Posted by Csaba Gabor on 12/02/07 22:07

Shane is given an edge array ($aEdges) and wants to
know the distinct connected components. This can be done
by my function connectedComponents($aEdges). The first
part walks each edge once to build an adjacency array.
The second part, which does the real work, picks an
unvisited edge and visits each vertex it can get to from
that selected vertex, processing each edge once, so that
the total running time is O(E). It'd be O(V+E) for the
second part, if singletons (isolated vertices) were
to have been allowed.

Csaba Gabor from Vienna


function connectedComponents ($aEdges) {
// given an edge array, $aEdges, this will return an array
// of connected components. Each element of the returned
// array, $aTrees, will correspond to one component and
// have an array of the vertices in that component.
$aAdj = array(); $aTree = array(); $ctr=-1;
foreach ($aEdges as $br) // Construct V/E adjacancy array
foreach ($br as $i=>$v) {
if (!array_key_exists($v,$aAdj)) $aAdj[$v]=array($br[1-$i]);
else array_push ($aAdj[$v], $br[1-$i]); }

foreach ($aAdj as $v => &$aTrees[++$ctr]) // Now build distinct
for ($i=0;$i<sizeof($aTrees[$ctr]);++$i) { // components
$aV = array_keys(array_flip(array_merge(
$aV = &$aTrees[$ctr], $aAdj[$aV[$i]])));
unset ($aAdj[$aV[$i]]); }

return $aTrees; }


//Example usage:
$aEdges = array(array (30, 31), array (29, 26),
array (29, 27), array (29, 28),
array (26, 27), array (27, 28));
$aComponents = connectedComponents ($aEdges);


//Example 2:
$aEdges = array(
array (a, b), array (b, d), array (b, e),
array (d, g), array (c, i), array (e, h),
array (h, j), array (c, f), array (f, i),
array (g, j), array (j, k), array(j, b));
$aComponents = connectedComponents ($aEdges);



On Dec 2, 6:33 pm, LittleCake <shaneda...@gmail.com> wrote:
> Hi All,
> I have a multidimensional array where each sub-array contains just two
> entries, which indicates a relationship between those two entries. for
> example the first sub-array:
> [0] => Array
> (
> [0] => 30
> [1] => 31
> )
>
> This states that value 30 is related to 31. I would like to search
> through the entire multidimensional array (it could be empty or
> contain hundreds of entries), to see if multiple relationships exist
> and hence group these relationships into one entry. so for the array
> below:
>
> Array
> (
> [0] => Array
> (
> [0] => 30
> [1] => 31
> )
>
> [1] => Array
> (
> [0] => 29
> [1] => 26
> )
>
> [2] => Array
> (
> [0] => 29
> [1] => 27
> )
>
> [3] => Array
> (
> [0] => 29
> [1] => 28
> )
>
> [4] => Array
> (
> [0] => 26
> [1] => 27
> )
>
> [5] => Array
> (
> [0] => 27
> [1] => 28
> )
> )
>
> This should be represented as:
> Array
> (
> [0] => Array
> (
> [0] => 30
> [1] => 31
> )
>
> [1] => Array
> (
> [0] => 29
> [1] => 26
> [2] => 27
> [3] => 28
> )
> )
>
> I am new enough to PHP so I would appreciate your help.
> Thanks

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