1. A First Book of ANSI C Fourth Edition Chapter 8 Arrays

2. A First Book of ANSI C, Fourth Edition2 Objectives One-Dimensional Arrays Array Initialization Arrays as Function Arguments Case Study: Computing Averages and Standard Deviations Two-Dimensional Arrays Common Programming and Compiler Errors

3. A First Book of ANSI C, Fourth Edition3 Chapter 8 Arrays The variables used so far have all had a common characteristic : each variable can only be used to store a single value at a time. These types of variables are called scalar variables.

4. A First Book of ANSI C, Fourth Edition4 A scalar variable is a single variable whose stored value is an atomic type. This means that the value cannot be further subdivided or separated into a legitimate data type Frequently we may have a set of values, all of the same data type, that form a logical group.

5. A First Book of ANSI C, Fourth Edition5 A simple list consisting of individual items of the same scalar data type is called a single- dimensional array. In this chapter we describe how single- dimensional arrays are declared, initialized, stored inside a computer, and used. We will explore the use of single- dimensional arrays with example programs and present the procedures for declaring and using multidimensional arrays.

6. A First Book of ANSI C, Fourth Edition6 8.1 One Dimensional Arrays A single-dimensional array, which is also referred to as a one-dimensional array, is a list of values of the same data type. To declare that grades is to be used to store five individual integer values requires the declaration statement int grades[5] ;

7. A First Book of ANSI C, Fourth Edition7 Further examples of array declarations are char code[4] ; /* an array of four character codes */ double prices[6] ;/* an array of six double precision prices */ float amount [100] ;/*an array of 100 floating point amounts */

8. A First Book of ANSI C, Fourth Edition8 Each array has sufficient memory reserved for it to hold the number of data items given in the declaration statement. Thus, the array named code has storage reserved for four characters,the prices array has storage reserved for six double precision numbers, and the array named amount has storage reserved for 100 floating point numbers.

9. A First Book of ANSI C, Fourth Edition9 Each item in a list is officially called an element or component of the array. Because each item in the list is stored sequentially, any single item can be accessed by giving the name of the array and the position of the item in the array.

10. A First Book of ANSI C, Fourth Edition10 The element’s position is called its subscript or index value. The first element has a subscript of 0, the second element has subscript of 1, and so on. The subscript gives the number of elements to move over, starting from the beginning of the array, to locate the desired element. In C, the array name and subscript are combined by listing the subscript in square brackets after the array name.

11. A First Book of ANSI C, Fourth Edition11 Introduction (continued)

12. A First Book of ANSI C, Fourth Edition12 Subscripted variables can be used anywhere that scalar variables are valid. Examples using the elements of the grades array are grades [0] = 98 ; grades [1] = grades [0] – 11 grades [2] = 2 * ( grades [0] – 6 ); grades [3] = 79 ; grades [4] = (grades [2] + grades [3] – 3 ) / 2 ; total = grades [0] + grades [1] + grades [2] + grades [3] + grades [4] ;

13. A First Book of ANSI C, Fourth Edition13 The subscript contained within square brackets need not be an integer. Any expression that evaluates to an integer may be used as a subscript. For example, assuming that i and j are integer variables, the following subscripted variables are valid : grades [i] grades [2*i] grades [j-i]

14. A First Book of ANSI C, Fourth Edition14 One extremely important advantage of using integer expressions as subscripts is that it allows sequencing through an array using a for loop. This makes statements such as total = grades[1]+ grades[2]+ grades[3]+ grades[4]+ grades[5] ; unnecessary.

15. A First Book of ANSI C, Fourth Edition15 The subscript value in each of the subscripted variables in this statement can be replaced by the counter in a for loop to access each element in the array sequentially. For example, the code total = 0 ; /* initialize total to zero */ for (i = 0 ; i <= 4 ; ++i ) total = total + grades [i] ;/* add in a grade */ sequentially retrieves each array element and adds the element to the total.

16. A First Book of ANSI C, Fourth Edition16 Here the variable i is used both as the counter in the for loop and as a subscript. As i increases by one each time through the for loop, the next element in the array is referenced. The procedure for adding the array elements within the for loop is the same procedure we have used many times before.

17. A First Book of ANSI C, Fourth Edition17 When an element with a higher value is located, that element becomes the new maximum. maximum = price[0] ; for (i = 1 ; i <= 999 ; ++i) if (price[i] > maximum) maximum = price[i] ;

18. A First Book of ANSI C, Fourth Edition18 Input and Output of Array Values Individual array elements can be assigned values using individual assignment statements or, interactively, using the scanf( ) function.

