PHP: Determining Grid Count Between 2 Grids

Question 1

The number of diagonal moves you can make is limited to the number of either rows or columns you have to traverse to get to your destination. All other moves can be left/right or up/down and will preserve the shortest distance.

That said, and assuming you know the row and col numbers for your cells, I believe this will give you your shortest distance:

$startCol = [column of starting cell];
$startRow = [row of starting cell];

$endCol = [column of end cell];
$endRow = [row of end cell];

$numMoves = 0;

$moveCol = 0;
$moveRow = 0;

/*
 * figure out which direction the end cell is, in relation to the
 * start cell.
 */

// end is to the right, so we need to add columns to the start
if( $startCol < $endCol ) {
    $moveCol = 1;
}
// end is to the left (or in the same column), so we need to subtract
// column from the start
else {
    $moveCol = -1;
}

// end is below the start, so we need to add rows
if( $startRow < $endRow ) {
    $moveRow = 1;
}
// end is above (or in the same row), so we need to subtract rows to the start
else {
    $moveRow = -1;
}

/*
 * now go diagnoal until you hit either the row or the column
 * that the end cell is in
 */

while( $startCol != $endCol && $startRow != $endRow ) {
    $startCol += $moveCol;
    $startRow += $moveRow;
    $numMoves++;
}

/* at this point, we're either in the same row or the same column
 * as our destination, so just move down that row or col until we
 * reach the destination
 */

// already at the destination, don't do anything
if( $startCol == $endCol && $startRow == $endRow ) {
}
// in the same column, so move up/down rows
else if( $startCol == $endCol ) {
    while( $startRow != $endRow ) {
        $startRow += $moveRow;
        $numMoves++;
    }
}
// in the same row, so move left/right cols
else {
    while( $startCol != $endCol ) {
        $startCol += $moveCol;
        $numMoves++;
    }
}

echo "min moves: $numMoves";

In this example, you don't need any knowledge of the grid, as long as you assume the start and end co-ordinates are actually within the grid.

Question 2

Perhaps not the most elegant, and could surely be simplified. But it works:

Given:

$from = 3001;
$to   = 3025;

$grids = array(
    1 => array(
        1 => 3001,
        2 => 3002,
        3 => 3003,
        4 => 3004,
        5 => 3005
    ),
    2 => array(
        1 => 3006,
        2 => 3007,
        3 => 3008,
        4 => 3009,
        5 => 3010
    ),
    3 => array(
        1 => 3011,
        2 => 3012,
        3 => 3013,
        4 => 3014,
        5 => 3015
    ),
    4 => array(
        1 => 3016,
        2 => 3017,
        3 => 3018,
        4 => 3019,
        5 => 3020
    ),
    5 => array(
        1 => 3021,
        2 => 3022,
        3 => 3023,
        4 => 3024,
        5 => 3025
    ),
);

Algorithm:

// Determine the (x,y) coordinates of $from and $to
foreach($grids as $row=>$g) {

    if (in_array($from, $g)) {
        $from_row = $row;
        foreach ($g as $col=>$val) {
            if ($val==$from)
                $from_col = $col;
        }
    }
    if (in_array($to, $g)) {
        $to_row = $row;
        foreach ($g as $col=>$val) {
            if ($val==$to)
                $to_col = $col;
        }
    }
}

// Difference between $from cols, $to cols and $from rows, $to rows
$col_diff = abs($from_col-$to_col);
$row_diff = abs($from_row-$to_row);

if ($col_diff==4) {
    $d = 5;
}
elseif ($col_diff==3) {
    if ($row_diff==4) 
        $d = 5;
    else
        $d = 4;
}
elseif ($col_diff==2) {
    if ($row_diff==4)
        $d = 5;
    elseif ($row_diff==3)
        $d = 4;
    else
        $d = 3;
}
elseif ($col_diff==1) {
    if ($row_diff==4)
        $d = 5;
    elseif ($row_diff==3)
        $d = 4;
    elseif ($row_diff==2)
        $d = 3;
    else
        $d = 2;
}
elseif ($col_diff==0) {
    if ($row_diff==4)
        $d = 5;
    elseif ($row_diff==3)
        $d = 4;
    elseif ($row_diff==2)
        $d = 3;
    elseif ($row_diff==1)
        $d = 2;
    else
        $d = 1;
}

echo $from . ' -> ' . $to . ' = ' . $d;