1.  2003 Prentice Hall, Inc. All rights reserved. Using Arrays in Abstract Data Types

2.  2003 Prentice Hall, Inc. All rights reserved. What is an Abstract Data Type A built-in data type is an int, float, double, etc. An Abstract Data Type (ADT) is a collection of data and a set of operations on the data. You can use an ADT’s operations, if you know their specifications, without knowing how the operations are implemented or how the data is stored. Ultimately, you will implement an ADT with a data-structure, which is a construct you can define within a programming language to store a collection of data. Examples of ADT: lists, stacks, queues, trees, graphs, etc.

3.  2003 Prentice Hall, Inc. All rights reserved. ADT: SIMPLE LIST Examples of lists: lists of student id’s in a class, grocery items, lists of records in a collection, list of club members, etc…. Create a list Insert an element Arrange elements in sorted order Find if an element is in the list Delete an element Print the list of elements WHAT ARE BASIC OPERATIONS ON A LIST?

4.  2003 Prentice Hall, Inc. All rights reserved. What operations are likely to be performed on lists? Create/Insert an element Delete an element Arrange elements in sorted order (whatever sort criteria) Print the list of elements Find if an element is in the list Print statistics about list (if numeric) Grocery items: Chips Salsa Coke Tissues Sprite Jelly beans Original list Grocery items: Chips Salsa Coke Tissues Sprite Jelly beans Beer Add Beer Grocery items: Chips Salsa Coke Sprite Jelly beans Beer Delete tissues Grocery items: Beer Chips Coke Jelly beans Salsa Sprite Sort alphabetically Grocery items: Beer Coke Sprite Jelly beans Chips Salsa Sort by grocery aisles Is beer on the list?

5.  2003 Prentice Hall, Inc. All rights reserved. Implementation of the ADT List One way to implement a “list” is using an array to hold the elements in the list….. Now have to figure out how to : insert, delete, sort, find, etc…. In the next lessons, we will slowly build up these functionalities until we can integrate them all into a “list” program. EVENTUAL GOAL : CREATE A PROGRAM TO MAINTAIN A LIST OF STUDENTS……….

6.  2003 Prentice Hall, Inc. All rights reserved. Let’s make a simpler list Instead of strings, we will have a list of letters const int MAXCHARS = 7; char alpharray[MAXCHARS]; B J K M S Z 0 1 2 3 4 5 6 7

7.  2003 Prentice Hall, Inc. All rights reserved. Print Elements in a list for (i=0; i<numofelements; i++) cout << alpharray[i] << endl; Input elements into the list: // numtoinsert should be set to the number of initial elements to insert for (i=0; i<numtoinsert; i++) cin >> alpharray[i];

8.  2003 Prentice Hall, Inc. All rights reserved. Insert an element into an array Simple insert routine: find end of array, insert element: alpharray[endofarray] = newelement; endofarray++; B J K M S ZB J K M S Z L Before: After inserting L

9.  2003 Prentice Hall, Inc. All rights reserved. Insert a letter in the list Should it be inserted at the end of the list (in this case we need to know what is the end of the list)? Should the new element be inserted into the beginning of the list? Is the list stored in some special order and elements should be inserted to maintain that order – e.g., if the list is stored in alphabetical order the new element must be inserted in alphabetical order? Should the user choose where to store the new element?

10.  2003 Prentice Hall, Inc. All rights reserved. Assume the following letters are stored in array named alpharray: B, J, K, M, S, and Z. Write a program which calls a function adlet(), which accepts both the alphabet array and a new letter as parameters and inserts the new letter in the correct alphabetical order in the alphabet array. B J K M S Z alphabet [0] [1] [2] [3] [4] [5] [6] [7] …... B J K L M S Z After adding ‘L’ Before: INSERTING INTO A ARRAY BASED Alphabetical LIST

11.  2003 Prentice Hall, Inc. All rights reserved. ALGORITHM: Prompt user for new letter to add Find the position (index) of where this letter should go in the alphabetical array. (This is called a linear search.) Move all letters after this position down to free up the space Insert letter into array ****

12.  2003 Prentice Hall, Inc. All rights reserved. #include void insertletter(char[],char,int&); int main() { const int MAXCHARS = 30; const int STARTCHARS=6; char alpharray[MAXCHARS] = {‘B’, ‘J’, ‘K’, ‘M’,’S’,’Z’}; char newlet; int sizeofarray=STARTCHARS; while (5) { //loop forever cout << “ Enter a letter to add:”; cin >> newlet; insertletter(alpharray,newlet,sizeofarray); } CONTINUED…..

