I am using an SplHeap to hold graph nodes of a tree with directed edges that will be traversed from the leaves to the root. For this, I precalculate the "fan-in" of nodes and put them into the heap so that I can always retrieve the node with the smallest fan-in (0) from it.
After visiting a node, I reduce the fan-in of its successor by 1. Then obviously, the heap needs to be recalculated because the successor is now in the wrong place there. I have tried recoverFromCorruption(), but it doesn't do anything and keeps the heap in the wrong order (node with larger fanIn stays in front of smaller fanIn).
As a workaround, I'm now creating a new heap after each visit, amounting to a full O(N*log(N)) sort each time.
It should be possible, however, to make up-heap operations on the changed heap entry until it's in the right position in O(log(N)).
The API for SplHeap doesn't mention an up-heap (or deletion of an arbitrary element - it could then be re-added). Can I somehow derive a class from SplHeap to do this or do I have to create a pure PHP heap from scratch?
EDIT: Code example:
class VoteGraph {
private $nodes = array();
private function calculateFanIn() { /* ... */ }
// ...
private function calculateWeights() {
$this->calculateFanIn();
$fnodes = new GraphNodeHeap(); // heap by fan-in ascending (leaves are first)
foreach($this->nodes as $n) {
// omitted: filter loops
$fnodes->insert($n);
}
// traversal from leaves to root
while($fnodes->valid()) {
$node = $fnodes->extract(); // fetch a leaf from the heap
$successor = $this->nodes[$node->successor];
// omitted: actual job of traversal
$successor->fanIn--; // will need to fix heap (sift up successor) because of this
//$fnodes->recoverFromCorruption(); // doesn't work for what I want
// workaround: rebuild $fnodes from scratch
$fixedHeap = new GraphNodeHeap();
foreach($fnodes as $e)
$fixedHeap->insert($e);
$fnodes = $fixedHeap;
}
}
}
class GraphNodeHeap extends SplHeap {
public function compare($a, $b) {
if($a->fanIn === $b->fanIn)
return 0;
else
return $a->fanIn < $b->fanIn ? 1 : -1;
}
}
Complete code also available: https://github.com/md2k7/civicracy/blob/master/civi-php/protected/components/VoteGraph.php#L73
EDIT 2:
$this->putNode(new GraphNode(4));
$this->putNode(new GraphNode(1, 2));
$this->putNode(new GraphNode(3, 2));
$this->putNode(new GraphNode(2, 4));
This means user 1 and user 3 are voting for user 2, and user 2 is voting for user 4, passing on 3 votes (2 received + his/her own). This is called delegative voting: my algorithm is passing on votes "from the bottom" (the leaves) where I already know how much weight (responsibility/representation/as you like it...) each user has.
I was solving very similar problem recently, it seems like SPL doesn't support updates. So
I had to write my own heap.
It isn't extra efficient, but it does what I need and it's much faster than sorting an array repeatedly... SPL heap is still much faster though...
here it is...
class heap
{
public $members=array();
// these two are just for statistics
private $swaps=0;
private $recurs=array('lups'=>0, 'ldowns'=>0);
public function insert($val){
if(is_array($val) && empty($this->members)){ // because heapify is (in theory) more efficient
foreach($val as $v){
$this->members[]=$v;
}
$this->heapify();
}else{
$emptyPosition=count($this->members); // count(members) gets index of first empty position, not last key
$this->members[]=$val; // puts $val in
$this->ladderup($emptyPosition);
}
}
public function heapify(){
/* in case all the heap is broken, we can always use this to repair it.
