## 15 Puzzle game – rosetta code gas and water mix

##########

The initial version had me so enamoured by the notion of consecutive cells for the solution having the number of their index as their value (as in CELL(0) = 0 (the blank square), CELL(1) = 1, … CELL(15) = 15) and the prospect of the check for this being simple, that I failed to perceive that the nice big diagram of the board shown at the head of the article in fact clearly shows the solution state having the blank cell at the end, not the start. Once again it is demonstrated that what you see is … influenced … by what you would like to see. After that diversion, the cells shall now be numbered one to sixteen, not zero to fifteen, and so there static electricity jokes is no need for the ability introduced by F90 whereby arrays can have a lower bound other than one.

The plan is to use parameters for the board size, which need not be square. As often with Fortran, messing with arrays is the key, though not without opportunities for confusion. Because Fortran stores arrays in column-major order, the arrays are accessed as BOARD(column,row) even though the arrangement is treated as rows down the page and columns across as is usual. By this means, consecutive elements in storage of array BOARD(c,r 1 electricity unit in kwh) are such that the same storage accessed via array BORED(i) thanks to EQUIVALENCE(BOARD,BORED) indexes them as consecutive elements, and so the test that the values are in consecutive order becomes delightfully simple, though alas there is no equivalent of the iota function of APL whereby the test could be ALL(BORED(1:N – 1) .EQ. IOTA(N – 1))

The game plan is to start with an ordered array so that each cell electricity ground explained definitely has a unique code, then jumble them via random swaps. Possible arrangements turn out to have either odd or even parity based on the number of out-of-sequence squares, and as the allowed transformations do not change the parity and the solution state has even parity, odd parity starting states should not be presented except by those following Franz Kafka. The calculation is simplified by always having the blank square in the last position, thus in the last row. Once an even-parity starting state is floundered upon, the blank square is re-positioned using allowable moves so that the parity is not altered thereby. Then the game begins: single-square moves only are considered, though in practice groups of squares could be moved horizontally or vertically rather than one-step-at-a-time – a possible extension.

The source style uses F90 for its array arithmetic abilities, especially the functions ALL, ANY and COUNT. A statement LOCZ = MINLOC (BOARD ) !Find the zero. 0 = BOARD(LOCZ(1),LOCZ(2)) == BOARD(ZC,ZR) could be used but is unnecessary thanks to tricks with EQUIVALENCE. For earlier Fortran, various explicit DO-loops would have to be used. This would at least make clear whether or not the equivalents of ANY and ALL terminated on the first failure or doggedly scanned the entire array no matter what. SUBROUTINE SWAP (I,J ) !Alas, furrytran does not provide this.

Output: Not so good. As ever, the character cell sizes are not square so a square game board comes out as a rectangle. Similarly, underlining gas after eating red meat is unavailable (no overprints!) so the layout is not pleasing. There are special box-drawing glyphs available, but they are not standardised and there is still no overprinting so that a flabby waste of space results. Further, there is no ability to re-write the display, even though one could easily regard the output to the screen as a random-access file: WRITE (MSG,REC = 6) STUFF would rewrite the sixth line of the display. Instead, output relentlessly rolls forwards, starting as follows:

The initial version had me so enamoured gas vs diesel mpg by the notion of consecutive cells for the solution having the number of their index as their value (as in CELL(0) = 0 (the blank square), CELL(1) = 1, … CELL(15) = 15) and the prospect of the check for this being simple, that I failed to perceive that the nice big diagram of the board shown at the head of the article in fact clearly shows the solution state having the blank cell at the end, not the start. Once again it is demonstrated that what you see is … influenced … by what you would like to see. After gas 1940 that diversion, the cells shall now be numbered one to sixteen, not zero to fifteen, and so there is no need for the ability introduced by F90 whereby arrays can have a lower bound other than one.

The plan is to use parameters for the board size, which need not be square. As often with Fortran, messing with arrays is the key, though not without opportunities for confusion. Because Fortran stores arrays in column-major order, the arrays are accessed as BOARD(column,row) even though the arrangement is treated as rows down the page and columns across as is usual. By this means, consecutive elements in storage of array BOARD(c,r) are such that the same storage accessed via array BORED(i) thanks to EQUIVALENCE(BOARD,BORED) indexes them as consecutive elements 1 electricity unit is equal to how many kwh, and so the test that the values are in consecutive order becomes delightfully simple, though alas there is no equivalent of the iota function of APL whereby the test could be ALL(BORED(1:N – 1) .EQ. IOTA(N – 1))

The game plan is to start with an ordered array so that each cell definitely has a unique code, then jumble them via random swaps. Possible arrangements turn out to have either odd or even parity based on the number of out-of-sequence squares, and as the allowed transformations do not change the parity and the solution state has even parity, odd parity starting states should not be presented except by those following Franz Kafka. The calculation is simplified by always having the blank square in the last position, thus in the last row. Once an even-parity starting state is floundered upon, the blank square is re-positioned using allowable moves so that the parity is not altered thereby. Then the game begins: single-square electricity calculator moves only are considered, though in practice groups of squares could be moved horizontally or vertically rather than one-step-at-a-time – a possible extension.

The source style uses F90 for its array arithmetic abilities, especially the functions ALL, ANY and COUNT. A statement LOCZ = MINLOC (BOARD ) !Find the zero. 0 = BOARD(LOCZ(1),LOCZ(2)) == BOARD(ZC,ZR) could be used but is unnecessary thanks to tricks with EQUIVALENCE. For earlier Fortran, various explicit DO-loops would have to be used. This would at least make clear whether or not the equivalents of ANY and ALL terminated on the first failure or doggedly scanned the entire array no matter what. SUBROUTINE SWAP (I,J ) !Alas, furrytran does not provide this.

Output: Not so good. As ever, the character cell sizes are not square so a square game board comes out as a rectangle. Similarly, underlining is unavailable (no overprints!) so the layout is not pleasing gas news. There are special box-drawing glyphs available, but they are not standardised and there is still no overprinting so that a flabby waste of space results. Further, there is no ability to re-write the display, even though one could easily regard the output to the screen as a random-access file: WRITE (MSG,REC = 6) STUFF would rewrite the sixth line of the display. Instead, output relentlessly rolls forwards, starting as follows: