1. Multi-Dimensional Arrays

2. A Table of Values Balances for Various Interest Rates Compounded Annually (Rounded to Whole Dollar Amounts) Year5.00%5.50%6.00% 1$1050$1055$1060 2$1103$1113$1124 3$1158$1174$1191

3. Row and Column Indices for an Array Indices012 0$1050$1055$1060 1$1103$1113$1124 2$1158$1174$1191

4. Multi-Dimensional Array Basics  We declare a variable, table, to be a two- dimensional array as follows: int [][] table = new int [10][6];  This is the same as for one-dimensional arrays except we use a second pair of square brackets in two places.  You can have arrays of any number of dimensions.

5. Multi-Dimensional Array Basics (cont’d)  In a two-dimensional array we consider the first index to represent the row number and the second to represent the column.  As was true of the indexed variables for one-dimensional arrays, indexed variables of multi-dimensional arrays are variables of the base type and can be used anyplace that a variable of the base type is allowed.

6. Example of Using a Two- Dimensional Array /** Displays a two-dimensional table showing how interest rates affect bank balances. */ public class InterestTable { public static void main(String[] args) { int[][] table = new int[10][6]; int row, column; for (row = 0; row < 10; row++) for (column = 0; column < 6; column++) table[row][column] = balance(1000.00, row + 1, (5 + 0.5*column)); System.out.println("Balances for Various Interest Rates"); System.out.println("Compounded Annually"); System.out.println("(Rounded to Whole Dollar Amounts)"); System.out.println("Years 5.00% 5.50% 6.00% 6.50% 7.00% 7.50%"); System.out.println( ); for (row = 0; row < 10; row++) { System.out.print((row + 1) + " "); for (column = 0; column < 6; column++) System.out.print("$" + table[row][column] + " "); System.out.println( ); } }

7. Example of Using a Two- Dimensional Array (cont’d) /** Returns the balance in an account that starts with startBalance and is left for the indicated number of years with rate as the interest rate. Interest is compounded annually. The balance is rounded to a whole number. */ public static int balance(double startBalance, int years, double rate) { double runningBalance = startBalance; int count; for (count = 1; count <= years; count++) runningBalance = runningBalance*(1 + rate/100); return (int) (Math.round(runningBalance)); } }

8. Multi-Dimensional Array Parameters and Returned Values  Methods may have multi-dimensional array parameters and may return a multi- dimensional array.  The situation is similar to that of the one- dimensional case, except that you use more square brackets.

9. Example Using a Multi- Dimensional Array Parameter /** Displays a two-dimensional table showing how interest rates affect bank balances. */ public class InterestTable2 { public static void main(String[] args) { int[][] table = new int[10][6]; int row, column; for (row = 0; row < 10; row++) for (column = 0; column < 6; column++) table[row][column] = balance(1000.00, row + 1, (5 + 0.5*column)); System.out.println("Balances for Various Interest Rates"); System.out.println("Compounded Annually"); System.out.println("(Rounded to Whole Dollar Amounts)"); System.out.println("Years 5.00% 5.50% 6.00% 6.50% 7.00% 7.50%"); System.out.println( ); showTable(table); }

10. Example Using a Multi- Dimensional Array Parameter (cont’d) /** Precondition: The array displayArray has 10 rows and 6 columns. Postcondition: The array contents are displayed with dollar signs. */ public static void showTable(int[][] displayArray) { int row, column; for (row = 0; row < 10; row++) { System.out.print((row + 1) + " "); for (column = 0; column < 6; column++) System.out.print("$" + displayArray[row][column] + " "); System.out.println( ); } } public static int balance(double startBalance, int years, double rate) { double runningBalance = startBalance; int count; for (count = 1; count <= years; count++) runningBalance = runningBalance*(1 + rate/100); return (int) (Math.round(runningBalance)); } }

11. Implementation of Multi- Dimensional Arrays  In Java, multi-dimensional arrays are implemented using one-dimensional arrays.  The array table declared as follows: int [][] table = new int[10][6]; is a one-dimensional array of length 10 whose elements are one-dimensional arrays of length 6.  In other words, multi-dimensional arrays are arrays of arrays.