It should be more efficient to fill $members randomly and "repair" it with heapify after,
than inserting things one by one*/
$start=max(0, floor( (count($this->members)-1)/2)); // find last parent
for($i=$start;$i>=0;$i--){
$this->ladderdown($i);
}
}
private function ladderdown($index){
// recursively sifts down $index
$this->recurs['ldowns']++;
/*
indexes of children
they are stored at parent_position*2 and parent_position*2+1
but becouse php uses null-based array indexing, we have to modify it a little
*/
$iA=$index*2+1;
$iB=$index*2+2;
if($iA<count($this->members)){ // check if children exist
if($iB<count($this->members)){
if($this->compare($iA, $iB)>=0) $bigger=$iA; // if both exist, compare them, cause we want to swap with the bigger one ; I'm using ">=" here, that means if they're equal, left child is used
else $bigger=$iB;
}else{
$bigger=$iA; // if only one children exists, use it
}
if($this->compare($bigger, $index)>0){ // not using ">=" here, there's no reason to swap them if they're same
$this->swap($bigger, $index);
$this->ladderdown($bigger); // continue with $bigger because that's the position, where the bigger member was before we swap()ped it
}
}
}
private function ladderup($index){
// sift-up,
$this->recurs['lups']++;
$parent=max(0, floor( ($index-1)/2)); // find parent index; this way it actualy swaps one too many times: at the end of sift-up-ing swaps the root with itself
if($this->compare($index, $parent)>0){
$this->swap($index, $parent);
$this->ladderup($parent);
}
}
public function root(){
if(count($this->members)){
return $this->members[0];
}
return false;
}
public function extract(){
// removes and returns root member
if(!count($this->members)) return false;
$this->swap(0,count($this->members)-1); // swaps root with last member
$result=array_pop($this->members); // removes last member (now root)
$this->ladderdown(0); // root is on wrong position, sifts it down
return $result;
}
public function update($index, $value){
if($index<count($this->members)){
$this->members[$index]=$value;
$this->ladderup($index);
$this->ladderdown($index);
}
}
public function delete($index){
// removes index from heap the same way as root is extracted
$this->swap(count($this->members)-1, $index); // swaps index with last one
array_pop($this->members);
$this->ladderup($index);
$this->ladderdown($index);
}
private function swap($iA, $iB){
// swaps two members
$this->swaps++;
$swap=$this->members[$iA];
$this->members[$iA]=$this->members[$iB];
$this->members[$iB]=$swap;
}
private function compare($iA, $iB){
$result=$this->members[$iA] - $this->members[$iB];
return $result;
}
public function stats($text=""){
// prints and resets statistics
echo "STATS: $text... Sift-ups: ".$this->recurs['lups']." Sift-downs: ".$this->recurs['ldowns']." Swaps: ".$this->swaps." <br>";
$this->recurs=array('lups'=>0, 'ldowns'=>0);
$this->swaps=0;
}
}
//here's how to use it...
$h=new heap;
for($i=0; $i<10000; $i++){
$h->insert(rand(1,1000));
}
$h->stats("after inserting one-by-one");
while($biggest=$h->extract()); // note that $h->extract might return FALSE, but might return zero as well, if there was zero in the heap
$h->stats("after extracting all roots (like in heapsort)");
echo "Now, heap is empty. Let's try whole array at once <br>";
for($i=0; $i<10000; $i++){
$a[]=rand(1,1000);
}
$h->insert($a); // inserting whole array here, so heap will use more efficient heapify()
$h->stats("after heapify");
echo "let's update two indexes<br>";
$h->update(1234,44444);// sure on top
$h->stats("after update");
$h->update(8888,40000);// second place
$h->stats("after update");
echo "extract biggest three indexes<br>";
echo $h->extract()." - this should be 44444<br>";
echo $h->extract()." - this should be 40000<br>";
echo $h->extract()." - this should be biggest number given by rand(1,1000)<br>";
$h->stats("after three extracts");
while($h->extract());
$h->stats("after extracting the rest");
and result is:
STATS: after inserting one-by-one... Sift-ups: 22651 Sift-downs: 0 Swaps: 12651
STATS: after extracting all roots (like in heapsort)... Sift-ups: 0 Sift-downs: 116737 Swaps: 116737
Now, heap is empty. Let's try whole array at once
STATS: after heapify... Sift-ups: 0 Sift-downs: 12396 Swaps: 7396
let's update two indexes
STATS: after update... Sift-ups: 11 Sift-downs: 1 Swaps: 10
STATS: after update... Sift-ups: 13 Sift-downs: 1 Swaps: 12
extract biggest three indexes
44444 - this should be 44444
40000 - this should be 40000
1000 - this should be biggest number given by rand(1,1000)
STATS: after three extracts... Sift-ups: 0 Sift-downs: 42 Swaps: 42
STATS: after extracting the rest... Sift-ups: 0 Sift-downs: 116652 Swaps: 116652
You will have to modify it a bit, but anyway, hope it helps..