Lab #10 Multi-dimensional Arrays

Transcription

1 Multi-dimensional Arrays Sheet s Owner Student ID Name Signature Group partner 1. Two-Dimensional Arrays Arrays that we have seen and used so far are one dimensional arrays, where each element is indexed by a single integer. C# allows programmers to create and use multi-dimensional arrays, meaning that each of their elements is indexed by a fixed number of integers (e.g., two, three or four). However, two-dimensional arrays are the most common. In this case, the array looks like a table that can store multiple items rather than just a single row of items. Consider the two arrays: (a) One-dimensional array of size (b) Two-dimensional array of size 3x4 The array on the left is considered a one-dimensional array, so its elements are indexed by a single integer. For instance, the element with index 2 has the value of 57. In contrast, the array on the right is a two-dimensional array which requires a pair of integers to index an element. For example, the element with index (1,3) has the value of 10, and the element with index (2,4) has the value of 21. A two-dimensional array can be declared as follows: DataType [,] ArrayName ; where ArrayName is the name of the array, and DataType is the data type of each array element. Similar to one-dimensional arrays, two-dimensional arrays must be initialized to a specified size after the declaration prior to their use, as shown in the following syntax. ArrayName = new DataType [ M, N]; The above statement will create a two-dimensional array of type DataType with M N items. However, the value of each item is not specified. Example 1.1: Declare an array, students, which stores students names in accordance with their seats (row, column) in a class. Then initialize it for storing 5 3 students. string [,] students ; students = new string [5,3]; or string [,] students = new string [5,3];

2 We can also initialize a two-dimensional array using bracketed lists of values as follows: ArrayName = new DataType [ M, N] { { value (0,0), value (0,1),..., value (0,N -1), { value (1,0), value (1,1),..., value (1,N -1), : : : { value (M -1,0), value (M -1,1),..., value (M -1,N -1) ; or simply ArrayName = { { value (0,0), value (0,1),..., value (0,N -1), { value (1,0), value (1,1),..., value (1,N -1), : : : { value (M -1,0), value (M -1,1),..., value (M -1,N -1) ; Example 1.2: Create an array of integers, called A, to represent a 4 3 matrix with the following members A = int [,] A = new int [4,3] { { 5, 3, 8, { 2, 6, 10, { 1, 8, 25, {12, 3, 30 Unlike one dimensional arrays, each element in a two-dimensional array must be referenced using two integers. For example, to access an element located at row R and column C, we can use: ArrayName [R,C] Example 1.3: Consider the matrix A used in Example 1.2. Display the value of the element A[3, 2] (i.e., a 3,2 ) Console. WriteLine (A [2,1]); Note: The reason A[2,1] is used instead of A[3,2] is due to the fact that array indices (both row and column) start at 0, while row and column indices of a matrix start at 1. Assign the value 33 to the element A[4, 3] A [3,2] = 33;

3 Initialize all the elements in the first column of matrix A to 1 for ( int i = 0; i < 4; i ++) A[i,0] = 1; Make the matrix A a zero matrix for ( int i = 0; i < 4; i ++) for ( int j = 0; i < 3; j ++) A[i,j] = 0; following program in SharpDevelop then answer the ques- Exercise 1.1: Typethe tions 1 using System ; 2 class Matrix { 3 public static void Main () { 4 int i, j; 5 int [,] A = new int [4,3] { 6 { 5, 3, 8, 7 { 2, 6, 10, 8 { 1, 8, 25, 9 {12, 3, ; for (i = 0; i < 4; i ++) { 13 for (j = 0; j < 3; j ++) { 14 Console. Write (" {0,4 ", A[i,j ]); Console. WriteLine (); What is the output of the program?

4 What is the output of the program when line 14 is changed to Console.Write("{0", A[i,j]); instead? Exercise 1.2: Write a program to read a matrix from the user, then display the entire matrix on the screen. The size of the matrix is also specified by the user. using System ; class Matrix { public static void Main () { int i, j; int nrow, ncol ; int [,] A; Console. Write (" Enter number of rows : "); nrow = int. Parse ( Console. ReadLine ()); Console. Write (" Enter number of columns : "); ncol = int. Parse ( Console. ReadLine ()); A = new int[ (a), (b) ]; for ( i = 0; i < nrow ; i ++) Console. Write (" Enter A [{0,{1]: ", i+1, j +1); (c) = int. Parse ( Console. ReadLine ()); Console. WriteLine (" Matrix A is"); for (i = 0; i < nrow ; i ++) { Console. Write (" {0,4 ", (d) ); (e)

5 Position (a) Expression/Statement (b) (c) (d) (e) Enter number of rows: 2 Enter number of columns: 3 Enter A[1,1]: 10 Enter A[1,2]: 4 Enter A[1,3]: 22 Enter A[2,1]: 65 Enter A[2,2]: 34 Enter A[2,3]: 18 Matrix A is Exercise 1.3: Enhance the program used in Exercise 1.2 so that it now also outputs the transpose of A. Write the extended part in the box provided.

6 Enter number of rows: 3 Enter number of columns: 2 Enter A[1,1]: 1 Enter A[1,2]: 2 Enter A[2,1]: 3 Enter A[2,2]: 4 Enter A[3,1]: 5 Enter A[3,2]: 6 Matrix A is Transpose of matrix A is Exercise 1.4: The following (incomplete) program intends to take two matrices from the user. Then perform an addition operation on the two matrices and display the result. Complete the program by filling in an appropriate expression/statement for each of the positions marked as(a) (g). using System ; class Matrix { public static void Main () { int i, j; int nrow, ncol ; int [,] A; int [,] B; Console. Write (" Enter number of rows : "); nrow = int. Parse ( Console. ReadLine ()); Console. Write (" Enter number of columns : "); ncol = int. Parse ( Console. ReadLine ()); A = new int[ (a), (b) ]; for ( i = 0; i < nrow ; i ++) Console. Write (" Enter A [{0,{1]: ", i+1, j +1); (c) = int. Parse ( Console. ReadLine ()); B = new int[ (d), (e) ]; for ( i = 0; i < nrow ; i ++) Console. Write (" Enter B [{0,{1]: ", i+1, j +1); (f) = int. Parse ( Console. ReadLine ());

7 Console. WriteLine (" Matrix A+B is"); for (i = 0; i < nrow ; i ++) { Console. Write (" {0,4 ", (g) ); Console. WriteLine (); Enter number of rows: 2 Enter number of columns: 2 Enter A[1,1]: 1 Enter A[1,2]: 2 Enter A[2,1]: 3 Enter A[2,2]: 4 Enter A[1,1]: 5 Enter A[1,2]: 6 Enter A[2,1]: 7 Enter A[2,2]: 8 Matrix A+B is Position (a) Expression/Statement (b) (c) (d) (e) (f) (g)

8 2. Programming Exercises Task 2.1: Write a program to find the determinant of a 2 2 matrix. Hint. For a matrix A = (a i,j ) 2 2, its determinant is defined as: Enter A[1,1]: 1 Enter A[1,2]: 2 Enter A[2,1]: 3 Enter A[2,2]: 4 The determinant of A is -2 det(a) = (a 11 a 22 a 12 a 21 )

9 Task 2.2: Write a program to multiply two 2 2 matrices and display the result. Note that if C m o = A m n B n o, then: Enter A[1,1]: 1 Enter A[1,2]: 2 Enter A[2,1]: 3 Enter A[2,2]: 4 Enter B[1,1]: 5 Enter B[1,2]: 6 Enter B[2,1]: 7 Enter B[2,2]: 8 Matrix A*B is: c ij = n k=1 a ik b kj