1. CNG 140 C Programming (Lecture set 8)
Spring
Chapter 8
Arrays

2. Objectives: arrays Declaring Arrays Array Initialization
Arrays as Function Arguments
Case Study: Computing Averages and Standard Deviations
Two-Dimensional Arrays
Common Programming and Compiler Errors
CNG 140 C Programming 20062

3. Introduction
Atomic variable: variable whose value cannot be further subdivided into a built-in data type
Also called a scalar variable
Data structure (aggregate data type): data type with two main characteristics
Its values can be decomposed into individual data elements, each of which is either atomic or another data structure
It provides an access scheme for locating individual data elements within the data structure
CNG 140 C Programming 20062

4. Introduction (continued)
CNG 140 C Programming 20062

5. Arrays
One of the simplest data structures, called an array, is used to store and process a set of values, all of the same data type, that forms a logical group
Arrays could be multi dimensional
A one-dimensional array, also called a single-dimensional array and a single-subscript array, is a list of values of the same data type that is stored using a single group name
CNG 140 C Programming 20062

6. One-Dimensional Arrays (example)
CNG 140 C Programming 20062

7. One-Dimensional Arrays (continued)
To create a one-dimensional array: required: name and size
#define NUMELS 5 // size as constant symbol
int grades[NUMELS]; // declaration with a name
In C, the starting index value for all arrays is 0
Each item in an array is called an element or component of the array
Any element can be accessed by giving the name of the array and the element’s position
The position is the element’s index or subscript
Each element is called an indexed variable or a subscripted variable
CNG 140 C Programming 20062

8. One-Dimensional Arrays: int grades[5]
CNG 140 C Programming 20062

9. One-Dimensional Arrays (continued)
Subscripted variables can be used anywhere scalar variables are valid
grades[0] = 98;
grades[1] = grades[0] - 11;
Any expression that evaluates an integer may be used as a subscript
#define NUMELS 5
total = 0; /* initialize total to zero */
for (i = 0; i < NUMELS; i++)
total = total + grades[i]; /* add a grade */
CNG 140 C Programming 20062

10. Input and Output of Array Values
Individual array elements can be assigned values using individual assignment statements or, interactively, using the scanf() function
#define NUMELS 5
for(i = 0; i < NUMELS; i++) {
printf("Enter a grade: ");
scanf("%d", &grades[i]); }
Be careful: C does not check the value of the index being used (called a bounds check)
CNG 140 C Programming 20062

11. Input and Output of Array Values (continued)
Sample output:
Enter a grade: 85
Enter a grade: 90
Enter a grade: 78
Enter a grade: 75
Enter a grade: 92
grades 0 is 85
grades 1 is 90
grades 2 is 78
grades 3 is 75
grades 4 is 92
CNG 140 C Programming 20062

12. Input and Output of Array Values (continued)
Statement is outside of the second for loop; total is displayed only once, after all values have been added
CNG 140 C Programming 20062

13. Example Problem
Write a function to find the index of the maximum and minimum numbers in an array.
Write the main program which reads the size of an array and all the elements of the array. It shoul then call the previous function MaxMin to display the index and values of the maximum and minimum numbers
CNG 140 C Programming 20062

14. Example Problem (Cont.)
void MaxMin(int array ar[100], numels, *I, *j) {
int max, min, count;
min=ar[0]; max=ar[0];
for(count = 0; count < numels; ++count)
if (max < temp[count])
max = temp[count];
*i=count; }
if (min > temp[count])
min = temp[count];
*j=count;
return;
CNG 140 C Programming 20062

15. Example Problem (Cont.)
#include <stdio.h>
void MaxMin(int array ar[100], int, int *, int *)
int main() {
int ar[100], max, min;
……….
MaxMin(ar,numels, &max, &min);
printf("\nMax Element #%d = %d \nMin Element #%d = %d", max, ar[max], min, ar[min]);
return 0; }
CNG 140 C Programming 20062

16. Exercises
8.1.4 and 8.1.5
CNG 140 C Programming 20062

17. Array Initialization
All global arrays are created once at compilation time.
They retain their values during the execution
All static arrays are created once at compilation time.
All auto arrays have local scope, thus they are lost once the function declaring them exits
Array elements can be assigned values in the declaration statements
CNG 140 C Programming 20062

18. Array Initialization (cont.)
The individual elements of all global and static arrays (local or global) are, by default, set to 0 at compilation time
The values within auto local arrays are undefined
Examples of initializations:
int grades[5] = {98, 87, 92, 79, 85};
double length[7] = {8.8, 6.4, 4.9, 11.2};
char codes[6] = {'s', 'a', 'm', 'p', 'l', e'};
char codes[] = {'s', 'a', 'm', 'p', 'l', 'e'};
char codes[] = "sample"; /* size is 7 */
CNG 140 C Programming 20062