13.  2003 Prentice Hall, Inc. All rights reserved. Find position for new letter //find position for new letter while (alpharray[i] < addlet && i < sizeofarray) i++; newpos =i;

14.  2003 Prentice Hall, Inc. All rights reserved. Find position for new letter //move chars over --- should check for full array first if (sizeofarr == MAXCHARS) ….. for (i=sizeofarr; i>newpos; i--) alpharray[i] = alpharray[i-1];

15.  2003 Prentice Hall, Inc. All rights reserved. void insertletter(char alpharray[], char addlet, int& sizeofarr) { int i=0, endpos,newpos; //find position for new letter while (alpharray[i] < addlet && i < sizeofarr) i++; newpos =i; //move chars over --- should check for full array first for (i=sizeofarr; i>newpos; i--) alpharray[i] = alpharray[i-1]; alpharray[newpos] = addlet; //insert new letter sizeofarr++; //print out array for(i=0; i<sizeofarr; i++) cout <<alpharray[i]; }

16.  2003 Prentice Hall, Inc. All rights reserved. Analysis of the simple insertion algorithm In the worst case --- How many comparisons are needed to find the position of the letter to be inserted? In the worst case --- How many letters have to be shifted to make room for a new letter to be inserted? Are these the same cases?

17.  2003 Prentice Hall, Inc. All rights reserved. void insertletter(char alpharray[], char addlet, int& sizeofarr) { int i=0, endpos,newpos; //find position for new letter while (alpharray[i] < addlet && i < sizeofarr) i++; newpos =i; //move chars over --- should check for full array first for (i=sizeofarr; i>newpos; i--) alpharray[i] = alpharray[i-1]; alpharray[newpos] = addlet; //insert new letter sizeofarr++; //print out array for(i=0; i<sizeofarr; i++) cout <<alpharray[i]; What happens if the array is full? Can we use this code to insert elements into an empty list? If (sizeofarr == 0) { alpharray[0] = addlet; sizeofarr++; return 0; }

18.  2003 Prentice Hall, Inc. All rights reserved. Delete an element from a list Must find the element to delete: Then move everything over

19.  2003 Prentice Hall, Inc. All rights reserved. Delete Let’s assume we are given the position of the item to delete in delpos; DeleteElement(char alpharray[], int delpos, int& sizeofarr) { for (i=delpos+1; i<sizeofarr; i++) alpharray[i-1] = alpharray[i]; sizeofarr--; }

20.  2003 Prentice Hall, Inc. All rights reserved. ADT LIST: DONE: Insert element at end of a list; Insert element into previously sorted list TO DO: Sort List, Delete element, Create list, Find Element…..

21.  2003 Prentice Hall, Inc. All rights reserved. ADT: List Operation: sort. Given a list of unordered values in an array, sort the values so that they can be printed in sorted order.

22.  2003 Prentice Hall, Inc. All rights reserved. SIMPLE Sorting Sorting is a typical operation to put the elements in an array in order. Internal Sorts [for small data sets] selection bubble (exchange) External Sorts [for large data sets]

23.  2003 Prentice Hall, Inc. All rights reserved. Simple Sorting Selection sort Find smallest element, and put at the head of the list, repeat with remainder of list. The algorithm can also be formulated by finding the largest element and putting that at the head of the list

24.  2003 Prentice Hall, Inc. All rights reserved. Selection Sort index (k)sm_index 02 swap 21, 9 11 swap 13, 13 23 swap 21, 15 34 swap 21, 17 211591317 151791321 915211317 152191317 21159 17 Find smallest element, and put at the head of the list,repeat with remainder of list Scan 1 Scan 2 Scan 3 Scan 4

