This assignment is comprised of 3 parts:

Part 1: Implementation of Dynamic Array, Stack, and Bag First, complete the Worksheets 14 (Dynamic Array), 15 (Dynamic Array Amortized Execution Time Analysis), 16 (Dynamic Array Stack), and 21 (Dynamic Array Bag). These worksheets will get you started on the implementations, but you will NOT turn them in. Next, complete the dynamic array and the dynamic array-based implementation of a stack and a bag in dynamicArray.c. The comments for each function will help you understand what each function should do. We have provided the header file for this assignment, DO NOT change the provided header file (dynamicArray.h). You can test your implementation by using the code in testDynArray.c.

Part 2: Amortized Analysis of the Dynamic Array (written) Consider the push() operation for a Dynamic Array Stack. In the best case, the operation is O(1). This corresponds to the case where there was room in the space we have already allocated for the array. However, in the worst case, this operation slows down to O(n). This corresponds to the case where the allocated space was full and we must copy each element of the array into a new (larger) array. This problem is designed to discover runtime bounds on the average case when various array expansion strategies are used, but first some information on how to perform an amortized analysis is necessary.

1. Each time an item is added to the array without requiring reallocation, count 1 unit of cost. This cost will cover the assignment which actually puts the item in the array.

2. Each time an item is added and requires reallocation, count X + 1 units of cost, where X is the number of items currently in the array. This cost will cover the X assignments which are necessary to copy the contents of the full array into a new (larger) array, and the additional assignment to put the item which did not fit originally. To make this more concrete, if the array has 8 spaces and is holding 5 items, adding the sixth will cost 1. However, if
the array has 8 spaces and is holding 8 items, adding the ninth will cost 9 (8 to move the existing items + 1 to assign the ninth item once space is available). When we can bound an average cost of an operation in this fashion, but not bound the worst case execution time, we call it amortized constant execution time, or average execution time. Amortized constant execution time is often written as O(1)+, the plus sign indicating it is not a guaranteed execution time bound. In a file called amortizedAnalysis.txt, please provide answers to the following questions:

1. How many cost units are spent in the entire process of performing 32 consecutive push operations on an empty array which starts out at capacity 8, assuming that the array will double in capacity each time a new item is added to an already full dynamic array? As N (ie. the number of pushes) grows large, under this strategy for resizing, what is the big-oh complexity for a push?

2. How many cost units are spent in the entire process of performing 32 consecutive push operations on an empty array which starts out at capacity 8, assuming that the array will grow by a constant 2 spaces each time a new item is added to an already full dynamic array? As N (ie. the number of pushes) grows large, under this strategy for resizing, what is the big-oh complexity for a push?

3. Suppose that a dynamic array stack doubles its capacity when it is full, and shrinks (on Pop only) its capacity by half when the array is half full or less. Can you devise a sequence of N push() and pop() operations which will result in poor performance (O(N^2) total cost)? How might you adjust the array's shrinking policy to avoid this? (Hint: You may assume that the initial capacity of the array is N/2.)

Part 3: Application of the Stack - RPN Calculator Your job in this part of the assignment is to write a program called calc.c that uses one stack (in dynamicArray.c) to implement a command line RPN (Reverse Polish Notation) calculator. The main function reads in, from the command line, a sequence of numbers and operators separated by white spaces (an example command line entry would look like calc 5 3.12 x 4 + 78 29.35 6 - / x) and computes and displays the resulting value. The sequence of numbers (including negatives and the constants pi and e) and operators are passed to main via the int argc and char *argv[] parameters. Your program should change the strings pi and e into the values 3.14159265... and 2.7182818... respectively. Your RPN calculator should treat all numbers as doubles and should implement the following operators:

Operator Description Example Output
+ addition 4 5 + 9
- subtraction 4 5 - -1
/ division 4 5 / 0.8
x multiplication (* is treated as wildcard) 4 5 x 20
^ power (use pow function in math.h 4 5 ^ 1024
^2 squared (no space between '^' and '2') 4 ^2 16
^3 cubed (no space between '^' and '3') 4 ^3 64
abs absolute value -4 abs 4
sqrt square root 16 sqrt 4
exp exponential (same as "e x ^" = ex) 2 exp 7.389
ln natural logarithm 7.389 ln 2
log base 10 logarithm 100 log 2

Of course, you are free to add more operators if you would like (such as asin, acos, atan, ceil, floor, rand, etc.). Many of these functions, as well as the exponential and trigonometric functions above, are found in the math.h library. Your RPN calculator should test for illegal input--incorrect count of numbers (too many, 4 5 3 +, or too few, 4 +), unknown operators (which should be treated as an incorrectly formatted number), and/or numbers that do not have a
valid format (e.g., 45+, 5.32.1, etc.)--and report an error along with the offending argument string when illegal input is detected.
Hint: one way to implement this is to read in each string and compare it with the list of accepted operators, if it is not
a valid operator then assume that it is a number, convert it to a double using the following method (provided in
calc.c):

int isNumber(char *s, double *num)
and push it onto the stack. isNumber returns 1 if s is a number and 0 otherwise. The function will store the number in
num whenever it returns 1. If the argument string is a valid operator, pop the appropriate number of double precision
values off the stack (depending on the given operator), perform the appropriate computation, and then push the result
back onto the stack. When all of the command line arguments are processed, the result is output by popping the stack
(which should result in an empty stack) and printing the value.
After compiling your program, you should be able to type commands like the following:
file:///C|/Users/eecs/Desktop/Samina/boishakh/CS261_Programming_Assignment_2.html[10/21/2013 10:20:34 AM]
./calc pi 5 ^2 x
(compute the area of circle with radius 5 -- uses the "squared" operator, not "power")
Grading
Compile without warnings = 15
Implementation of the Dynamic Array, Stack, and Bag:
void _dynArrSetCapacity(DynArr *v, int newCap) = 10
void addDynArr(DynArr *v, TYPE val) = 5
TYPE getDynArr(DynArr *v, int pos) = 5
void putDynArr(DynArr *v, int pos, TYPE val) = 5
void swapDynArr(DynArr *v, int i, int j) = 2
void removeAtDynArr(DynArr *v, int idx) = 5
int isEmptyDynArr(DynArr *v) = 2
void pushDynArr(DynArr *v, TYPE val) = 2
TYPE topDynArr(DynArr *v)= 2
void popDynArr(DynArr *v)= 2
int containsDynArr(DynArr *v, TYPE val) = 5
void removeDynArr(DynArr *v, TYPE val) = 5
Amortized Analysis = 20
Stack application
calc.c = 15
Files You Will Need
dynamicArray.c
dynamicArray.h
calc.c- contains the RPN's code that you will be implementing .

testDynArray.c - contains test cases for dynamicArray.c. Your implementation should pass all these test cases. You should write your own test code as well.
makefile.txt - after downloading, rename to "makefile".
What to submit (3 files)
1. amortizedAnalysis.txt
2. dynamicArray.c
3. calc.c