19. Array Initialization (continued)
1 #define SIZE1 20
2 #define SIZE2 25
3 #define SIZE3 15 4
5 int gallons[SIZE1]; /* a global array */
6 static int dist[SIZE2]; /* a static global array */ 7
8 int main()
9 {
10 int miles[SIZE3]; /* an auto local array */
11 static int course[SIZE3]; /* static local array */
12 .
13 .
14 return 0;
15 }
CNG 140 C Programming 20062

20. Array Initialization (Strings)
The last character in a string is always assigned a NULL character \0
The NULL character, which is the escape sequence \0, is automatically appended to all strings by the C compiler.
For example \0 is added as the last character to the following string:
char codes[6] = {'s', 'a', 'm', 'p', 'l', e'};
CNG 140 C Programming 20062

21. Array Initialization (continued)
CNG 140 C Programming 20062

22. Array Initialization (Example program)
Assign values to an array and find the maximum
CNG 140 C Programming 20062

23. Problem 8.2.2
Write a program that declares a string, say “This is CNG140 course” and prints the characters using “%c” and “%s” format specifications
CNG 140 C Programming 20062

24. Problem Description: 8.2 Exercise 2a
#include <stdio.h>
int main() {
char strtest[22] = "This is CNG140 course";
int i;
for ( i = 0; i <=21; i++ )
printf ( "%c", strtest[i] );
printf ( "%s", strtest ); /*For this the last char must be \0 */
return 0; }
CNG 140 C Programming 20062

25. Exercise
Input number of students, and their grades as an array, before finding the maximum, minimum and the average and print all…
CNG 140 C Programming 20062

26. Arrays as Function Arguments
Individual array elements are passed to a function by including them as subscripted variables in the function call argument lists:
Pass by value
findMin(grades[2], grades[6]);
When passing a complete array to a function, the called function receives access to the actual array, rather than a copy of the values in the array
Pass by reference
findMax(grades);
CNG 140 C Programming 20062

27. Arrays as Function Arguments (continued)
Maximum array size is set to 5
Size can be omitted
CNG 140 C Programming 20062

28. Arrays as Function Arguments (continued)
Array size in the function header better be omitted!
CNG 140 C Programming 20062

29. Arrays as Function Arguments (continued)
CNG 140 C Programming 20062

30. Arrays as Function Arguments (a complete program)
CNG 140 C Programming 20062

31. Insertion sort-1
use a function called insert, designed to insert a value into a sorted sequence at the beginning of an array.
Ex: 3, 8, 5 becomes 3, 5, 8
To perform insertion sort, start at the left end of the array and invoke insert to insert each element encountered into its correct position.
Sorted: 3, 5, 8, unsorted: 1, 15, 4, 7, 6, 20, 11, 2
CNG 140 C Programming 20062

32. Insertion sort-2
/*Insertion sort: insert the the value in its place in the sorted part of the array */
insert(array a, int length, value) {
int i = length - 1;
while (i >= 0 && a[i] > value)
a[i + 1] = a[i];
i = i - 1; }
a[i + 1] := value;
insertionSort(array a, int length) /* each time one value find its place in the sorted array */
for (int i = 0; i < length; i = i + 1) insert(a, i, a[i]);
CNG 140 C Programming 20062

33. Case Study: Computing Averages and Standard Deviations
Two statistical functions are created to determine the average and standard deviation, respectively, of an array of numbers.
Standard deviation is square root of the sum of the square of the differences between individual elements and the average divided by the number of elements.
Sqrt(∑(x-avg)2/n)
CNG 140 C Programming 20062

34. Requirements Specification
Need two functions
Determine the average…
Determine the standard deviation…
Each function must accept the numbers as an array and return the calculated values to the calling function
CNG 140 C Programming 20062

35. Analyze the Problem Determine the input items: list of integer numbers
Determine the desired outputs: (1) average, and (2) standard deviation
List the algorithms relating the inputs and outputs:
Average Function: Calculate the average by adding the grades and dividing by the # of the grades
Standard Deviation Function:
Subtract the average from each individual grade. Each number in the new set is called a deviation.
Square each deviation found in Step 1.
Add the squared deviations and divide the sum by the number of deviations.
The square root of the number found in Step 3 is the standard deviation.
CNG 140 C Programming 20062

36. Select an Overall Solution
Initialize an array of integers
Call the average function
Call the standard deviation function
Display the returned value of the average function
Display the returned value of the standard deviation function
CNG 140 C Programming 20062

37. Write the main Function which calls functions findAvg and stdDev
CNG 140 C Programming 20062

38. Write the Functions (continued)
CNG 140 C Programming 20062

39. Test and Debug the Functions
Write a main() program unit to call the function and display the returned results (see Program 8.6)
A test run using Program 8.6 produced the following display:
The average of the numbers is 76.40
The standard deviation of the numbers is 13.15
Testing is not complete without verifying the calculation at the boundary points
Checking the calculation with all of the same values, such as all 0s and all 100s
Use five 0s and five 100s
CNG 140 C Programming 20062