19. A First Book of ANSI C, Fourth Edition19 Examples of individual data entry statements are price[5] = 10.69 ; scanf (“%d %lf”, &grades[0], &price[2] ) scanf (“%c”, &code[0] ); scanf (“%d %d %d”, &grades[0], &grades[1], &grades[2]);

20. A First Book of ANSI C, Fourth Edition20 Alternatively, a for statement can be used to cycle through the array for interactive data input. For example, the code for (i = 0 ; i <= 4 ; ++i ) { printf (“Enter a grade : ”); scanf (“%d”, &grade[i] ); } prompts the user for five grades. The first grade entered is stored in grades[0], the second in grades[1], and so on until all five grades are entered.

21. A First Book of ANSI C, Fourth Edition21 One caution should be mentioned about storing data in an array. C does not check the value of the index being used. If an array has been declared as consisting of 10 elements, for example, and you use an index of 12, which is outside the bounds of the array, C will not notify you of the error when the program is compiled.

22. A First Book of ANSI C, Fourth Edition22 During output, individual array elements can be displayed using the printf( ) function or complete sections of the array can be displayed by including a printf( ) function call within a for loop. Examples of this are printf (“%lf,” price[6] ); printf (“The value of element %d is %d”, i, grades[i] ); for ( n = 5 ; n <= 20 ; ++n ) printf (“%d %lf”, n, price[n] );

23. A First Book of ANSI C, Fourth Edition23 The first call to printf( ) displays the value of the double precision subscripted variable price[6]. The second call to printf( ) displays the value of i and the value of grades[i]. Before this statement can be executed, i needs to have an assigned value. Finally, the last example includes printf( ) within a for loop. Both the value of the index and the value of the elements from 5 to 20 are displayed.

24. A First Book of ANSI C, Fourth Edition24 Program 8.1 illustrates these input and output techniques using an array named grades that is defined to store five integer numbers. Included in the program are two for loops. The first for loop is used to cycle through each array element and allows the user to input individual array values. After five values have been entered, the second for loop is used to display the stored values.

25. A First Book of ANSI C, Fourth Edition25 Program 8.1 #include int main ( ) { int i, grades[5] ; for (i = 0 ; i <= 4 ; ++i) /* Enter five grades */ { printf (“Enter a grade :”) ; scanf (“%d”, &grades[i] ) ; } for ( i = 0 ; i <= 4 ; ++i ) /* Print five grades */ printf (“\ngrades %d is %d”, i, grades[i] ); return 0 ; }

26. A First Book of ANSI C, Fourth Edition26 In reviewing the output produced by Program 8.1, pay particular attention to the difference between the subscript value displayed and the numerical value stored in the corresponding array element. The subscript value refers to the location of the element in the array, whereas the subscripted variable refers to the value stored in the designed location.

27. A First Book of ANSI C, Fourth Edition27 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 Input and Output of Array Values (continued)

28. A First Book of ANSI C, Fourth Edition28 Program 8.2 #include int main( ) { int i, grades[5], total = 0 ; for (i = 0 ; i <= 4 ; ++i ) /* Enter five grades */ { printf (“Enter a grade : ”) ; scanf (“%d”, &grades[i] ) ; }

29. A First Book of ANSI C, Fourth Edition29 printf (“\nThe total of the grades ”) ; for (i = 0 ; i <= 4 ; ++i) /* Display and total the grades */ { printf (“%d ”, grades[i] ); total += grades[i] ; } printf (“ is %d ”, total ); return 0 ; }

30. A First Book of ANSI C, Fourth Edition30 Following is a sample run using Program 7. 2 : Enter a grade : 85 Enter a grade : 90 Enter a grade : 78 Enter a grade : 75 Enter a grade : 92 The total of the grades 85 90 78 75 92 is 420

31. A First Book of ANSI C, Fourth Edition31 Notice that in Program 8.2, unlike Program 8.1, only the numerical value stored in each array element is displayed and not their subscript values. Although the second for loop was used to accumulate the total of each element, the accumulation could also have been accomplished in the first loop by placing the statement total += grades[i] ; after the scanf( ) call used to enter a value..

