itself followed by your answer to that problem, one by one. The grading
will be based on the correctness of your answers to the problems, and the format. Fail
to comply with the aforementioned format (file name, header, problem, answer,
problem, answer,…), will certainly degrade your score. If you have any questions,
please feel free to ask me.
Part 1 (50%)
1. (30%) A linear list is being maintained circularly in an array with front and rear
set up as for circular queues.
(a) Obtain a formula in terms of the array capacity, front, and rear, for the number
of elements in the list.
(b) Assume the kth element in the list is to be deleted, the elements after it should
be moved up one position. Give a formula describing the positions of those
elements to be moved up one position, i.e., from ??? to ???.
(c) Assume that we want to insert an element y immediately after the kth element
and array doubling is needed (as Program 3.11 shows or pptx page 83 void
Queue<T>::Push(const T& x) shows), please explain the code using a
graphical illustration and explanation.
2. (20%) Using the operator priorities of Figure 3.15 (or pptx page 130 Parentheses
Handling) together with those for ‘(‘ and ‘#’ to answer the following:
(a) In function Postfix (Program 3.19, pptx Infix to Postfix Algorithm), what is
the maximum number of elements that can be on the stack at any time if the
input expression has n operators and delimiters?
(b) What is the answer to (a) if the input expression e has n operators and the
depth of nesting of parentheses is at most 6?

3. (50%) Write the postfix form and prefix form of the following infix expressions:
(a) –A + B – C + D
(b) A * -B + C
(c) (A + B) * D + E / (F + A * D) + C
(d) A && B || C || !(E > F)
(e) !(A && !((B < C) || (C > D))) || (C < E)

Part 2 Coding (50%)
You should submit:
(a) All your source codes (C++ file).
(b) Show the execution trace of your program.
1. (30%) Based on the circular queue and template queue ADT in ADT 3.2 in
textbook (or pptx pp.79), write a C++ program to implement the queue ADT.
Then add two more functions to
(a) Return the size and capacity of a queue.
(b) Merge two queues into a one by alternately taking elements from each queue.
Te relative order of queue elements is unchanged. What is the complexity of
your function?
You should demonstrate all the functions using at least one example.
2. (35%) Referring to Program 3.13 in textbook (pptx pp.94),
(a) Implement Stack as a publicly derived class of Bag using template.
Demonstrate your C++ code using at least two element types (e.g., int,
float,…). Show results of a series of Pushes and Pops and Size functions.
(b) Implement Queue as a publicly derived class of Bag using template.
Demonstrate your C++ code using at least two element types (e.g., int,
float,…). Show results of a series of Pushes and Pops and Size functions.
(c) A template double-ended queue (deque) is a linear list in which additions and
deletions may be made at either end. Implement the class Deque as a publicly
derived templated class of Queue. The class Deque must have public functions
(either via inheritance from Queue or by direct implementation in Deque) to
add and delete elements from either end of the deque and also to return an
element from either end. The complexity of each function (excluding array
doubling) should be Θ(1).
Demonstrate your C++ code using at least two element types (e.g., int,
float,…). Show results of a series of two types of Pushes and Pops and Size
functions to illustrate your code is working.
3. (35%) Write a C++ program to implement the maze in textbook using the example
codes of Program 3.15 (pptx pp.106 Algorithm()) and 3.16 (pptx void
Path(const int m, const int p). You should use a text editor to edit a file
containing the maze matrix and then read in the file to establish the maze matrix
in your program. The default entrance and exit are located in the upper left corner
and lower right corner, respectively as shown in textbook.
(a) Demonstrate your maze program using the maze shown in Figure 3.11 in
textbook.
(b) Find a path through the maze shown Figure 3.14 in textbook.
(c) Trace out the action of function path (Program 3.16) on the maze shown.
Compare this to your own attempt in (b).
010001100011111
100011011100111
011000011110011
110111101101100
110100101111111
001101110100101
001101110100101
011110011111111
001101101111101
110001101100000
001111100011110
010011111011110
入口
出口
Figure 3.11：一個迷宮的例子（你能找出一條路徑嗎？）
000000001
111111110
100000001
011111111
100000001
111111110
100000001
011111111
100000000
入口
出口
Figure 3.14：唯一路徑的迷宮圖