Part 4
Looping

Subjects covered...

	FOR, NEXT
	TO, STEP

Suppose you wish to input five numbers and add them together.

One way (don't type this in unless you are feeling dutiful) [like me]
is as follows...

	 10 LET total=0
	 20 INPUT a
	 30 LET total=total+a
	 40 INPUT a
	 50 LET total=total+a
	 60 INPUT a
	 70 LET total=total+a
	 80 INPUT a
	 90 LET total=total+a
	100 INPUT a
	110 LET total=total+a
	120 PRINT total

This method is not good programming practice. It may be just about
controllable for five numbers, but you can imagine how tedious a
program like this to add twenty numbers would be, and to add a hundred
or more would be out of the question.

Much better is to set up a variable to count up to 5 and then stop the
program, like this (which you should type in)...

	10 LET total=0
	20 LET count=1
	30 INPUT a
	40 REM count is number of times that a has been input so far
	50 LET total=total+a
	60 LET count=count+1
	70 IF count <= 5 THEN GO TO 30
	80 PRINT total

Notice how easy it would be to change line 70 so that this program
adds ten numbers, or even a hundred.

This sort of thing is so useful that there are two special commands to
make it easier - the FOR command and the NEXT command. They are always
used together. Using these, the program you have just typed in does
exactly the same as...

	10 LET total=0
	20 FOR c=1 TO 5
	30 INPUT a
	40 REM c is number of times that a has been input so far
	50 LET total=total+a
	60 NEXT c
	80 PRINT total

(To get this program from the previous one, you just have to edit
lines 20, 40 and 60, then delete line 70.)

Note that we have changed 'count' to 'c'. This is because the control
variable of a FOR...NEXT loop must have a single letter as its name.

The effect of this program is that 'c' runs through the values 1 (the
initial value), 2, 3, 4 and 5 (the limit), and each time, lines 30, 40
and 50 are executed. Then, when 'c' has finished its five values, line
80 is executed.

At this point, attempt exercise 2 (which refers to the above program),
at the end of this section.

An extra subtlety to the FOR...NEXT structure is that the control
variable does not have to go up by 1 each time - you can change this 1
to anything you like by using a STEP part in the FOR command. The most
general form of a FOR command is...

	FOR control variable = initial value TO limit STEP step

...where the control variable is a single letter, and where the
initial value, the limit and the step are all things that the +3 can
calculate as numbers - like the actual numbers themselves, or sums, or
the names of numeric variables. So, if you replace line 20 in the
program by...

	20 FOR c=1 TO 5 STEP 3/2

...this will step the control variable by the amount 3/2 each time the
FOR loop is executed. Note that we could have simply said 'STEP 1.5',
or we could have assigned the step value to a variable, say 's', and
then said 'STEP s'.

With the above modification, 'c' will run through the values 1, 2.5 and
4. Notice that you don't have to restrict yourself to whole numbers,
and also that the control value does not have to hit the limit
exactly; it carries on looping as long as it is less than or equal to
the limit.

At this point, attempt exercise 3 at the end of this section (which
refers to the above program).

Step values can be negative instead of positive. Try this program
which prints out the numbers from 1 to 10 in reverse order.
(Remember, use the command NEW before typing in a new program.)

	10 FOR n=10 to 1 STEP -1
	20 PRINT n
	30 NEXT n

We said before that the program carries on looping as long as the
control variable is less than or equal to the limit. If you consider
what that would mean in this case, you'll see that it now doesn't hold
true. Hence, the rule has to be modified to say that when the step is
negative, the program carries on looping as long as the control
variable is greater than or equal to the limit.

At this point, attempt exercises 4 and 5 at the end of this section
(which refer to the above program).

You must be careful if you are running two FOR...NEXT loops together,
one inside the other. Try this program, which prints out the numbers
for a complete set of six dot dominoes.

	10 FOR m=0 TO 6				}
	20 FOR n=0 TO m		}		}
	30 PRINT m;":";n;" ";	}- 'n' loop	} - 'm' loop
	40 NEXT n		}		}
	50 PRINT				}
	60 NEXT m				}

You can see that the 'n' loop is entirely inside the 'm' loop. This
means that they are properly nested.

However, what must be avoided is having two FOR...NEXT loops that
overlap without either being entirely inside the other, like this...

	 5 REM this program is wrong
	10 FOR m=0 TO 6		}
	20 FOR n=0 TO m		}		}
	30 PRINT m;":";n;" ";	}- 'm' loop	} - 'n' loop
	40 NEXT m		}		}
	50 PRINT				}
	60 NEXT n				}

Two FOR...NEXT loops must either be one inside the other, or
completely separate.

Another thing to avoid is jumping into the middle of a FOR...NEXT loop
from the outside. The control variable is only set up properly when
its FOR statement is executed, and if you miss this out, then the NEXT
statement will confuse the +3. You will probably get an error report
saying 'NEXT without FOR' or 'Variable not found'.

There is nothing to stop you using a FOR...NEXT loop in a direct
command. For example, try...

	FOR m=0 TO 10: PRINT m: NEXT m

You can sometimes use this as a (somewhat artificial) way of getting
around the restriction that you cannot GO TO anywhere inside a command
- because a command has no line number. For instance...

	FOR m=0 TO 1 STEP 0: INPUT a: PRINT a: NEXT m

The step size of zero here makes the command repeat itself forever.

This sort of thing is not really recommended, because if an error
crops up then you have lost the command and will have to type it in
again; moreover, CONTINUE will not work.


Exercises...

1. Make sure that you understand that a control variable not only has
a name and a value (like an ordinary variable), but also a limit, a
step, and a reference to the statement after the corresponding FOR
statement. Ensure that when the FOR statement is executed all this
information is available (using the initial value as the first value
the variable takes), and also that this information is enough for the
NEXT statement to know by how much to increase the value, whether to
jump back, and if so where to jump back to.

2. Run the third program in this section, then type...

	PRINT c

Why is the answer 6, and not 5?

(Answer: The NEXT command in line 60 is executed five times, each
time 1 being added to 'c'. On the last time, 'c' becomes 6 so the
NEXT command decides not to loop back but to carry on, 'c' now being
part its limit.)

3. What happens if you put 'STEP 2' at the end of line 20 of the third
program? Try 'STEP 10'.

Now change the third program so that instead of automatically adding
five numbers, it asks you to input the amount of numbers you wish to
add. When you run this program, what happens if you input '0' (meaning
that you don't wish to add any numbers)? Why would you expect this to
cause problems for the +3, even though it is clear what you mean?

4. In line 10 of the fourth program in this section, change '10' to
'100' and run the program. It will print the numbers from 100 down to
79 on the screen, and then say 'scroll?' at the bottom. This is to
give you a chance to see the numbers that are about to be scrolled off
the top. If you press N, BREAK or the space bar, the program will stop
with the report 'D BREAK - CONT repeats'. If you press any other key,
then it will print another 22 lines and ask you again if you wish to
scroll.

5. Delete line 30 from the fourth program. When you run the new
curtailed program, it will print the first number and stop with the
message '0 OK'. If you then type...

	NEXT n

...the program will go once round the loop, printing out the next
number.