32. A First Book of ANSI C, Fourth Edition32 Also notice that the printf( ) call used to display the total made outside of the second for loop so that the total is displayed only once, after all values have been added to the total. If this printf( ) call is placed inside the for loop five totals are displayed, with only the last displayed total containing the sun of all of the array values

33. A First Book of ANSI C, Fourth Edition33 Statement is outside of the second for loop; total is displayed only once, after all values have been added Input and Output of Array Values (continued)

34. A First Book of ANSI C, Fourth Edition34 8.2 Array Initialization Arrays, like scalar variables, can be declared either inside or outside a function. Arrays declared inside a function are local arrays, and arrays declared outside a function are global arrays.

35. A First Book of ANSI C, Fourth Edition35 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 }

36. A First Book of ANSI C, Fourth Edition36 For example, consider the following section of code : int gallons[20] ; /* a global array */ static double dist[25] ; /* a static global array */ void mpg (int) ; /* function prototype */ int main ( ) { int i ; for ( i = 1 ; i <= 10 ; ++i ) mpg (i) ; … return 0 ; }

37. A First Book of ANSI C, Fourth Edition37 void mpg (int carNum) { int miles[15] ; /* an automatic local array */ static double course[15] ; /* a static local array */ … return ; }

38. A First Book of ANSI C, Fourth Edition38 As indicated in the code, both the dist and gallons arrays are globally declared arrays, miles is an automatic local array, and course is a static local array. As with scalar variables, all global arrays and local static arrays are created once, at compilation time, and retain their values until main( ) finishes executing. auto arrays are created and destroyed each time the function they are local to is called. Thus, the dist, gallons, and course arrays are created once, and the miles array is created and destroyed ten times.

39. A First Book of ANSI C, Fourth Edition39 Array elements can be initialized within their declaration statements in the same manner as scalar variables, except that the initializing elements must be included in braces. Examples of such initializations for automatic, static, and global arrays are int grades[5] = { 98, 87, 92, 79, 85 }; char codes[6] = { ‘s’,‘a’,‘m’,‘p’,‘l’,‘e’}; double width[7] = { 10.96, 6.43, 2.58,.86, 5.89, 7.56, 8.22} ; static int temp[4] = {10, 20, 30, 40 } ; static float temp[4] = { 98.6, 97.2, 99.0, 101.5} ;

40. A First Book of ANSI C, Fourth Edition40 Initializers are applied in the order they are written, with the first value used to initialize element 0, the second value used to initialize element 1, and so on, until all values have been used.

41. A First Book of ANSI C, Fourth Edition41 Because white space is ignored in C, initializations may be continued across multiple lines. For example, the declaration int gallons[20]={19,16,14,19,20,18, /* initializing values */ 12,10,22,15,18,17, /* may extend across */ 16,14,23,19,15,18, /* multiple lines */ 21,5 } uses four lines to initialize all of the array elements.

42. A First Book of ANSI C, Fourth Edition42 If the number of initializers is less than the declared number of elements listed in square brackets the initializers are applied starting with array element 0. Thus, in the declaration float length[7] = { 7.8, 6.4, 4.9, 11.2 } ; only length[0], length[1], length[2] and length[3] are initialized with the listed values. The other array elements will be initialized to zero.

43. A First Book of ANSI C, Fourth Edition43 Unfortunately, there is no method to either indicate repetition of an initialization value or initialize later array elements without first specifying values for earlier elements. If no specific initializers are given in the declaration statement, all numerical array elements are set to zero.

44. A First Book of ANSI C, Fourth Edition44 A unique feature of initializers is that the size of an array may be omitted when initializing values are included in the declaration statement. For example, the declaration int gallons[ ] = { 16, 12, 10, 14, 11 } ; reserves enough storage room for five elements. Similarly, the following two declarations are equivalent : char codes[6] = { ‘s’,‘a’,‘m’,‘p’,‘l’,‘e’}; char codes[ ] = { ‘s’,‘a’,‘m’,‘p’,‘l’,‘e’}

45. A First Book of ANSI C, Fourth Edition45 Both of these declarations set aside six character locations for an array named codes. An interesting and useful simplification can also be used when initializing character arrays. For example, the declaration char codes[ ] = “sample”; /* no braces or commas */ uses the string “sample” to initialize the codes array.

46. A First Book of ANSI C, Fourth Edition46 Recall that a string is any sequence of characters enclosed in double quotes. This last declaration creates an array named codes having seven elements and fills the array with the seven characters illustrated in Figure 8.6. The first six characters, as expected, consist of the letters s, a, m, p, l, and e. The last character, which is the escape sequence \0, is called the null character.

