Previously I discussed several approaches to printing out the Christmas tree pattern for this challenge.

The method that produced the smallest Color BASIC program looked like this:

0 FORC=1TO14:W=ASC(MID$("ACEGCGKOEKQWCC",C,1))-64:PRINTTAB(16-W/2)STRING$(W,42):NEXT

That uses 66 byte of BASIC program space (though will use more RAM for strings as it runs).

It appears there are still optimizations to make! In the comments. Stewart Orchard pointed out this one:

Not a big gain but two bytes can be saved by removing the third argument from MID$().

The two argument version of MID$() returns the remainder of the string starting from the specified position, and ASC() returns its result based on the first character of its argument.

– Stewart Orchard

In Color BASIC, MID$ can accept three parameters:

If you had as string of 10 characters, and wanted to print the third character, you could do it like this:

A$="ABCDEFGHIJ"
OK
PRINT MID$(A$,3,1)
C

Stewart pointed out that if you left off the final parameter, it returns the rest of the string:

A$="ABCDEFGHIJ"
OK
PRINT MID$(A$,3,1)
CDEFGHIJ

Now that I look at it, it appears MID$ with two parameters is sort of like an inverted RIGHT$. MID$ would give you all the characters starting at the one you specify, and RIGHT$ gives you the number of ending characters you specify.

PRINT MID$(A$,3)
CDEFGHIJ

PRINT RIGHT$(A$,3)
HIJ

I don’t recall using MID$ like this, but I have simulated the same behavior using RIGHT$ like:

PRINT RIGHT$(A$,LEN(A$)-3+1)
CDEFGHIJ

PRINT MID$(A$,3)
CDEFGHIJ

I am a bit embarrassed to admit I think I even did something like this:

PRINT MID$(A$,3,LEN(A$)-3)
CDEFGHIJ

…but let’s not speak of that.

And if MID$ can work like RIGHT$, it can also work like LEFT$:

PRINT LEFT$(A$,3)
ABC

PRINT MID$(A$,1,3)
ABC

But I digress…

If MID$(A$,3,1) gives you one character starting as location 3, and MID$(A$,3) gives you all the characters starting at position 3, how does that work? Stewart explained that ASC will still work if you pass it a string since it only works on the first character of the string. It is even documented that way:

Thus, ASC(“HELLO”) produces the same result as ASC(“H”) — the ASCII value of letter H.

With that in mind, we can remove “,1” from the program and reduce it by two bytes:

0 FORC=1TO14:W=ASC(MID$("ACEGCGKOEKQWCC",C))-64:PRINTTAB(16-W/2)STRING$(W,42):NEXT

64 bytes!

Thank you, Stewart, for leaving that comment.

Until next time…

Another programming challenge seems to be occupying folks this Christmas season:

http://logiker.com/Vintage-Computing-Christmas-Challenge-2021

The challenge is simple: Write a program that prints out a centered text Christmas tree using the same layout of their example program. I thought it would be fun to work through several methods to do this.

PRINT

We start with their simple example, which displays the centered tree using PRINT statements. Here is their example with spaces altered so it centers on the CoCo’s 32 column screen:

100 PRINT "               *
110 PRINT "              ***
120 PRINT "             *****
130 PRINT "            *******
140 PRINT "              ***
150 PRINT "            *******
160 PRINT "          ***********
170 PRINT "        ***************
180 PRINT "             *****
190 PRINT "          ***********
200 PRINT "       *****************
210 PRINT "    ***********************
220 PRINT "              ***
230 PRINT "              ***

386 bytes.

You will see one memory optimization they did was leaving off the ending quote. BASIC will stop parsing a quoted string if it reaches the end of a line, so the ending quote is only necessary if more statements follow the PRINT.

I do not know if the space between PRINT and the quote is required for the system they wrote this example, but on the CoCo we could remove it and save 23 bytes of program space right there.

PRINT TAB

Speaking of spaces, each space takes up a character. BASIC has a command that will jump forward a certain amount of spaces — TAB. It works like this:

PRINT TAB(5);"FIVE SPACES OVER"

From my test, it appears TAB takes up one byte(for the “TAB(” portion, then a byte for each digit, then a byte for the closing parenthesis. If tabbing a single digit of spaces, it takes three bytes of program space. Thus, any time we are spacing over more than 3 spaces, it would save memory to use TAB. Also, the semicolon between TAB and the item being printed is optional, so we can leave that out as well.