25.  2003 Prentice Hall, Inc. All rights reserved. Selection Sort const int size = 5; void sort(double [size]); void swap(double [size], int, int) // prototypes int main(void) {int index; double my_list[ ] = {21, 13, 9, 15, 17}; sort(my_list); // function call cout<<"\nThe sorted array is: \n"; for(index=0; index<size; index++) cout<<'\t'<<my_list[index]<<endl; … }

26.  2003 Prentice Hall, Inc. All rights reserved. Let’s build up the algorithm outer loop – array scans, each scan starts from the element after the previous scan inner loop – find smallest element swap smallest element with start of scan next outer loop

27.  2003 Prentice Hall, Inc. All rights reserved. Selection Sort void sort(double testArray[]) { int n, k, sm_index, moves=0;double smallest; for(k=0; k<size; k++) // size-1 = number of passes { } } smallest=testArray[k]; sm_index=k; swap(testArray, sm_index, k);// call to swap() for(n=k+1; n<size; n++) if(testArray[n]<smallest) {smallest=testArray[n]; sm_index=n; }

28.  2003 Prentice Hall, Inc. All rights reserved. Selection Sort void swap(double testArray[], int smaller, int pass) {// pass = current position: k double temp; temp=testArray[pass]; testArray[pass]=testArray[smaller]; testArray[smaller]=temp; }

29.  2003 Prentice Hall, Inc. All rights reserved. for(k=0; k<size; k++) // size-1 = number of passes { } } smallest=testArray[k]; sm_index=k; swap(testArray, sm_index, k);// call to swap() for(n=k+1; n<size; n++) if(testArray[n]<smallest) {smallest=testArray[n]; sm_index=n; } How many times is the inner if statement called? How many times is the “sm_index” being reset? How many times is the swap() function called?

30.  2003 Prentice Hall, Inc. All rights reserved. 30 4.6Sorting Arrays Sorting data –Important computing application –Virtually every organization must sort some data Massive amounts must be sorted Bubble sort (sinking sort) –Several passes through the array –Successive pairs of elements are compared If increasing order (or identical), no change If decreasing order, elements exchanged –Repeat these steps for every element

31.  2003 Prentice Hall, Inc. All rights reserved. 31 Simple Sorting Bubble sort As we scan the list swap elements out of order. After the first scan, the largest element will be at the end of the list. Keep scanning the list until all of the elements are in the correct place. Bubble sort – because the small elements bubble up to the top…..

32.  2003 Prentice Hall, Inc. All rights reserved. 32 4.6Sorting Arrays Example: –Go left to right, and exchange elements as necessary One pass for each element –Original: 3 4 2 7 6 –Pass 1: 3 2 4 6 7 (elements exchanged) –Pass 2: 2 3 4 6 7 –Pass 3: 2 3 4 6 7 (no changes needed) –Pass 4: 2 3 4 6 7 –Pass 5: 2 3 4 6 7 –Small elements "bubble" to the top (like 2 in this example)

33.  2003 Prentice Hall, Inc. All rights reserved. Bubble Sort Put smaller first No change Put smaller first 212513917 2125 917 925211317 925132117

34.  2003 Prentice Hall, Inc. All rights reserved. Bubble Sort Begin again and put smaller first No change Put smaller first 211791325 172191325 211713925 211791325

35.  2003 Prentice Hall, Inc. All rights reserved. Bubble Sort Example 2 Begin --Put smaller first Put smaller first No change Put smaller first 1925181312 1925181312 13251918121325181912

36.  2003 Prentice Hall, Inc. All rights reserved. Bubble Sort – Example 2 Begin again and put smaller first No change Put smaller first 1912131825 1219131825 1912181325 1912131825

37.  2003 Prentice Hall, Inc. All rights reserved. Bubble Sort – Example 2 Begin again -- no change Swap – put smaller first Begin Again -- swap Sorted list 12191318251819121325 1219131825 1819131225

38.  2003 Prentice Hall, Inc. All rights reserved. 38 Let’s build up the algorithm – bubble sort outer loop – array scans, each scan starts from the first element of the list until _________ inner loop compare adjacent elements and swap next outer loop

39.  2003 Prentice Hall, Inc. All rights reserved. 39 4.6Sorting Arrays Swapping variables int x = 3, y = 4; y = x; x = y; What happened? –Both x and y are 3! –Need a temporary variable Solution int x = 3, y = 4, temp = 0; temp = x; // temp gets 3 x = y; // x gets 4 y = temp; // y gets 3