47. A First Book of ANSI C, Fourth Edition47 codes[0]codes[1]codes[2]codes[3]codes[4]codes[5]codes[6] sample\0 The null character is automatically appended to all strings by the C compiler.

48. A First Book of ANSI C, Fourth Edition48 Array Initialization (continued)

49. A First Book of ANSI C, Fourth Edition49 Array Initialization (continued)

50. A First Book of ANSI C, Fourth Edition50 8.3 Arrays as Function Arguments Individual array elements are passed to a function by simply including them as subscripted variables in the function call argument list. For example, the function call findMin (grades[2], grades[6] ) ; passes the values of the elements grades[2] and grades[6] to the function findMin ( ).

51. A First Book of ANSI C, Fourth Edition51 Passing a complete array to a function is in many respects an easier operation than passing individual elements. The called function receives access to the actual array, rather than a copy of the values in the array. For example, if grades is an array, the function call findMax (grades) ; makes the complete grades array available to the findMax ( ) function. This is different from passing a single variable to a function.

52. A First Book of ANSI C, Fourth Edition52 Recall that when a single scalar argument is passed to a function, the called function receives only a copy of the passed value, which is stored in one of the function’s value parameters. If arrays were passed in this manner, a copy of the complete array would have to be created. For large arrays, making duplicate copies of the array for each function call would waste computer storage, consume execution time, and frustrate the effort to return multiple element changes made by the called program.

53. A First Book of ANSI C, Fourth Edition53 To avoid these problems, the called function is given direct access to the original array. Thus, any changes made by the called function are made directly to the array itself. For the following specific examples of function calls, assume that the arrays nums, keys, units, and prices are declared as : int nums[5] ; char keys[256] ; double units[500],prices[500] ;

54. A First Book of ANSI C, Fourth Edition54 For these arrays, the following function calls can be made : findMax(nums) ; findCh(keys) ; calcTot(nums, units, prices) ; In each case, the called function receives direct access to the named array.

55. A First Book of ANSI C, Fourth Edition55 On the receiving side, the called function must be alerted that an array is being made available. For example, suitable function headers for the previous functions are int findMax (int vals[5]) char findCh (chr inKeys[256]) void calcTot (int arrl[5], double arr2[500], double arr3[500])

56. A First Book of ANSI C, Fourth Edition56 In each of these function declarations, the names in the parameter list are chosen by the programmer and are local to the function. However, the internal local names used by the functions still refer to the original array created outside the function. This is made clear in Program 8.4.

57. A First Book of ANSI C, Fourth Edition57 Program 8.4 #include void findMax (int [5]) ; /* function prototype */ int main( ) { int nums[5] = { 2, 18, 1, 27, 16} ; findMax (nums) ; return 0 ; }

58. A First Book of ANSI C, Fourth Edition58 void findMax(int vals[5]) /* find the maximum value */ { int i, max = vals[0] ; for ( i = 1 ; i <= 4 ; ++i ) if (max < vals[i]) max = vals[i] ; printf (“The maximum value is %d”, max ); return ; }

59. A First Book of ANSI C, Fourth Edition59 Size can be omitted Arrays as Function Arguments (continued)

60. A First Book of ANSI C, Fourth Edition60 Since only one item is passed to findMax, the number of elements in the array need not be included in the declaration for vals. In fact, it is generally advisable to omit the size of the array in the function header line. For example, consider the more general form of findMax ( ), which can be used to find the maximum value of an integer array of arbitrary size.

61. A First Book of ANSI C, Fourth Edition61 int findMax(int vals[ ], int numEls ) /* find the maximum value */ { int i, max = vals[0] ; for ( i = 1 ; i < numEls ; ++i ) if (max < vals[i]) max = vals[i] ; return(max) ; }

62. A First Book of ANSI C, Fourth Edition62 The more general form of findMax( ) declares that the function returns an integer value. The function expects the starting address of an integer array and the number of elements in the array as arguments. Then, using the number of elements as the boundary for its search, the function’s for loop causes each array element to be examined in sequential order to locate the maximum value. Program 8.5 illustrates the use of findMax( ) in a complete program.