40. Two-Dimensional Arrays
CNG 140 C Programming 20062

41. Two-Dimensional Arrays (continued)
CNG 140 C Programming 20062

42. Two-Dimensional Array Declaration
A two-dimensional array, or table, consists of both rows and columns of elements
int val[3][4];
CNG 140 C Programming 20062

43. Two-Dimensional Arrays (continued)
Initialization:
#define NUMROWS 3
#define NUMCOLS 4
int val[NUMROWS][NUMCOLS] = { {8,16,9,52},
{3,15,27,6},
{14,25,2,10} };
The inner braces can be omitted:
int val[NUMROWS][NUMCOLS] = {8,16,9,52,3,15,27, 6,14,25,2,10};
Initialization is done in row order
CNG 140 C Programming 20062

44. Two-Dimensional Arrays (continued)
CNG 140 C Programming 20062

45. Printing Two-Dimensional Arrays
CNG 140 C Programming 20062

46. Two-Dimensional Arrays: printing methods
Print using individual elements
Print using for loops
CNG 140 C Programming 20062

47. Two-Dimensional Arrays (continued)
The display produced by Program 8.7 is
Display of val array by explicit element
Display of val array using a nested for loop
CNG 140 C Programming 20062

48. Two-Dimensional Arrays (continued)
Multiply each element of the array by 10 and print
CNG 140 C Programming 20062

49. Two-Dimensional Arrays: all in main function
CNG 140 C Programming 20062

50. Two-Dimensional Arrays: call a function to print
Row size can be omitted
CNG 140 C Programming 20062

51. Two-Dimensional Arrays: offset computation
Column size is used to locate (compute the address of) the individual elements in the memory
CNG 140 C Programming 20062

52. Internal Array Element Location Algorithm
Each element in an array is reached by adding an offset to the starting address of the array
Address element i = starting array address + offset
For single-dimensional arrays:
Offset = i * the size of an individual element
For two-dimensional arrays:
Offset = column index value * the size of an individual element + row index value * # of bytes in a complete row
# of bytes in a complete row = maximum column specification * the size of an individual element
CNG 140 C Programming 20062

53. Internal Array Element Location Algorithm (continued)
CNG 140 C Programming 20062

54. Larger Dimensional Arrays
A three-dimensional array can be viewed as a book of data tables (the third subscript is called the rank)
int response[4][10][6];
A four-dimensional array can be represented as a shelf of books where the fourth dimension is used to declare a desired book on the shelf
A five-dimensional array can be viewed as a bookcase filled with books where the fifth dimension refers to a selected shelf in the bookcase
Arrays of three, four, five, six, or more dimensions can be viewed as mathematical n-tuples
CNG 140 C Programming 20062

55. Common Programming Errors
Forgetting to declare the array
Using a subscript that references a nonexistent array element
Not using a large enough conditional value in a for loop counter to cycle through all the array elements
Forgetting to initialize the array
CNG 140 C Programming 20062

56. Common Compiler Errors
CNG 140 C Programming 20062

57. Summary
A single-dimensional array is a data structure that can store a list of values of the same data type
Elements are stored in contiguous locations
Referenced using the array name and a subscript
Single-dimensional arrays may be initialized when they are declared
Single-dimensional arrays are passed to a function by passing the name of the array as an argument
CNG 140 C Programming 20062

58. Summary (continued)
A two-dimensional array is declared by listing both a row and a column size with the data type and name of the array
Two-dimensional arrays may be initialized when they are declared
Two-dimensional arrays are passed to a function by passing the name of the array as an argument
CNG 140 C Programming 20062

59. Linear Search #include <stdio.h> #define TRUE 1 #define FALSE 0
#define NUMEL 10
int linearSearch (int [], int, int);
CNG 140 C Programming 20062

60. Linear Search: main() int main() {
int nums[NUMEL] = {5,10,22,32,45,67,73,98,99,101};
int item, location;
printf("Enter the item you are searching for: ");
scanf("%d", &item);
location = linearSearch(nums, NUMEL, item);
if (location > -1)
printf("The item was found at index location %d\n",
location);
else
printf("The item was not found in the list\n");
return 0; }
CNG 140 C Programming 20062

61. Linear Search: linearSearch()
int linearSearch(int list[], int size, int key)
/* this function returns the location of key in the list */
/* a -1 is returned if the value is not found */ {
int index, found, i;
index = -1;
found = FALSE;
i = 0;
while (i < size && !found)
if (list[i] == key)
found = TRUE;
index = i; }
i++; /* move to next item in the list */
return (index);
CNG 140 C Programming 20062