For the tree example centered on a 32 column screen, every line starts with at least 4 spaces, so using TAB should save memory. Let’s try this:

100 PRINT TAB(15)"*
110 PRINT TAB(14)"***
120 PRINT TAB(13)"*****
130 PRINT TAB(12)"*******
140 PRINT TAB(14)"***
150 PRINT TAB(12)"*******
160 PRINT TAB(10)"***********
170 PRINT TAB(8)"***************
180 PRINT TAB(13)"*****
190 PRINT TAB(10)"***********
200 PRINT TAB(7)"*****************
210 PRINT TAB(4)"***********************
220 PRINT TAB(14)"***
230 PRINT TAB(14)"***

279 bytes.

That looks icky, but produces the same result with less code space.

Pattern Matching

If we take a look at the tree design, we see it has a pattern to how each of the three seconds is printed:

           *            1
          ***           3
         *****          5
        *******         7
          ***           3
        *******         7
      ***********       11
    ***************     15
         *****          5
      ***********       11
   *****************    17
*********************** 23
          ***           3
          ***           3

It is drawing three sections, with the first expanding on each side by 1 (adding two asterisks to each row), then the next section expanded each side by 2 (adding four asterisks to each row), then the final section expands each side by 3 (adding six asterisks to each row).

There is probably a simple way to math it. But first…

Centering

Since one of the requirements is centering the tree on the screen, let’s look at how we center a string. To do this, we simply subtract the length of the string we want to center from the width of the string then divide the result by two:

A$="CENTER THIS"
PRINT TAB((32-LEN(A$))/2);A$

Or, to eliminate some parenthesis, we can start with half the width of the screen (the center of the screen) and subtract half the length of the string:

A$="CENTER THIS"
PRINT TAB(16-LEN(A$)/2);A$

With that out of the way, now we need to figure out how to draw the three triangle shapes of the tree, each time getting wider.

Numbers and patterns.

I decided to lookat the number sequences of each line length for each section of the tree (skipping the trunk lines).

Section 1: 1  3  5  7
Section 2: 3  7 11 15
Section 3: 5 11 17 23

I could easily create the first pattern by doing a FOR/NEXT loop with a step of 2:

FOR I=1 TO 7 STEP 2:PRINT I:NEXT

And then I could do 3 to 15 with a STEP 4, and 5 to 23 with a STEP 6.

FOR I=1 TO 7 STEP 2:PRINT I:NEXT
FOR I=3 TO 15 STEP 4:PRINT I:NEXT
FOR I=5 TO 23 STEP 6:PRINT I:NEXT

This would generate the number sequence I need, and then I could simply print a centered string of that many asterisks, and manually print the tree trunk at the end.

10 FOR I=1 TO 7 STEP 2:GOSUB 50:NEXT
20 FOR I=3 TO 15 STEP 4:GOSUB 50:NEXT
30 FOR I=5 TO 23 STEP 6:GOSUB 50:NEXT
40 I=3:GOSUB 50:GOSUB 50:END
50 PRINT TAB(16-I/2)STRING$(I,42):RETURN

127 bytes.

That’s much better! Though, I saved a bit more by combining lines, and I could save even more by removing spaces and combining lines further:

10 FORI=1TO7STEP2:GOSUB50:NEXT:FORI=3TO15STEP4:GOSUB50:NEXT:FORI=5TO23STEP6:GOSUB50:NEXT:I=3:GOSUB50:GOSUB50:END
50 PRINTTAB(16-I/2)STRING$(I,42):RETURN

(Compressed down to 94 bytes.)

Now we’re getting somewhere! But ignoring the compressing, can we do better than 127 using better math?

Math. Why did there have to be math?

I am slow and bad at math, but I am convinced there is a math solution to this, as well.

Let’s look at how the numbers for START value and STEP value work. I know there are going to be three sections of the tree, so it seems logical I’d start with something like this:

10 FOR I=1 TO 3
20 PRINT I*2-1
30 NEXT

That would print out 1, 3 and 5, which is the start width of each section of the tree. I could have also done the FOR loop using 0 to 2 and added 1 to get the same result:

10 FOR I=0 TO 2
20 PRINT I*2+1
30 NEXT

Maybe one will be more useful than the other depending on what comes next…

Once we know how wide a section starts, we need to know how much the length increases for each line.