63. A First Book of ANSI C, Fourth Edition63 Program 8.5 #include int findMax(int [ ], int); /* function prototype */ int main( ) { int nums[5] = { 2, 18, 1, 27, 16} ; printf (“The maximum value is %d”, findMax(nums,5)) ; return 0 ; }

64. A First Book of ANSI C, Fourth Edition64 int findMax(int vals[ ], int numEls) { int i, max = vals[0] ; for (i = 1 ; i < numEls ; ++i) if (max < vals[i]) max = vals[i] ; return(max) ; } The output displayed when Program 8. 5 is executed is The maximum value is 27

65. A First Book of ANSI C, Fourth Edition65 Arrays as Function Arguments (continued)

66. A First Book of ANSI C, Fourth Edition66 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

67. A First Book of ANSI C, Fourth Edition67 Write the Functions

68. A First Book of ANSI C, Fourth Edition68 Write the Functions (continued)

69. A First Book of ANSI C, Fourth Edition69 8.5 Two-Dimensional Arrays A two-Dimensional array, which is sometimes referred to as a table, consists of both rows and columns of elements. For example, the array of numbers is a two-dimensional array of integers. 816952 315276 1425210

70. A First Book of ANSI C, Fourth Edition70 This array consists of three rows and four columns. To reserve storage for this array, both the number of rows and the number of columns must be included in the array’s declaration.

71. A First Book of ANSI C, Fourth Edition71 Calling the array val, the appropriate declaration for this two-dimensional array is int val[3] [4] ; Similarly, the declarations double prices[10] [5] ; char code[6] [26] ; declare that the array prices consists of 10 rows and 5 columns of double precision numbers and that the array code consists of 6 rows and 26 columns of characters.

72. A First Book of ANSI C, Fourth Edition72 Each element in a two-dimensional array is located by identifying its position in the array. As illustrated in Figure 8.9, the term val[1] [3] uniquely identifies the element in row 1, column 3. As with single-dimensional array variables, double-dimensional array variables can be used anywhere that scalar variables are valid.

73. A First Book of ANSI C, Fourth Edition73 Two-Dimensional Arrays (continued)

74. A First Book of ANSI C, Fourth Edition74 As with single-dimensional arrays, double-dimensional arrays can be initialized from within their declaration statements. This is done by listing the initial values within braces and separating them by commas. Additionally, braces can be used to separate individual rows.

75. A First Book of ANSI C, Fourth Edition75 For example, the declaration int val[3][4] = { { 8, 16, 9, 52 }, { 3, 15, 27, 6 }, { 14, 25, 2, 10 } } ; declares val to be an array of integers with three rows and four columns, with the initial values given in the declaration. The first set of internal braces contains the values for row 0 of the array, the second set of internal braces contains the values for row 1, and the third set of braces the values for row 2.

76. A First Book of ANSI C, Fourth Edition76 Although the commas in the initialization braces are always required, the inner braces can be omitted. Thus, the initialization for val may be written as int val[3][4] = { 8, 16, 9, 52, 3, 15, 27, 6, 14, 25, 2, 10 } ;

77. A First Book of ANSI C, Fourth Edition77 As with single-dimensional arrays, double- dimensional arrays may be displayed by individual element notation or by using loops. This is illustrated by Program 8.7, which displays all the elements of a three-by-four two-dimensional array using two different techniques.

78. A First Book of ANSI C, Fourth Edition78 Program 8.7 #include int main( ) { int i, j, val[3][4] = { 8, 16, 9, 52, 3, 15, 27, 6, 14, 25, 2, 10} printf(“\nDisplay of val array by explicit element”); printf(“\n%2d %2d %2d %2d”, val[0][0], val[0][1], val[0][2], val[0][3]) ; printf(“\n%2d %2d %2d %2d”, val[1][0], val[1][1], val[1][2],val[1][3]) ; printf(“\n%2d %2d %2d %2d”, val[2][0], val[2][1], val[2][2],val[2][3]) ;

79. A First Book of ANSI C, Fourth Edition79 printf(“\nDisplay of val array using a nested for loop”) ; for ( i = 0 ; i < 3 ; ++i ) { printf(“\n”) ; /* start a new line for each row */ for (j = 0 ; j < 4 ; ++j ) printf(“%2d ”, val[i][j]) ; } return 0 ; }

80. A First Book of ANSI C, Fourth Edition80 The display produced by Program 8.7 is Display of val array by explicit element 8 16 9 52 3 15 27 6 14 25 2 10 Display of val array using a nested for loop 8 16 9 52 3 15 27 6 14 25 2 10

81. A First Book of ANSI C, Fourth Edition81 Two-Dimensional Arrays (continued)

82. A First Book of ANSI C, Fourth Edition82 The first display of the val array produced by Program 8.7 is constructed by explicitly designating each array element. The second display of array element values, which is identical to the first, is produced using a nested for loop. Nested loops are especially useful when dealing with two-dimensional arrays because they allow the programmer to easily designate and cycle through each element.

