<?php
 
$result= <<<XML
<?xml version='1.0' encoding='WINDOWS-1251'?>
<categories>
    <category id="20001" >Сетевое оборудование</category>
    <category id="20002" >Контроль доступа</category>
    <category id="20003" >Видеонаблюдение</category>
    <category id="20004" >Источники питания</category>
    <category id="20011"  parentId="20004" >Аккумуляторы</category>
    <category id="20012"  parentId="20003" >Аналоговые видеокамеры</category>
    <category id="20013"  parentId="20002" >Считыватели</category>
    <category id="21247"  parentId="20001" >GOAL city</category>
    <category id="20326"  parentId="20013" >Komkom</category>
    <category id="20400"  parentId="20012" >HikVision</category>
    <category id="20618"  parentId="20011" >ITV</category>
    <category id="20619"  parentId="20011" >ISS</category>
    <category id="20620"  parentId="20011" >DSSL</category>
</categories>
XML;
 
$text =	iconv('UTF-8', 'CP1251', $result);
 
$xml = simplexml_load_string($text);
 
$tree = [];
$count = count($xml);
 
/********************************************
* Функции для помощи в построениии крошек
*******************************************/
function haveChild($tree, $id) {
	foreach ($tree as $item) {
		if (isset($item['parentId']) && $item['parentId'] == $id) {
			return true;
		}
	}
 
	return false;	
}
 
 
function buildBreadcrumbs($tree, $elem, $level) {
 
	$breadcrumbs = $elem['text'];
	if (isset($elem['parentId'])) {
		$item = [];
		for ($i = 0; $i < count($tree); ++$i) {
			if ($elem['parentId'] == $tree[$i]['id']) {
				$item = $tree[$i];				
				break;
			}				
		}
 
		$tmp = $breadcrumbs; 
		$arrow = ($level == 0 ? '' : ' > ' );
		$level = $level + 1;
		$breadcrumbs = buildBreadcrumbs($tree, $item, $level).$tmp.$arrow; 
		$level = $level - 1;		
	}
 
	return $breadcrumbs;
}
 
/**********************************************/
 
 
 
// формируем массив из xml структуры 
for ($i = 0; $i < $count; ++$i) {				
	$arr = [];
	$attr = $xml->category[$i]->attributes();		
 
	$arr['id'] = (int)$attr->id;
	$arr['parentId'] = (int)$attr->parentId;
	$arr['text'] = (string)$xml->category[$i];
 
	$tree[$i] = $arr;	
}
 
$breadcrumbsArray = [];
foreach ($tree as $item) {
	// Если у узла нет потомка, значит это крайний узел. 
	// Будем строить путь до него
	if (!haveChild($tree, $item['id'])) {
		$breadcrumbsArray[$item['id']] = buildBreadcrumbs($tree, $item, 0);
	}
}
 
echo '<pre>';
print_r($breadcrumbsArray); 
//print_r($tree); 
echo '</pre>';

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