Best 3D puzzle



Judges' comments

To build

  cc -o anon anon.c

Or, if the above does not work

  cc -DNO_STTY -o anon anon.c

To run

  anon 4 4
  anon 3 3 3

Author's comments


Remember Sam Loyd's Fifteen Puzzle? It consists of a 4x4 board with 15 tiles numbered 1 to 15, and an empty spot. The goal of the game is to slide the tiles around without lifting them off the board, so that they become sorted.

Well, that was then. This program is the 21st century version of the Fifteen Puzzle: not only does it allow arbitrary board sizes, it also supports 3D boards! The tiles are numbered from 1 to N, where N is one less the number of spaces on the board, and the goal is to rearrange them so that they appear sorted in the order they appear on the screen.

The program takes 2 or 3 arguments, specifying the dimensions of the board. For example, to play the original version of the Fifteen Puzzle:

       prog 4 4

To play in a 3D board, do something like this:

       prog 3 3 3

(WARNING: do NOT run the program with more than 3 command-line arguments. This will trigger a bug that will cause it to crash or do something strange. :-) )

Also, resist the temptation to create very large puzzles. The program does not attempt to resize your terminal for you, and will produce confusing output. It may also crash on you if you insist on running it with excessively large board dimensions. :-) (10x10x10 is considered a safe upper limit.)

The empty space on the board is represented by a space filled with '#' characters instead of digits. To slide the tiles around, use the following keys:

       i       Slide the tile above the current empty space downwards.
j Slide the tile to the left of the current empty space to
the right.
k Slide the tile below the current empty space upwards.
l Slide the tile to the right of the current empty space to
the left.
o Slide the tile behind the current empty space forwards.
n Slide the tile in front of the current empty space backwards.

To quit the game:

       q       Quit the game.

Note that , for example, sliding the tile above the current empty spot downwards will fill up the empty spot, and create a new empty spot above where the current empty spot was. Hence, you could think of the movement keys in terms of how they effectively "move" the empty spot:

       i       Move empty spot up
j Move empty spot left
k Move empty spot down
l Move empty spot right
n Move empty spot forwards
o Move empty spot backwards

NOTE: as a measure of alleviating counter-productivity due to addiction to this game, particularly for those hardcore gamers who insist on solving a 10x10x10 puzzle during work hours, and also to give an upper bound to user frustration when the program generates an impossible puzzle (which it does roughly half the time, just to hook you), the program will, after a very large number of moves (which is system-specific) terminate itself by forcefully destroying its own runtime stack. This will result in a core dump and/or an abnormal termination message; but this is a feature, not a bug! :-)


This program complies with ANSI/C99. It uses ANSI terminal control sequences, and so requires a terminal that understands ANSI sequences, such as vt100 or xterm.

Some compilers may emit lots of warnings about how things ought to be parenthesized (e.g. gcc -Wall). This is deliberate, since if everything were parenthesized "properly" the program would fail to work. It (ab)uses C operator precedence to accomplish some cool hacks. :-) However, there are no compiler errors. I have tested this with 'gcc -pedantic -std=c99'.

The program also uses `stty cbreak`. If this breaks on your system, compile it with -DNO_STTY. The game interface will be a bit annoying (you will need to hit enter after every key), but it works.

The game requires lots of space on the runtime stack space due to deep recursion, among other things. :-)

See spoilers below for more notes about portability.


Clearly, the author is very, very confused. Although he has broken up the file into sections labelled with helpful headings, and although he has left ample whitespace between all those #define's to make them easier to read, :-) and although he has helpfully formatted the code with beautiful indentation, something is clearly very, very wrong.

In fact, the closer you look at this code, the more you realize something is horribly wrong with it. For example, why is it that the first statement in main() is a return? What do all those nested do-loops do? (pun intended) Why is the first statement inside the first do-loop a mere integer literal? Why are there such strange statements, like that empty string on line 64, or that isolated || on line 67?

But wait... why aren't any statements terminated by semicolons? Why is there only ONE semicolon in the entire program?! Why is the author opening nested blocks by such strange things as || and (, and closing them by || and ))? The for-loop isn't a for-loop! The do-loop isn't a do-loop! Or... are they? Well, the for-loop is defined in terms of a while-loop. But wait, the while loop is defined in terms of the do-loop. And the do-loop is defined in terms of ... Huh???

And that switch statement toward the end of the program... wait a minute, that's not a switch statement! Why is a case defined in terms of a switch statement?! And that initial return isn't a return! Well, it is... but not what you might think!

Let's see if it all makes sense after we run it through CPP...

Uh oh. The result looks like the diseased imagination of a mind more confused than the one who wrote the original code. Unfortunately, unless you're a Lisp expert, it is probably easier to understand the program in its original form. (And even then.) But that's just so, so wrong...