83. A First Book of ANSI C, Fourth Edition83 In Program 8.7, the variable i controls the outer loop and the variable j controls the inner loop. Each pass through the outer loop corresponds to a single row, with the inner loop supplying the appropriate column elements. After a complete row is printed a new line is started for the next row. The effect is a display of the array in a row- by-row fashion.

84. A First Book of ANSI C, Fourth Edition84 Once two-dimensional array elements have been assigned, array processing can begin. Typically, for loops are used to process two- dimensional arrays because, as previously noted, they allow the programmer to easily designate and cycle through each array element. For example, the nested for loop in Program 8.8 is used to multiply each element in the val array by the scalar number 10 and display the resulting value.

85. A First Book of ANSI C, Fourth Edition85 Program 8.8 #include int main( ) { int i, j, val[3][4] = { 8,16,9,52, 3,15,27,6, 14,25,2,10} ; /* multiply each element by 10 and display it */ printf (“\nDisplay of multiplied elements\n”) ;

86. A First Book of ANSI C, Fourth Edition86 for ( i = 0 ; i < 3 ; ++i ) { printf(“\n”) ; /* start a new line */ for ( j = 0 ; j < 4 ; ++j ) { val[i][j] = val[i][j] * 10 ; printf (“%3d ”, val[i][j] ) ; } /* end of inner loop */ } /* end of outer loop */ return 0 ; }

87. A First Book of ANSI C, Fourth Edition87 Two-Dimensional Arrays (continued)

88. A First Book of ANSI C, Fourth Edition88 Passing two-dimensional arrays into functions is a process identical to passing one-dimensional arrays. The called function receives access to the entire array. For example, the function call display(val) ; makes the complete val array available to the function named display( ). Thus, any changes made by display( ) are made directly to the val array.

89. A First Book of ANSI C, Fourth Edition89 If the array is a global one, there is no need to pass the array because the function could access the array by its global name. Program 8.9 illustrates passing a local, two- dimensional array into a function that displays the array’s values.

90. A First Book of ANSI C, Fourth Edition90 Program 8.9 #include void display(int [3][4]) ; /* function prototype */ int main( ) { int val[3][4] = { 8,16,9,52, 3,15,27,6, 14,25,2,10} ; display(val) ; return 0 ; }

91. A First Book of ANSI C, Fourth Edition91 void display(int nums[3][4]) { int rowNum, colNum ; for (rowNum = 0 ; rowNum < 3 ; ++rowNum) { for(colNum = 0 ; rowNum < 4 ; ++rowNum) printf(“%4d”, nums[rowNum][colNum]) ; printf(“\n”) ; } return ; }

92. A First Book of ANSI C, Fourth Edition92 Only one array is created in Program 8.9. This array is known as val in main( ) and as nums in display ( ). Thus, val[0][2] refers to the same element as nums[0][2]. Notice the use of the nested for loop in Program 8.9. Nested for statements are especially useful when dealing with multidimensional arrays because they allow the programmer to cycle through each element.

93. A First Book of ANSI C, Fourth Edition93 In Program 8.9, the variable rowNum controls the outer loop and the variable colNum controls the inner loop. For each pass through the outer loop, which corresponds to a row, the inner loop makes one pass through the column elements. After a complete row is printed, the \n escape sequence causes a new line to be started for the next row.

94. A First Book of ANSI C, Fourth Edition94 The effect is a display of the array in a row-by-row fashion : 8 16 9 52 3 15 27 6 14 25 2 10

95. A First Book of ANSI C, Fourth Edition95 Row size can be omitted Two-Dimensional Arrays (continued)

96. A First Book of ANSI C, Fourth Edition96 Internal Array Element Location Algorithm (continued)

97. A First Book of ANSI C, Fourth Edition97 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

98. A First Book of ANSI C, Fourth Edition98 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

99. A First Book of ANSI C, Fourth Edition99 Common Compiler Errors

100. A First Book of ANSI C, Fourth Edition100 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

101. A First Book of ANSI C, Fourth Edition101 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