C for Engineers and Scientists: An Interpretive Approach. Chapter 10: Arrays

Transcription

1 Chapter 10: Arrays

2 10.1 Declaration of Arrays 10.2 How arrays are stored in memory One dimensional (1D) array type name[expr]; type is a data type, e.g. int, char, float name is a valid identifier (cannot start w/digit!) expr is an expression that evaluates to an integer type Cannot involve variables! Can involve calculations of constants, e.g. 4x10 The value of expr is the number of elements in the array. For example, int a[6]; declares a one-dimensional array named a. The data type of each array element is int. Array a has 6 elements from a[0] to a[5]. a[6] is a big (although common) mistake!

3 How 1D Arrays are Stored in Memory An array is a group of consecutive memory locations. All the elements of an array have the same name and data type. Example1: int a[6]; This 1D array a has six elements. The data type of each array element is int. Array a occupies 24 consecutive bytes in memory The elements of an array can be referred as name[position_number] First element at position 0. In our example, the elements of array a can be referred to as a[0], a[1], a[2], a[3], a[4], a[5]. a.k.a. index

4 How array elements are referenced in a program int i, a[6]; a[0] = 10; a[5] = 2*a[0]; i = a[0] + a[5];

5 Two-dimensional (2D) arrays type name[expr1][expr2]; expr1 and expr2 evaluate to an integral type The value of expr1 is the # of rows and the value of expr2 is the # of columns of the array Example: int a[2][3]; declares a two-dimensional array. Array a has 2 rows and 3 columns, for a total of 6 elements.

6 Example2: int b[2][3]; Array b has six elements (2x3) with 2 horizontal rows and 3 vertical columns. From a programming point of view, it is a block of memory with each row of the array lying in a contiguous block of memory as show below. The elements of a two-dimensional array can be referred to like this: arrayname[row_index][column_index]

7 How 2D arrays are stored in memory int b[2][3]; Abstract matrix view Storage by rows

8 FYI only: Definitions Related to Arrays The number of dimensions in an array is the rank of the array. The number of elements in each dimension is the extent in the corresponding dimension of the array. The shape of an array is a vector where each element of the vector is the extent in the corresponding dimension of the array. The size of an array is the total number of bytes used to store the array. Example: int a[3][4]; The rank of array a is 2 The extents corresponding to the first and second dimensions are 3 and 4, respectively. The shape of the array is a vector with two elements 3 and 4 as [3, 4] The size of the array is sizeof(int)*3*4 = 4*3*4=48 bytes.

9 Size of an array The sizeof operator can be used to determine the size of an array (as for scalar data, in bytes) int a[6]; sizeof(a); //24 int c[3][4]; sizeof(c); //48 double d[3][4]; sizeof(d); //96 char c[6]; sizeof(c); //6

10 10.3 Initialization of Arrays Initializing 1D arrays 1. int a[5] = {1, 2, 3, 4, 5}; If not enough initializers, rightmost elements become 0 If too many, syntax error 2. int a[5] = {0}; All elements 0 3. int a[] = {1, 2, 3, 4, 5}; The size is omitted, initializers determine it 5 initializers, therefore, five-element array The size of array a is 20 bytes. 4. char str1[] = Hello"; null character '\0' terminates strings str1 actually has 6 elements 5. char str1[] = { H', e', l', l', o', '\0' };

11 Initializing 2D arrays 1. int a[2][2] = {{1, 2 }, { 3, 4 } }; Initializers grouped by row in braces a[0][0] = 1, a[0][1] = 2, a[1][0] = 3, a[1][1] = 4 2. int b[2][2] = {{1}, {3, 4 } }; If not enough, unspecified elements set to zero b[0][0] = 1, b[0][1] = 0, b[1][0] = 3, b[1][1] = 4 3. int c[2][2] = {1, 2, 3, 4}; c[0][0] = 1, c[0][1] = 2, c[1][0] = 3, c[1][1] = 4

12 10.4 Processing Data in Arrays The great secret: arrays and for loops were created for each other

13 Basic array-processing task #1: Generate evenly spaced data for an array Task: Fill an array x with N elements distributed evenly between x 0 and x f (endpoints included) Essential question: What is the distance between two consecutive elements? Hint: (N-1) of these distances equal the entire interval. step = (xf-x0)/(n-1); What data type would you pick for step?

14 Basic array-processing task #1: Generate evenly spaced data for an array Obviously, x[0] is x 0 Each other array element can be found by adding the required # of steps: x[i] = x0 + i*(xf-x0)/(n-1); Notes: Because the array indices start at 0, the # of steps is simply equal to the index i. In languages that use 1 for the first index of arrays (e.g. FORTRAN), we d have to use (i-1) in the formula above.

15 Basic array-processing task #1: Generate evenly spaced data for an array Final code #define N 100; double x[n]; for(i = 0; i < N; i++) { x[i] = x0 + i*(xf-x0)/(n-1); } See complete program 10.1/300

16 This is all the material for Friday s test Stop on p.301, before Mean Review in lab this afternoon

17 Let s start reviewing right now! Write a short program that creates an array of 10 integers, initialized with the first 10 prime numbers, then prints all its elements.