The entire program consists of a single expression, returned from main(). There are no if-statements, no for-loops or any looping or control constructs besides the 'return', in spite of the misleading appearance of the original source. :-) Yes I know, this has been attempted before, using ?: and the bad old comma operator. BUT this program does NOT use the ?: operator, and there are only TWO comma operators in the entire program---and they are only there because srand() and exit() return void.

The entire program consists of a single boolean expression returned from main(). Looping is achieved by recursion, of course, and branching is achieved by exploiting short-circuit evaluation of boolean expressions. :-)

But this is not all.

It is comprehensible that the program can achieve branching and looping using only boolean expressions and recursion. But HOW does the program STORE DATA??? There are no variables of any kind in the program except for the two arguments to main(). There are certainly no arrays declared anywhere. The program does not call any memory allocation routines, nor any function that indirectly returns allocated memory. Yet it happily looks up array references without crashing. How??

One might be tempted to think that this program would be highly non-portable because of such insane hacks. However, it has been tested and proven to work on the following architectures:

  • i386/linux
  • sparc/solaris
  • parisc64/linux
  • arm/linux
  • s390/linux
  • mips/linux
  • m68k/linux
  • ia64/linux
  • sparc64/linux

It probably will also compile and work on many (all?) other *nix platforms as well. How does it achieve this incredible feat?












(Read the following only if you give up figuring it out :-)










The Evil Hack

The program (ab)uses an implicit assumption underlying practically all architectures, and that is that parameters to C functions are implicit local variables allocated on the runtime stack. This runtime stack is a contiguous section of memory, and therefore, after N recursive calls of main() to itself, there is enough room on the stack to store whatever the program desires, so long as it does not exceed the maximum stack size.

(Theoretically, the runtime stack doesn't have to be contiguous... but all current architectures that are worth consideration make this assumption. I submit that this implies this program is 100% portable, even though theoretically it shouldn't even work in the first place.) :-)

There are two types of architectures the program must handle: those that allocate the stack top-down, and those that allocate the stack bottom-up. The program correctly detects this at run-time, and adjusts itself accordingly.  :-) (It is a simple matter of testing if the address of argc in a recursive call is greater or less than in the parent call.)

To avoid having to handle issues of int sizes, memory alignment, what exactly is on the stack between successive locations of argc, etc., the program (ab)uses the fact that argc must necessarily be allocated on an aligned address, and therefore, the range of memory between two argc's is aligned, and therefore safe to use as an array of longs.[*] The program also compares the pointers as (long*) pointers, so that it will not have to deal with mapping bytes to larger types. The initial memory allocation is done by recursively calling main() until there is enough space on the stack (the exact number of recursive calls is, of course, architecture-dependent).

[*] long was chosen instead of int, in order to skirt around pointer-size issues on architectures like ia64. It really can be made anything large enough to hold both ints and pointers. :-)

After the stack is deemed to have grown deep enough to be a sufficiently long array (pun intended), the program begins its real code. It uses argc to keep track of what it's supposed to be doing (since main() is the only function), and argv to point to the base of this array (which is computed differently based on how the architecture allocates the stack). Since this fills up the only two variables in the program, everything else is stored in the MASS [**] array.

[**] for "Memory Allocated by Stack Smashing" :-)

Note that from this point on, all bets are off as to what the contents of the runtime stack are below the current recursive call to main(). We are overwriting frame pointers, return addresses, etc., with data. Hence, the program must never return from this call, otherwise it will crash horribly. That's why I had to call exit() even though it meant I can no longer claim the program doesn't need the comma operator. :-) (I was going to skirt around the issue by indirectly calling exit(), such as via bsearch() or raise(), but I was getting too close to the size limit.)

Some notes about the macros

In spite of the frightening appearance, it is probably easiest to understand the code in its original form. (Don't even try running 'indent' on it: on my system it chokes and complains about nesting errors.)

Most of the #define's are just to keep the code size down, due to the abusive amounts of type casting employed. The others define a bizarre "programming language" (in the crudest, most twisted sense of the word) that the author used to write this mess.

R(i) and W(i,j) are macros to read/write the i'th position of the MASS.

