PHP Searching and Sorting Algorithm: Patience sort

PHP Searching and Sorting Algorithm: Exercise-16 with Solution

Write a PHP program to sort a list of elements using Patience sort.
Patience sorting is a sorting algorithm inspired by and named after, the card game patience. A variant of the algorithm efficiently computes the length of a longest increasing subsequence in a given array.
The algorithm's name derives from a simplified variant of the patience card game. This game begins with a shuffled deck of cards. These cards are dealt one by one into a sequence of piles on the table, according to the following rules.

• Initially, there are no piles. The first card dealt forms a new pile consisting of the single card.
• Each subsequent card is placed on the leftmost existing pile whose top card has a value greater than or equal the new card's value, or to the right of all of the existing piles, thus forming a new pile.
• When there are no more cards remaining to deal, the game ends.

This card game is turned into a two-phase sorting algorithm, as follows. Given an array of n elements from some totally ordered domain, consider this array as a collection of cards and simulate the patience sorting game. When the game is over, recover the sorted sequence by repeatedly picking off the minimum visible card; in order words, perform an p-way merge of the p piles, each of which is internally sorted.

Sample Solution :

PHP Code :

<?php
class PilesHeap extends SplMinHeap {
    public function compare($pile1, $pile2) {
        return parent::compare($pile1->top(), $pile2->top());
    }
}
function patience_sort($n) {
    $piles = array();
    // sort into piles
    foreach ($n as $x) {
        // binary search
        $low = 0; $high = count($piles)-1;
        while ($low <= $high) {
            $mid = (int)(($low + $high) / 2);
            if ($piles[$mid]->top() >= $x)
                $high = $mid - 1;
            else
                $low = $mid + 1;
        }
        $i = $low;
        if ($i == count($piles))
            $piles[] = new SplStack();
        $piles[$i]->push($x);
    }
     // priority queue allows us to merge piles efficiently
    $heap = new PilesHeap();
    foreach ($piles as $pile)
        $heap->insert($pile);
    for ($c = 0; $c < count($n); $c++) {
        $smallPile = $heap->extract();
        $n[$c] = $smallPile->pop();
        if (!$smallPile->isEmpty())
        $heap->insert($smallPile);
    }
    assert($heap->isEmpty());
}
$a = array(100, 54, 7, 2, 5, 4, 1);
patience_sort($a);
print_r($a);
?>

Sample Output:

Array                                                               
(                                                                   
    [0] => 100                                                      
    [1] => 54                                                       
    [2] => 7                                                        
    [3] => 2                                                        
    [4] => 5                                                        
    [5] => 4                                                        
    [6] => 1                                                        
)                 

Flowchart :

PHP Code Editor:

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