Apple II Print I,J Next Next J, Matrix Operations, Sort Program, Input AI, Print AI, Subroutines

10 FOR I=1 TO 5

20 FOR J=1 TO 3

30 PRINT I,J

40 NEXT I

50 NEXT J

It does not work because when the "NEXT I" is encountered, all knowledge of the J-loop is lost. This happens because the J-loop is "inside" the I-loop.

209 MATRIX OPERATIONS

It is often convenient to be able to select any element in a table of numbers. BASIC allows this to be done through the use of matrices.

A matrix is a table of numbers. The name of this table (the matrix name) is any legal variable name, "A" for example. The matrix name "A" is distinct and separate from the simple variable "A," and

you could use both in the same program.

To select an element of the table, we subscript "A": that is, to select the I'th element, we enclose I in parentheses "(I)" and then follow "A" by this subscript. Therefore, "A(I)" is the I'th element in the matrix "A."

"A(1)" is only one element of matrix A, and BASIC must be told how much space so allocate for the entire matrix. This is done with a "DIM" statement, using the format "DIM A(15)." In this case, we have reserved space for the matrix index "I" to go from 0 to 15. Matrix subscripts always start as 0; therefore, in the above example, we have allowed for 16 numbers in matrix A.

If "A(1)" is used in a program before is has been dimensioned, BASIC reserves space for 11 elements (0 through 10).

A SORT PROGRAM

As an example of how matrices are used, try the following program so sort a list of 8 numbers, in which you pick the numbers to be sorted:

10	DIM A(8)	110	A(I)=A(I+1)
20	FOR I=1 TO 8	120	A(I+1)=T
30	INPUT A(I)	130	F=1
50	NEXT I	140	NEXT I
70	F=0	150	IF F=1 THEN 70
80	FOR I=1 TO 7	160	FOR I=1 TO 8
90	IF A(I)<=A(I+1) THEN 140	170	PRINT A(I)
100	T=A(I)	180	NEXT I

When line 10 is executed, BASIC

sets

aside

space for

9 numeric values, A(0) through A(8).

Lines 20

through 50

get the unsorted

list from

the user. The

sorting

itself is

done

by going through

the list of numbers

and switching any

two that

are not in order.

"F"

is used to indicate if any

switches

were made;

if any were

made,

line

150

tells

BASIC to

go

back

and check

some

more.

If we did not switch any numbers, or after they are all in order, lines 160 through 180 will print out the sorted list. Note that a subscript can be any expression.

210 SUBROUTINES

If you have a program that performs the same action in several different places, you could duplicate the same statements for the action in each place within the program.

The "GOSUB" and "RETURN" statements can be used to avoid this duplication. When a "GOSUB" is encountered, BASIC branches to the line whose number follows the "GOSUB." However, BASIC remembers where it was in the program before it branches. When the "RETURN" statement is encountered, BASIC goes back to the first statement following the last "GOSUB" that was executed. Observe the following program:

10 PRINT "WHAT IS THE NUMBER";

30 GOSUB 100

40 T=N

50 PRINT "SECOND NUMBER";

70 GOSUB 100

80 PRINT "THE SUM IS"; T+N

90 STOP