12. The Method showTable Redefined /** The array displayArray can have any dimensions. Postcondition: The array contents are displayed with dollar signs. */ public static void showTable(int[][] displayArray) { int row, column; for (row = 0; row < displayArray.length; row++) { System.out.print((row + 1) + " "); for (column = 0; column < displayArray[row].length; column++) System.out.print("$" + displayArray[row][column] + " "); System.out.println( ); } }

13. Programming Example Using Multi-Dimensional Arrays /** Class for a one-week record of the time worked by each employee. Uses a five-day week (Mon.-Fri.). main has a sample application. */ public class TimeBook { private int numberOfEmployees; private int[][] hours; //hours[i][j] has the hours for employee j on day i. private int[] weekHours; //weekHours[i] has the week’s hours worked for //employee i+1. private int[] dayHours; //dayHours[i] has the total hours worked by all //employees on day i. Monday is 0, Tuesday 1, etc. /** Reads hours worked for each employee on each day of the week into the two-dimensional array hours. (The method for input is just a stub in this preliminary version.) Computes the total weekly hours for each employee and the total daily hours for all employees combined. */ public static void main(String[] args) { TimeBook book = new TimeBook(3); book.setHours( ); book.update( ); book.showTable( ); }

14. Programming Example Using Multi-Dimensional Arrays (cont’d) public TimeBook(int theNumberOfEmployees) { numberOfEmployees = theNumberOfEmployees; hours = new int[5][numberOfEmployees]; //the 5 is for the 5 days Monday through Friday. weekHours = new int[numberOfEmployees]; dayHours = new int[5]; } public void setHours( ) //This is just a stub. { hours[0][0] = 8; hours[0][1] = 0; hours[0][2] = 9; hours[1][0] = 8; hours[1][1] = 0; hours[1][2] = 9; hours[2][0] = 8; hours[2][1] = 8; hours[2][2] = 8; hours[3][0] = 8; hours[3][1] = 8; hours[3][2] = 4; hours[4][0] = 8; hours[4][1] = 8; hours[4][2] = 8; } public void update( ) { computeWeekHours( ); computeDayHours( ); }

15. Programming Example Using Multi-Dimensional Arrays (cont’d) private void computeWeekHours( ) { int dayNumber, employeeNumber, sum; for (employeeNumber = 1; employeeNumber <= numberOfEmployees; employeeNumber++) {//Process one employee: sum = 0; for(dayNumber = 0; dayNumber < 5; dayNumber++) sum = sum + hours[dayNumber][employeeNumber - 1]; //sum contains the sum of all the hours worked //in one week by employee with number employeeNumber. weekHours[employeeNumber - 1] = sum; } } private void computeDayHours( ) { int dayNumber, employeeNumber, sum; for (dayNumber = 0; dayNumber < 5; dayNumber++) {//Process one day (for all employees): sum = 0; for (employeeNumber = 1; employeeNumber <= numberOfEmployees; employeeNumber++) sum = sum + hours[dayNumber][employeeNumber - 1]; //sum contains the sum of all hours worked by all //employees on day dayNumber. dayHours[dayNumber] = sum; } }

16. Programming Example Using Multi-Dimensional Arrays (cont’d) public void showTable( ) { int row, column; System.out.print("Employee "); for (column = 0; column < numberOfEmployees; column++) System.out.print((column + 1) + " "); System.out.println("Totals"); System.out.println( ); for (row = 0; row < 5; row++) { System.out.print(day(row) + " "); for (column = 0; column < hours[row].length; column++) System.out.print(hours[row][column] + " "); System.out.println(dayHours[row]); } System.out.println( ); System.out.print("Total = "); for (column = 0; column < numberOfEmployees; column++) System.out.print(weekHours[column] + " "); System.out.println( ); }

17. Programming Example Using Multi-Dimensional Arrays (cont’d) //Converts 0 to "Monday", 1 to "Tuesday" etc. //Blanks used to make all strings the same length. private String day(int dayNumber) { String dayName = null; switch (dayNumber) { case 0: dayName = "Monday "; break; case 1: dayName = "Tuesday "; break; case 2: dayName = "Wednesday"; break; case 3: dayName = "Thursday "; break; case 4: dayName = "Friday "; break; default: System.out.println("Fatal Error."); System.exit(0); break; } return dayName; } }