40.  2003 Prentice Hall, Inc. All rights reserved. Outline 40 fig04_16.cpp (1 of 3) 1 // Fig. 4.16: fig04_16.cpp 2 // This program sorts an array's values into ascending order. 3 #include 4 5 using std::cout; 6 using std::endl; 7 8 #include 9 10 using std::setw; 11 12 int main() 13 { 14 const int arraySize = 10; // size of array a 15 int a[ arraySize ] = { 2, 6, 4, 8, 10, 12, 89, 68, 45, 37 }; 16 int hold; // temporary location used to swap array elements 17 18 cout << "Data items in original order\n"; 19 20 // output original array 21 for ( int i = 0; i < arraySize; i++ ) 22 cout << setw( 4 ) << a[ i ]; 23

41.  2003 Prentice Hall, Inc. All rights reserved. Outline 41 fig04_16.cpp (2 of 3) 24 // bubble sort 25 // loop to control number of passes 26 for ( int pass = 0; pass < arraySize - 1; pass++ ) 27 28 // loop to control number of comparisons per pass 29 for ( int j = 0; j < arraySize - 1; j++ ) 30 31 // compare side-by-side elements and swap them if 32 // first element is greater than second element 33 if ( a[ j ] > a[ j + 1 ] ) { 34 hold = a[ j ]; 35 a[ j ] = a[ j + 1 ]; 36 a[ j + 1 ] = hold; 37 38 } // end if 39 Do a pass for each element in the array. If the element on the left (index j ) is larger than the element on the right (index j + 1 ), then we swap them. Remember the need of a temp variable.

42.  2003 Prentice Hall, Inc. All rights reserved. Outline 42 fig04_16.cpp (3 of 3) fig04_16.cpp output (1 of 1) 40 cout << "\nData items in ascending order\n"; 41 42 // output sorted array 43 for ( int k = 0; k < arraySize; k++ ) 44 cout << setw( 4 ) << a[ k ]; 45 46 cout << endl; 47 48 return 0; // indicates successful termination 49 50 } // end main Data items in original order 2 6 4 8 10 12 89 68 45 37 Data items in ascending order 2 4 6 8 10 12 37 45 68 89

43.  2003 Prentice Hall, Inc. All rights reserved. 43 Can we improve the algorithm? In the first example, we did not have to keep scanning the list since the list was sorted after the “2 nd ” scan…… Check to see if any swaps were performed on the previous inner loop. If none were performed do not scan the list anymore since it is sorted. ---- WE CAN END THE ALGORITHM EARLY: EARLY TERMINATION how can we accomplish this?

44.  2003 Prentice Hall, Inc. All rights reserved. Outline 44 24 // bubble sort 25 int flag = 1; 26 for ( int pass = 0; (pass < arraySize – 1) && flag; pass++ ) 27 flag = 0; 28 // loop to control number of comparisons per pass 29 for ( int j = 0; j < arraySize - 1; j++ ) 30 31 // compare side-by-side elements and swap them if 32 // first element is greater than second element 33 if ( a[ j ] > a[ j + 1 ] ) { 34 hold = a[ j ]; 35 a[ j ] = a[ j + 1 ]; 36 a[ j + 1 ] = hold; 37 flag = 1; //set flag since swap occurred 37 38 } // end if 39 Bubble sort with early termination Possible early termination

45.  2003 Prentice Hall, Inc. All rights reserved. Outline 45 24 // bubble sort 25 // loop to control number of passes 26 for ( int pass = 0; pass < arraySize - 1; pass++ ) 27 28 // loop to control number of comparisons per pass 29 for ( int j = 0; j < arraySize - 1; j++ ) 30 31 // compare side-by-side elements and swap them if 32 // first element is greater than second element 33 if ( a[ j ] > a[ j + 1 ] ) { 34 hold = a[ j ]; 35 a[ j ] = a[ j + 1 ]; 36 a[ j + 1 ] = hold; 37 38 } // end if 39 How many times does the outer loop execute in the worst case? How many times is the swap performed (inner loop) in the worst case?