Section 1 increases by 2 each row, section 2 increases by 4 each row, and section 3 increases by 6 each row. That is a pattern of 2, 4, 6. It looks like I could get those values by taking the section (1 to 3) and multiplying it by 2. This will print 2, 4, 6:

10 FOR J=1 TO 3
20 PRINT J*2
30 NEXT

I am bad with math, as I mentioned, but I was able to work out that taking a value of 1 to 4 (for each layer of a section) and multiply that by the section (1 to 3), and subtracting one, I could get this:

10 FOR I=1 TO 3
20 FOR J=1 TO 4
30 PRINT J*I*2-1
60 NEXT
70 NEXT

The math looks like this:

 J * I       * 2       - 1
-------   -------   -------
(1 * 1) = (1 * 2) = (2 - 1) = 1
(2 * 1) = (2 * 2) = (4 - 1) = 3
(3 * 1) = (3 * 2) = (6 - 1) = 5
(4 * 1) = (4 * 2) = (8 - 1) = 7

(1 * 2) = (2 * 2) = (4 - 1) = 3
(2 * 2) = (4 * 2) = (8 - 1) = 7
(3 * 2) = (6 * 2) = (12 - 1) = 11
(4 * 2) = (8 * 2) = (16 - 1) = 15

(1 * 3) = (3 * 2) = (6 - 1) = 5
(2 * 3) = (6 * 2) = (12 - 1) = 11
(3 * 3) = (9 * 2) = (18 - 1) = 17
(4 * 3) = (12 * 2) = (24 - 1) = 23

…and that gets our number sequence we want:

Section 1: 1  3  5  7
Section 2: 3  7 11 15
Section 3: 5 11 17 23

To print the row of asterisks, I use the STRING$ function. It takes the number of characters to print, then the ASCII value of the character. The asterisk is ASCII character 42 so it I wanted to print ten of them I would do:

PRINT STRING$(10,42)

I can now print the layers of the tree like this:

10 FOR I=1 TO 3
20 FOR J=1 TO 4
30 W=J*I*2-1
50 PRINT TAB(16-W/2);STRING$(W,42)
60 NEXT
70 NEXT

But that still doesn’t handle the “trunk” at the bottom of the tree.

Since the trunk does not follow any pattern, I will simply treat it like an extra section, and increase the section loop (FOR I) by one, and add an IF that says if we are on that layer, the width will be 3. Then, since I don’t want this section to be four layers thick, I can use a second IF after the one that checks for the fourth section to know when to exit (checking for J to be larger than 2):

10 FOR I=1 TO 4
20 FOR J=1 TO 4
30 W=J*I*2-1
40 IF I>3 THEN W=3:IF J>2 THEN END
50 PRINT TAB(16-W/2);STRING$(W,42)
60 NEXT
70 NEXT

162 bytes.

Ah, well, being clever seems to have increase beyond the 127 bytes of just using three FOR/NEXT loops. I suspect it’s the overhead of the way I am trying to print the trunk section. Indeed, without it (like 40, above, and adjusting the I loop to 3) makes it 125.

Sometimes being clever doesn’t help. Even without trying to be clever about the trunk section, the “W=J*I*2-1” stuff takes up as much space as just doing another FOR/NEXT and a GOSUB to print the line.

DATA

We could just have a table to line lengths, and do it like this:

10 READ W
20 IF W=0 THEN END
30 PRINT TAB(16-W/2);STRING$(W,42):GOTO 10
40 DATA 1,3,5,7,3,7,11,16,5,9,13,17,3,3,

98 bytes.

Not bad at all! And that is before compressing it to fewer lines. Here’s a 79 byte attempt, removing spaces, removing the semicolon, altering the logic just a bit to be on LINE 0 (so you can just say GOTO) and changing the IF so there is no END token:

0 READW:IFW>0THENPRINTTAB(16-W/2)STRING$(W,42):GOTO:DATA1,3,5,7,3,7,11,16,5,9,13,17,3,3,

Another “DATA” technique which I have seen Jim Gerrie use is to simply encode the line lengths as characters in a string, and use that as data. For example, ASCII “A” (character 65) will represent 1, “B” will represent 2, and so on. Make a string of the appropriate characters and retrieve them using MID$() and get the ASCII value using ASC() then subtract 64 from that value and you have something like this.

10 FOR C=1 TO 14
20 W=ASC(MID$("ACEGCGKOEKQWCC",C,1))-64
30 PRINT TAB(16-W/2);STRING$(W,42)
40 NEXT

97 bytes.

If we compress the lines together, we can shrink it even further:

10 FORC=1TO14:W=ASC(MID$("ACEGCGKOEKQWCC",C,1))-64:PRINTTAB(16-W/2)STRING$(W,42):NEXT

66 bytes!

Is this as small as it gets? (Technically, this uses more memory, since string space has to be used to create temporary strings for MID$(), but we are only looking at program size and not memory usage.)

What else can we try? Leave a comment.

Until next time…