1. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 1 Chapter 7 Single-Dimensional Arrays

2. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 2 Motivations Often you will have to store a large number of values during the execution of a program. Suppose, for instance, that you need to read one hundred numbers, compute their average, and find out how many numbers are above the average. Your program first reads the numbers and computes their average, and then compares each number with the average to determine whether it is above the average. The numbers must all be stored in variables in order to accomplish this task. You have to declare one hundred variables and repeatedly write almost identical code one hundred times. From the standpoint of practicality, it is impossible to write a program this way. So, how do you solve this problem?

3. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 3 Objectives F To describe why an array is necessary in programming (§7.1). F To declare arrays (§7.2.1). F To access array elements using indexed variables (§7.2.2). F To initialize the values in an array (§7.2.3). F To program common array operations (displaying arrays, summing all elements, finding min and max elements, random shuffling, shifting elements) (§7.2.4). F To apply arrays in the LottoNumbers and DeckOfCards problems (§§7.3-7.4). F To develop and invoke functions with array arguments (§§7.5-7.6). F To develop functions involving array parameters in the CountLettersInArray problem (§7.7). F To search elements using the linear (§7.8.1) or binary search algorithm (§7.8.2). F To sort an array using the selection sort (§7.9.1) F To sort an array using the insertion sort (§7.9.2). F To process strings using C-strings (§7.10).

4. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 4 Introducing Arrays Array is a data structure that represents a collection of the same types of data.

5. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 5 Declaring Array Variables datatype arrayRefVar[arraySize]; Example: double myList[10]; C++ requires that the array size used to declare an array must be a constant expression. For example, the following code is illegal: int size = 4; double myList[size]; // Wrong But it would be OK, if size is a constant as follow: const int size = 4; double myList[size]; // Correct

6. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 6 Arbitrary Initial Values When an array is created, its elements are assigned with arbitrary values.

7. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 7 Indexed Variables The array elements are accessed through the index. Array indices are 0-based; that is, they start from 0 to arraySize-1. In the example in Figure 6.1, myList holds ten double values and the indices are from 0 to 9. Each element in the array is represented using the following syntax, known as an indexed variable: arrayName[index]; For example, myList[9] represents the last element in the array myList.

8. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 8 Using Indexed Variables After an array is created, an indexed variable can be used in the same way as a regular variable. For example, the following code adds the value in myList[0] and myList[1] to myList[2]. myList[2] = myList[0] + myList[1];

9. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 9 No Bound Checking C++ does not check array’s boundary. So, accessing array elements using subscripts beyond the boundary (e.g., myList[-1] and myList[11]) does not does cause syntax errors, but the operating system might report a memory access violation.

10. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 10 Array Initializers Declaring, creating, initializing in one step: dataType arrayName[arraySize] = {value0, value1,..., valuek}; double myList[4] = {1.9, 2.9, 3.4, 3.5};

11. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 11 Declaring, creating, initializing Using the Shorthand Notation double myList[4] = {1.9, 2.9, 3.4, 3.5}; This shorthand notation is equivalent to the following statements: double myList[4]; myList[0] = 1.9; myList[1] = 2.9; myList[2] = 3.4; myList[3] = 3.5;

12. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 12 CAUTION Using the shorthand notation, you have to declare, create, and initialize the array all in one statement. Splitting it would cause a syntax error. For example, the following is wrong: double myList[4]; myList = {1.9, 2.9, 3.4, 3.5};

13. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 13 I mplicit Size C++ allows you to omit the array size when declaring and creating an array using an initilizer. For example, the following declaration is fine: double myList[] = {1.9, 2.9, 3.4, 3.5}; C++ automatically figures out how many elements are in the array.

14. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 14 Partial Initialization C++ allows you to initialize a part of the array. For example, the following statement assigns values 1.9, 2.9 to the first two elements of the array. The other two elements will be set to zero. Note that if an array is declared, but not initialized, all its elements will contain “garbage”, like all other local variables. double myList[4] = {1.9, 2.9};

15. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 15 Initializing Character Arrays char city[] = {'D', 'a', 'l', 'l', 'a', 's'}; char city[] = "Dallas"; This statement is equivalent to the preceding statement, except that C++ adds the character '\0', called the null terminator, to indicate the end of the string, as shown in Figure 6.2. Recall that a character that begins with the back slash symbol (\) is an escape character.

16. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 16 Initializing arrays with random values The following loop initializes the array myList with random values between 0 and 99: for (int i = 0; i < ARRAY_SIZE; i++) { myList[i] = rand() % 100; }

17. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 17 Trace Program with Arrays int main() { int values[5]; for (int i = 1; i < 5; i++) { values[i] = values[i] + values[i-1]; } values[0] = values[1] + values[4]; } Declare array variable values, create an array, and assign its reference to values animation

18. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 18 Trace Program with Arrays int main() { int values[5]; for (int i = 1; i < 5; i++) { values[i] = values[i] + values[i-1]; } values[0] = values[1] + values[4]; } i becomes 1 animation

19. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 19 Trace Program with Arrays int main() { int values[5]; for (int i = 1; i < 5; i++) { values[i] = values[i] + values[i-1]; } values[0] = values[1] + values[4]; } i (=1) is less than 5 animation

20. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 20 Trace Program with Arrays int main() { int values[5]; for (int i = 1; i < 5; i++) { values[i] = values[i] + values[i-1]; } values[0] = values[1] + values[4]; } After this line is executed, value[1] is 1 animation

21. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 21 Trace Program with Arrays int main() { int values[5]; for (int i = 1; i < 5; i++) { values[i] = values[i] + values[i-1]; } values[0] = values[1] + values[4]; } After i++, i becomes 2 animation

22. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 22 Trace Program with Arrays int main() { int values[5]; for (int i = 1; i < 5; i++) { values[i] = values[i] + values[i-1]; } values[0] = values[1] + values[4]; } i (= 2) is less than 5 animation

23. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 23 Trace Program with Arrays int main() { int values[5]; for (int i = 1; i < 5; i++) { values[i] = values[i] + values[i-1]; } values[0] = values[1] + values[4]; } After this line is executed, values[2] is 3 (2 + 1) animation

24. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 24 Trace Program with Arrays int main() { int values[5]; for (int i = 1; i < 5; i++) { values[i] = values[i] + values[i-1]; } values[0] = values[1] + values[4]; } After this, i becomes 3. animation

25. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 25 Trace Program with Arrays int main() { int values[5]; for (int i = 1; i < 5; i++) { values[i] = values[i] + values[i-1]; } values[0] = values[1] + values[4]; } i (=3) is still less than 5. animation

26. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 26 Trace Program with Arrays int main() { int values[5]; for (int i = 1; i < 5; i++) { values[i] = values[i] + values[i-1]; } values[0] = values[1] + values[4]; } After this line, values[3] becomes 6 (3 + 3) animation

27. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 27 Trace Program with Arrays int main() { int values[5]; for (int i = 1; i < 5; i++) { values[i] = values[i] + values[i-1]; } values[0] = values[1] + values[4]; } After this, i becomes 4 animation

28. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 28 Trace Program with Arrays int main() { int values[5]; for (int i = 1; i < 5; i++) { values[i] = values[i] + values[i-1]; } values[0] = values[1] + values[4]; } i (=4) is still less than 5 animation

29. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 29 Trace Program with Arrays int main() { int values[5]; for (int i = 1; i < 5; i++) { values[i] = values[i] + values[i-1]; } values[0] = values[1] + values[4]; } After this, values[4] becomes 10 (4 + 6) animation

30. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 30 Trace Program with Arrays int main() { int values[5]; for (int i = 1; i < 5; i++) { values[i] = values[i] + values[i-1]; } values[0] = values[1] + values[4]; } After i++, i becomes 5 animation

31. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 31 Trace Program with Arrays int main() { int values[5]; for (int i = 1; i < 5; i++) { values[i] = values[i] + values[i-1]; } values[0] = values[1] + values[4]; } i ( =5) < 5 is false. Exit the loop animation

32. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 32 Trace Program with Arrays int main() { int values[5]; for (int i = 1; i < 5; i++) { values[i] = values[i] + values[i-1]; } values[0] = values[1] + values[4]; } After this line, values[0] is 11 (1 + 10) animation

33. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 33 Printing arrays To print an array, you have to print each element in the array using a loop like the following: for (int i = 0; i < ARRAY_SIZE; i++) { cout << myList[i] << " "; }

34. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 34 Printing Character Array For a character array, it can be printed using one print statement. For example, the following code displays Dallas: char city[] = "Dallas"; cout << city;

35. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 35 Copying Arrays Can you copy array using a syntax like this? list = myList; This is not allowed in C++. You have to copy individual elements from one array to the other as follows: for (int i = 0; i < ARRAY_SIZE; i++) { list[i] = myList[i]; }

36. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 36 Summing All Elements Use a variable named total to store the sum. Initially total is 0. Add each element in the array to total using a loop like this: double total = 0; for (int i = 0; i < ARRAY_SIZE; i++) { total += myList[i]; }

37. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 37 Finding the Largest Element Use a variable named max to store the largest element. Initially max is myList[0]. To find the largest element in the array myList, compare each element in myList with max, update max if the element is greater than max. double max = myList[0]; for (int i = 1; i < ARRAY_SIZE; i++) { if (myList[i] > max) max = myList[i]; }

38. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 38 Finding the smallest index of the largest element double max = myList[0]; int indexOfMax = 0; for (int i = 1; i < ARRAY_SIZE; i++) { if (myList[i] > max) { max = myList[i]; indexOfMax = i; }

39. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 39 Random Shuffling srand(time(0)); for (int i = 0; i < ARRAY_SIZE; i++) { // Generate an index randomly int index = rand() % ARRAY_SIZE; double temp = myList[i]; myList[i] = myList[index]; myList[index] = temp; }

40. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 40 Shifting Elements double temp = myList[0]; // Retain the first element // Shift elements left for (int i = 1; i < myList.length; i++) { myList[i - 1] = myList[i]; } // Move the first element to fill in the last position myList[myList.length - 1] = temp;

41. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 41 Problem: Lotto Numbers Your grandma likes to play the Pick-10 lotto. Each ticket has 10 unique numbers ranging from 1 to 99. Every time she buys a lot of tickets. She likes to have her tickets to cover all numbers from 1 to 99. Write a program that reads the ticket numbers from a file and checks whether all numbers are covered. Assume the last number in the file is 0. LottoNumbers Run

42. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 42 Problem: Deck of Cards The problem is to write a program that picks four cards randomly from a deck of 52 cards. All the cards can be represented using an array named deck, filled with initial values 0 to 52, as follows: int deck[52]; // Initialize cards for (int i = 0; i < NUMBER_OF_CARDS; i++) deck[i] = i; deck[0] to deck[12] are Clubs, deck[13] to deck[25] are Diamonds, deck[26] to deck[38] are Hearts, and deck[39] to deck[51] are Spades. Listing 6.2 gives the solution to the problem. DeckOfCards Run

43. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 43 Passing Arrays to Functions Just as you can pass single values to a function, you can also pass an entire array to a function. Listing 6.3 gives an example to demonstrate how to declare and invoke this type of functions. PassArrayDemo Run

44. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 44 Passing Size along with Array Normally when you pass an array to a function, you should also pass its size in another argument. So the function knows how many elements are in the array. Otherwise, you will have to hard code this into the function or declare it in a global variable. Neither is flexible or robust.

45. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 45 Pass-by-Reference Passing an array variable means that the starting address of the array is passed to the formal parameter. The parameter inside the function references to the same array that is passed to the function. No new arrays are created. This is pass- by-reference. PassByReferenceDemo Run

46. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 46 const Parameters Passing arrays by reference makes sense for performance reasons. If an array is passed by value, all its elements must be copied into a new array. For large arrays, it could take some time and additional memory space. However, passing arrays by reference could lead to errors if your function changes the array accidentally. To prevent it from happening, you can put the const keyword before the array parameter to tell the compiler that the array cannot be changed. The compiler will report errors if the code in the function attempts to modify the array. ConstArrayDemo Compile error

47. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 47 Returning an Array from a Function Can you return an array from a function using a similar syntax? For example, you may attempt to declare a function that returns a new array that is a reversal of an array as follows: // Return the reversal of list int[] reverse(const int list[], int size) This is not allowed in C++.

48. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 48 Modifying Arrays in Functions, cont. However, you can circumvent this restriction by passing two array arguments in the function, as follows: // newList is the reversal of list void reverse(const int list[], list newList[], int size) ReverseArray Run

49. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 49 Trace the reverse Function void reverse(const int list[], int newList[], int size) { for (int i = 0, j = size - 1; i < size; i++, j--) { newList[j] = list[i]; } int list1[] = {1, 2, 3, 4, 5, 6}; reverse(list1, list2); list newList 123456 000000 animation

50. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 50 Trace the reverse Method, cont. int list1[] = {1, 2, 3, 4, 5, 6}; reverse(list1, list2); list newList 123456 000000 animation void reverse(const int list[], int newList[], int size) { for (int i = 0, j = size - 1; i < size; i++, j--) { newList[j] = list[i]; } i = 0 and j = 5

51. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 51 Trace the reverse Method, cont. int list1[] = {1, 2, 3, 4, 5, 6}; reverse(list1, list2); list newList 123456 000000 animation void reverse(const int list[], int newList[], int size) { for (int i = 0, j = size - 1; i < size; i++, j--) { newList[j] = list[i]; } i (= 0) is less than 6

52. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 52 Trace the reverse Method, cont. int list1[] = {1, 2, 3, 4, 5, 6}; reverse(list1, list2); list newList 123456 000001 animation void reverse(const int list[], int newList[], int size) { for (int i = 0, j = size - 1; i < size; i++, j--) { newList[j] = list[i]; } i = 0 and j = 5 Assign list[0] to result[5]

53. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 53 Trace the reverse Method, cont. int list1[] = {1, 2, 3, 4, 5, 6}; reverse(list1, list2); list newList 123456 000001 animation void reverse(const int list[], int newList[], int size) { for (int i = 0, j = size - 1; i < size; i++, j--) { newList[j] = list[i]; } After this, i becomes 1 and j becomes 4

54. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 54 Trace the reverse Method, cont. int list1[] = {1, 2, 3, 4, 5, 6}; reverse(list1, list2); list newList 123456 000001 animation void reverse(const int list[], int newList[], int size) { for (int i = 0, j = size - 1; i < size; i++, j--) { newList[j] = list[i]; } i (=1) is less than 6

55. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 55 Trace the reverse Method, cont. int list1[] = {1, 2, 3, 4, 5, 6}; reverse(list1, list2); list newList 123456 000021 animation void reverse(const int list[], int newList[], int size) { for (int i = 0, j = size - 1; i < size; i++, j--) { newList[j] = list[i]; } i = 1 and j = 4 Assign list[1] to result[4]

56. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 56 Trace the reverse Method, cont. int list1[] = {1, 2, 3, 4, 5, 6}; reverse(list1, list2); list newList 123456 000021 animation void reverse(const int list[], int newList[], int size) { for (int i = 0, j = size - 1; i < size; i++, j--) { newList[j] = list[i]; } After this, i becomes 2 and j becomes 3

57. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 57 Trace the reverse Method, cont. int list1[] = {1, 2, 3, 4, 5, 6}; reverse(list1, list2); list newList 123456 000021 animation void reverse(const int list[], int newList[], int size) { for (int i = 0, j = size - 1; i < size; i++, j--) { newList[j] = list[i]; } i (=2) is still less than 6

58. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 58 Trace the reverse Method, cont. int list1[] = {1, 2, 3, 4, 5, 6}; reverse(list1, list2); list newList 123456 000321 animation void reverse(const int list[], int newList[], int size) { for (int i = 0, j = size - 1; i < size; i++, j--) { newList[j] = list[i]; } i = 2 and j = 3 Assign list[i] to result[j]

59. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 59 Trace the reverse Method, cont. int list1[] = {1, 2, 3, 4, 5, 6}; reverse(list1, list2); list newList 123456 000321 animation void reverse(const int list[], int newList[], int size) { for (int i = 0, j = size - 1; i < size; i++, j--) { newList[j] = list[i]; } After this, i becomes 3 and j becomes 2

60. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 60 Trace the reverse Method, cont. int list1[] = {1, 2, 3, 4, 5, 6}; reverse(list1, list2); list newList 123456 000321 animation void reverse(const int list[], int newList[], int size) { for (int i = 0, j = size - 1; i < size; i++, j--) { newList[j] = list[i]; } i (=3) is still less than 6

61. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 61 Trace the reverse Method, cont. int list1[] = {1, 2, 3, 4, 5, 6}; reverse(list1, list2); list newList 123456 004321 animation void reverse(const int list[], int newList[], int size) { for (int i = 0, j = size - 1; i < size; i++, j--) { newList[j] = list[i]; } i = 3 and j = 2 Assign list[i] to result[j]

62. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 62 Trace the reverse Method, cont. int list1[] = {1, 2, 3, 4, 5, 6}; reverse(list1, list2); list newList 123456 004321 animation void reverse(const int list[], int newList[], int size) { for (int i = 0, j = size - 1; i < size; i++, j--) { newList[j] = list[i]; } After this, i becomes 4 and j becomes 1

63. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 63 Trace the reverse Method, cont. int list1[] = {1, 2, 3, 4, 5, 6}; reverse(list1, list2); list newList 123456 004321 animation void reverse(const int list[], int newList[], int size) { for (int i = 0, j = size - 1; i < size; i++, j--) { newList[j] = list[i]; } i (=4) is still less than 6

64. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 64 Trace the reverse Method, cont. int list1[] = {1, 2, 3, 4, 5, 6}; reverse(list1, list2); list newList 123456 054321 animation void reverse(const int list[], int newList[], int size) { for (int i = 0, j = size - 1; i < size; i++, j--) { newList[j] = list[i]; } i = 4 and j = 1 Assign list[i] to result[j]

65. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 65 Trace the reverse Method, cont. int list1[] = {1, 2, 3, 4, 5, 6}; reverse(list1, list2); list newList 123456 054321 animation void reverse(const int list[], int newList[], int size) { for (int i = 0, j = size - 1; i < size; i++, j--) { newList[j] = list[i]; } After this, i becomes 5 and j becomes 0

66. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 66 Trace the reverse Method, cont. int list1[] = {1, 2, 3, 4, 5, 6}; reverse(list1, list2); list newList 123456 054321 animation void reverse(const int list[], int newList[], int size) { for (int i = 0, j = size - 1; i < size; i++, j--) { newList[j] = list[i]; } i (=5) is still less than 6

67. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 67 Trace the reverse Method, cont. int list1[] = {1, 2, 3, 4, 5, 6}; reverse(list1, list2); list newList 123456 654321 animation void reverse(const int list[], int newList[], int size) { for (int i = 0, j = size - 1; i < size; i++, j--) { newList[j] = list[i]; } i = 5 and j = 0 Assign list[i] to result[j]

68. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 68 Trace the reverse Method, cont. int list1[] = {1, 2, 3, 4, 5, 6}; reverse(list1, list2); list newList 123456 654321 animation void reverse(const int list[], int newList[], int size) { for (int i = 0, j = size - 1; i < size; i++, j--) { newList[j] = list[i]; } After this, i becomes 6 and j becomes -1

69. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 69 Trace the reverse Method, cont. int list1[] = {1, 2, 3, 4, 5, 6}; reverse(list1, list2); list newList 123456 654321 animation void reverse(const int list[], int newList[], int size) { for (int i = 0, j = size - 1; i < size; i++, j--) { newList[j] = list[i]; } i (=6) < 6 is false. So exit the loop.

70. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 70 Problem: Counting Occurrence of Each Letter F Generate 100 lowercase letters randomly and assign to an array of characters. F Count the occurrence of each letter in the array. CountLettersInArrayRun

71. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 71 Searching Arrays Searching is the process of looking for a specific element in an array; for example, discovering whether a certain score is included in a list of scores. Searching is a common task in computer programming. There are many algorithms and data structures devoted to searching. In this section, two commonly used approaches are discussed, linear search and binary search.

72. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 72 Linear Search The linear search approach compares the key element, key, sequentially with each element in the array list. The method continues to do so until the key matches an element in the list or the list is exhausted without a match being found. If a match is made, the linear search returns the index of the element in the array that matches the key. If no match is found, the search returns -1.

73. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 73 Linear Search Animation 64197328 64197328 64197328 64197328 64197328 64197328 3 3 3 3 3 3 animation KeyList

74. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 74 From Idea to Solution int[] list = {1, 4, 4, 2, 5, -3, 6, 2}; int i = linearSearch(list, 4); // returns 1 int j = linearSearch(list, -4); // returns -1 int k = linearSearch(list, -3); // returns 5 Trace the function

75. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 75 Binary Search For binary search to work, the elements in the array must already be ordered. Without loss of generality, assume that the array is in ascending order. e.g., 2 4 7 10 11 45 50 59 60 66 69 70 79 The binary search first compares the key with the element in the middle of the array.

76. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 76 Binary Search, cont. F If the key is less than the middle element, you only need to search the key in the first half of the array. F If the key is equal to the middle element, the search ends with a match. F If the key is greater than the middle element, you only need to search the key in the second half of the array. Consider the following three cases:

77. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 77 Binary Search 12346789 12346789 12346789 8 8 8 KeyList animation

78. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 78 Binary Search, cont.

79. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 79 Binary Search, cont.

80. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 80 Binary Search, cont. The binarySearch method returns the index of the search key if it is contained in the list. Otherwise, it returns –insertion point - 1. The insertion point is the point at which the key would be inserted into the list.

81. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 81 From Idea to Solution int binarySearch(const int list[], int key, int arraySize) { int low = 0; int high = arraySize - 1; while (high >= low) { int mid = (low + high) / 2; if (key < list[mid]) high = mid - 1; else if (key == list[mid]) return mid; else low = mid + 1; } return –low - 1; }

82. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 82 Sorting Arrays Sorting, like searching, is also a common task in computer programming. It would be used, for instance, if you wanted to display the grades from Listing 6.2, AssignGrade.cpp, in alphabetical order. Many different algorithms have been developed for sorting. This section introduces two simple, intuitive sorting algorithms: selection sort and insertion sort.

83. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 83 Selection sort finds the largest number in the list and places it last. It then finds the largest number remaining and places it next to last, and so on until the list contains only a single number. Figure 6.17 shows how to sort the list {2, 9, 5, 4, 8, 1, 6} using selection sort. Selection Sort

84. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 84 From Idea to Solution for (int i = 0; i < listSize; i++) { select the smallest element in list[i..listSize-1]; swap the smallest with list[i], if necessary; // list[i] is in its correct position. // The next iteration apply on list[i..listSize-1] } list[0] list[1] list[2] list[3]... list[10]... list[0] list[1] list[2] list[3]... list[10]

85. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 85 Expand for (int i = 0; i < listSize; i++) { select the smallest element in list[i..listSize-1]; swap the smallest with list[i], if necessary; // list[i] is in its correct position. // The next iteration apply on list[i..listSize-1] } double currentMin = list[i]; int currentMinIndex = i; for (int j = i; j < listSize; j++) { if (currentMin > list[j]) { currentMin = list[j]; currentMinIndex = j; }

86. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 86 Expand for (int i = 0; i < listSize; i++) { select the smallest element in list[i..listSize-1]; swap the smallest with list[i], if necessary; // list[i] is in its correct position. // The next iteration apply on list[i..listSize-1] } double currentMin = list[i]; int currentMinIndex = i; for (int j = i; j < listSize; j++) { if (currentMin > list[j]) { currentMin = list[j]; currentMinIndex = j; }

87. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 87 Expand for (int i = 0; i < listSize; i++) { select the smallest element in list[i..listSize-1]; swap the smallest with list[i], if necessary; // list[i] is in its correct position. // The next iteration apply on list[i..listSize-1] } if (currentMinIndex != i) { list[currentMinIndex] = list[i]; list[i] = currentMin; }

88. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 88 Insertion Sort int[] myList = {2, 9, 5, 4, 8, 1, 6}; // Unsorted The insertion sort algorithm sorts a list of values by repeatedly inserting an unsorted element into a sorted sublist until the whole list is sorted. Optional

89. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 89 Insertion Sort 2954816 2954816 2594816 2458916 1245896 2459816 1245689 int[] myList = {2, 9, 5, 4, 8, 1, 6}; // Unsorted animation

90. Liang, Introduction to Programming with C++, Second Edition, (c) 2010 Pearson Education, Inc. All rights reserved. 0136097200 90 How to Insert? The insertion sort algorithm sorts a list of values by repeatedly inserting an unsorted element into a sorted sublist until the whole list is sorted. Optional