ioccc/2004/kopczynski/README.md

## To build:

``` <!---sh-->
    make
```

**NOTE**: We **FORCE** the use of `-O0` even if someone overrides it because this entry
will not work with it enabled.


## To use:

``` <!---sh-->
    ./kopczynski < input_file
```


## Try:

``` <!---sh-->
    ./try.sh
```

What happens if you feed the program source to the program? Can you figure out
why?


## Alternate code:

The judges modified the program to print its result.  The original
program returned the result as an exit code which is what the alternate version
does.


### Alternate build:

``` <!---sh-->
    make alt
```


### Alternate try:

``` <!---sh-->
    ./kopczynski.alt < kopczynski-10
    echo $?
```


## Judges' remarks:

What is in a line?  A lot when you obfuscate the way Eryk Kopczynski
did it.  This small one line program is an outstanding technical
work of art as well as one of the better one-liner programs that
we have seen in years!

Compile and run without arguments.  As input, give it an ASCII graphics
figure 8, 9, 10, or 11 made of pound signs and spaces, of any size,
shape, or orientation (that's right, an upside down 9 is still 9 :-) ).
There is one restriction: the only line not containing `#` characters
must be the last.

The program will print what it thinks you've entered. If you enter
anything that does not resemble 8, 9, 10, or 11, the result is
seemingly arbitrary.  Actually it is not pseudo-random; can you find
a pattern when it does not resemble 8, 9, 10 or 11?

Here is a related puzzle: how to continue the sequence:

>  `1, 0, 0, 0, 0, 0, 1, 0, 2, 1, ...`

With certain arguments, you can alter the exit value / output.  Can you figure
out how and why?


## Author's remarks:

The program proves it is not as hard to recognize numbers. The current
one liner version should correctly recognize all numbers from 8 to 11.
(Unless you give it some very hard cases. For example, it cannot
recognize negatives, zeros which have dots or slashes inside them,
digits should be separated, and numbers should be "complete".)

This program returns the number as its exit status. (In most shells,
you can see the exit status of the last command with `echo $?` (or
just `$?`).)

**NOTE**: The judges altered the primary version to output a number.

On the input, give numbers formed as a sequences of empty spaces and `#`
signs (you can also use dots instead of spaces), ending with an empty
line. (No number has an empty line in it.) The program should return
the number from 8 to 11 that it thinks it is.

* The line is 131 bytes long (in 1986, 165 bytes was OK, and the size
  limit has grown from 1986...).

* I have decided that it is better for this program to return the
  number, not to print it, but if you think otherwise, the change would
  cost 6 chars (plus a warning). Change `return *` to `printf("%d",*)`.
  (`$?` is shorter)

* I achieved some additional tightness by `-Dif=while` which saved 9 chars of
source for the cost of 11 chars of the [Makefile](%%REPO_URL%%/2004/kopczynski/Makefile). If I used
`-DB=while`, I would save 12 for 10, but I think the current version is slightly
more obfuscated.

### Portability

It only requires two's complement arithmetics, as far as I know. The maximum
length of an input line is `N-9`, where `N` is the size of `int` in bits
(you can try to compile with an option `'-Dint=long long'` for longer
lines).

### Algorithm & Obfuscation

1. This program works by calculating the [Euler
characteristics](https://en.wikipedia.org/wiki/Euler_characteristic) of input,
plus 9. It is the number of digits (i.e. separated `#`-regions) minus the number
of holes in them. It turns out that this algorithm works correctly for all
numbers from 8 to 11.

2. We know that [Euler
characteristics](https://en.wikipedia.org/wiki/Euler_characteristic) is the number of "vertexes"

```
            #
```

minus the number of "edges"

```
           ## # #. .#
              # .# #.
```

(`.` must be empty) plus the number of "faces"

```
           ##
           ##
```

3. If we fill all these patterns to 2x2 squares,

```
           #? ## #? #. .# ##
           ?? ?? #? .# #. ##
           +1 -1 -1 -1 -1 +1
```

substitute all possible "values" of `?` and sum them up, we get that it is
enough to calculate:

```
           #. .# ##
           .. #. #.
           +1 -1 -1
```

Note now it is simple and obfuscated enough to be used as
a "magic trick".

4. I make a 16-character array; when indexed by 4-bit value which
represents the 2x2 squares, it will return a number to add/subtract
`{-1,0,+1}`.

5. We convert lines of input to bitmaps (`N-bit` integers). Additionally, it is
heavily obfuscated by using negative numbers (two's complement).  For example,
it turns out that `6` in `z=6` is the only 1-digit number which works here (and
it's not only because we have `z>5` in the following `while`). The conversion
routine also sets `n=8` in an obfuscated and concise way.

6. Since we always return the number from 8 to 11, we can calculate modulo 4.
Instead of `16 {-1,0,+1}` values, we use a 15-character string which agrees
modulo 4 to the array in (`4`). (`'\0'` fits very well as the 16th character, so
we use 15-character string.)

7. Since the rule found in (3) did not produce any funny messages, I changed it
until it did. (The `#` character to find vertexes is in the top right corner,
not the top left one.) The following messages will also work instead of `has
dirtiest IF`:

```
    HighlandYachter
    TestDirtiestTen
    has lintiest IF
    TighterLaughter
    HustlerDaughter
    TighterDemoThen
```

They can be mixed, of course!

8. The variable names are confusing.

9. Finally, the program tries to be as concise as possible. Some obfuscation
comes from this. For additional obfuscation and conciseness, `if` means `while`.


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