A(i) retrieves the i'th command-line argument. This is slightly tricky, because by the time the MASS is setup, we no longer have access to the original values of argc and argv. So what is done is that the initial memory allocation code will save argc and argv into positions 8 and 9 in the MASS after the allocation. It does this by using argv, which at that time contains a pointer to the top-level argc, to compute the location of the top-level argv. This is done before the rest of the MASS is used, since otherwise they may be overwritten.

do(x,y) has nothing to do with do-loops. :-) It defines a "state" in main(), essentially, what to do when main() is called with argc containing a particular value. (This is why the user must never run the program with more than 3 arguments. :-) The state number is x, and y is the code. The program's boolean expression consists of a number of states &&'d together. Within each state, it is assumed that statements are separated by ||. All statements are assumed to evaluate to false. This makes it easy to write conditional statements: "if (a) { b } ..." can simply be written "a && b || ...". All states created by do(x,y) are assumed to evaluate to false. There is only 1 state which can return true or false: state 5, a "manually-implemented" state which determines whether the system uses top-down or bottom-up stack allocation. It's the only state that needs to return a value from the boolean expression, since once the MASS is initialized any return value can simply be stored in a well-known location in the MASS.

if(p,q,r,s) is, in fact, an if-statement. :-) It is equivalent to:

       if (p) { q; r } else {s}

Why are q and r split up? Because it's cleaner (in whatever twisted sense of the word that can be applied to an IOCCC entry) to implement using boolean expressions. Keep in mind that all statements are assumed to evaluate to false. The proof that this macro in fact implements an if-then-else construct is left as an exercise for the reader.

while(x,y,z) is actually a while-loop after all. :-) It implements the loop using, of course, recursive calls to main(). However, this macro doesn't actually run a while loop; it implements the loop in the state numbered x. It is used for defining a while loop, which can then be called from another state using f(x). (The reason we can't directly implement a while-loop inside another state ought to be clear: we can't recursively call main() to enter into the middle of a state.)

However, it is possible to implement a for-loop directly inside a state! The for(s,i,x,y,z,Z) macro does exactly this. Well, actually, technically speaking this macro can only be used as the last thing in a state, because it secretly closes the current state and opens a new one behind the programmer's back.  :-) Its intended usage is this: s is the state number for the loop body, and i is the index variable (well, the index into the MASS of the index variable); x and y-1 define the starting and ending values of i, and z is the loop body. Z is the post-loop code in the current state. For example:

       for(s,i, 0, 10,

is equivalent to:

       for (i=0; i<10; i++) {

Note the "wrong" indentation in the former: the author prefers to write it that way, since the analogy to the usual for-loop is clearer. This is why it's easier to understand the pre-CPP code, since after CPP, the macro reshuffles some_code after other_code so that it can close the current state and define the one containing the loop body. (Have I told you that the author of this program is horribly, horribly, confused? :-) This confusion also shows up in the superficial appearance of the program, which heavily suffers from wrong indentation.)

In spite of all appearances, switch() really is just a shorthand macro for reducing code size. The evil choice of macro name is just to instill more confusion into the would-be decipherer of this entry. :-) After all, case() really is the equivalent of a case statement, implemented using &&, and conveniently encapsulating code common to the cases in the only switch-statement in the program, which is the code that decides what to do with a keypress. What could be more fun than to define such a case in terms of a switch? :-)

Finally, for those who give up deciphering this horribly confused code, here are the mappings of various locations of the MASS to their usage in the program, and what the various state numbers are meant to do:

MASS usage map

    0       Function return value
1 Function argument 1
2 Function argument 2
3 Function argument 3
4 Scratch register 1
5 Scratch register 2
6 Scratch register 3
7 Scratch register 4
8 Value of original argv :-)
9 Value of original argc :-)
11 Zero register (always set to 0)
12 Width of board
13 Length of board
14 Height of board
15 Current position of hole
16 Random seed for rand_r()
18 Scratch register used by state 18 :-)
31 field width for printing tiles
32- Start of board data

(CAVEAT: not all of these mappings ended up in the final version of the program, mainly due to size limitations which entailed the trimming off of a lot of neat features in the game. It is left as an exercise for the reader to figure out which of these are actually used.)

Note that argv and argc necessarily needs to stay away from lower indices of the MASS, because otherwise they may overwrite their original values when the memory allocation code saves them. Index 8 is deemed "safe enough". (It seems to be on all tested architectures.)

State number assignments

     1       showhelp
2 showhelp
3 is 2D: start init
4 is 3D: start init
5 find allocation type
6 MASS init, bottom-up
7 MASS init, top-down
8 main program
9 generate() outer loop
13 render()
14 render() loop
15 exit(0)
16 pick a tile that hasn't occurred yet
17 inner loop of 16.
18 main loop
19 checkwin() loop

Note that some of the manually-implemented states (those not implemented by do()) respond to multiple state numbers. Also note that states 1-4 conveniently correspond to what the program should do when 1-4 arguments are given at the command-line. :-)

The original intention was to include a parity-checking routine in the game so that it will always generate a solvable game. However, size limits necessitated the removal of this code. And besides, the game is more addictive when it's sometimes unsolvable. Especially when it taunts the user with a smiley. :-)