Dynamic Array_Assignment 2 solution

Main/Programming Assignment 2
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 indynamicArray.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 (dynArray.h).
You can test your implementation by using the code in testDynArray.c. This file contains several test cases for thefunctions in dynamicArray.c. Try to get all the test cases to pass. You should also write more test cases on your own,but do not submit 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 tothe case where there was room in the space we have already allocated for the array. However, in the worst case, thisoperation slows down to O(n). This corresponds to the case where the allocated space was full and we must copy eachelement of the array into a new (larger) array. This problem is designed to discover runtime bounds on the average casewhen various array expansion strategies are used, but first some information on how to perform an amortized analysisis necessary.
1. Each time an item is added to the array without requiring reallocation, count 1 unit of cost. This cost will coverthe 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 itemscurrently in the array. This cost will cover the X assignments which are necessary to copy the contents of thefull 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 assignthe 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, wecall it amortized constant execution time, or average execution time. Amortized constant execution time is oftenwritten 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 emptyarray which starts out at capacity 8, assuming that the array will double in capacity each time a new item isadded to an already full dynamic array? As N (ie. the number of pushes) grows large, under this strategy forresizing, 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 emptyarray which starts out at capacity 8, assuming that the array will grow by a constant 2 spaces each time a newitem is added to an already full dynamic array? As N (ie. the number of pushes) grows large, under this strategyfor 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 willresult 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 - &KHFNLQJEDODQFHGSDUHWKHVHVEUDFHVDQGEUDFNHWV
1RWH)RUWKLVH[HUFLVH\RXQHHGWRILUVWPDNHWKHIROORZLQJFKDQJHLQG\Q$UUD\K&KDQJHGHILQH7<3(LQWWRGHILQH7<3(FKDU   $VGLVFXVVHGLQWKHOHFWXUHQRWHVVWDFNVDUHDYHU\FRPPRQO\XVHGDEVWUDFWGDWDW\SH$SSOLFDWLRQVRIVWDFNVLQFOXGHLPSOHPHQWDWLRQRI UHYHUVH3ROLVKQRWDWLRQH[SUHVVLRQHYDOXDWLRQDQGXQGREXIIHUV6WDFNVFDQDOVREHXVHGWRFKHFNZKHWKHUDQH[SUHVVLRQKDVEDODQFHG SDUHWKHVHVEUDFHVDQGEUDFNHWV^RUQRW)RUH[DPSOHH[SUHVVLRQVZLWKEDODQFHGSDUHQWKHVHVDUH[\[\]DQGZLWK XQEDODQFHGDUH[\[\]   )RUWKLVSDUWRIWKHDVVLJQPHQW\RXDUHWRZULWHDIXQFWLRQWKDWVROYHVWKLVSUREOHPXVLQJDVWDFNQRFRXQWHULQWHJHUVRUVWULQJ IXQFWLRQVDUHDOORZHG,I\RXXVHDFRXQWHURUVWULQJRSHUDWLRQRIDQ\NLQG\RXZLOOQRWUHFHLYHFUHGLWIRUFRPSOHWLQJWKLVSDUW RIWKHDVVLJQPHQW   7KHILOHVWDFNDSSFFRQWDLQVWZRIXQFWLRQV  FKDUQH[W&KDUFKDU V±UHWXUQVWKHQH[WFKDUDFWHURUµ?¶LIDWWKHHQGRIWKHVWULQJ  LQWLV%DODQFHGFKDU V±UHWXUQVLIWKHVWULQJLVEDODQFHGDQGLILWLVQRWEDODQFHG  <RXKDYHWRLPSOHPHQWLQWLV%DODQFHGFKDU V±ZKLFKVKRXOGUHDGWKURXJKWKHVWULQJXVLQJµQH[W&KDU¶DQGXVHDVWDFNWRGRWKHWHVW ,WVKRXOGUHWXUQHLWKHU7UXHRU)DOVH
Grading
Compile without warnings = 15 Implementation of the Dynamic Array, Stack, and Bag: void _dynArrSetCapacity(DynArr *v, int newCap) = 10void addDynArr(DynArr *v, TYPE val) = 5 TYPE getDynArr(DynArr *v, int pos) = 5 void putDynArr(DynArr *v, int pos, TYPE val) = 5void 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 LQWLV%DODQFHGFKDU V = 15
dynamicArray.c dynArray.h VWDFNDSSF±,WFRQWDLQVPDLQIXQFWLRQDQG\RXFDQWHVW\RXUSURJUDPXVLQJLW testDynArray.c - contains test cases for dynamicArray.c. Your implementation should pass all these testcases. 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. VWDFNDSSF