PHP Program - Bubble Sort

Bubble sort is the simplest sorting algorithm. The Bubble sort is based on the idea that every adjacent elements are compared and swapped if found in wrong order.

Example:

To understand the bubble sort, lets consider an unsorted array [1, 23, 10, -2] and discuss each step taken to sort the array in ascending order. In every pass, two adjacent elements are checked and swapped if found in wrong order.

First Pass: (1) and (23) are compared and found in correct order(ascending order in this case). After that (23) and (10) are compared, since (23>10), hence these numbers are swapped. Then (23) and (-2) are compared and swapped.

Second Pass: (1) and (10) are compared and found in correct order. Then (10) and (-2) are compared, since (10>-2), hence these numbers are swapped. After that (10) and (23) are compared and found in correct order.

Third Pass: (1) and (-2) are compared, since (1>-2), hence these numbers are swapped. After that (1,10) and (10,23) are checked and found in correct order.

Implementation of Bubble Sort

<?php
// function for bubble sort
function bubblesort(&$Array, $n) {
  $temp;
  for($i=0; $i<$n; $i++) {
    for($j=0; $j<$n-$i-1; $j++) {
      if($Array[$j]>$Array[$j+1]) {
        $temp = $Array[$j];
        $Array[$j] = $Array[$j+1];
        $Array[$j+1] = $temp;
      }
    }
  }
}

// function to print array
function PrintArray($Array, $n) { 
  for ($i = 0; $i < $n; $i++) 
    echo $Array[$i]." ";
  echo "\n"; 
} 

// test the code
$MyArray = array(1, 10, 23, 50, 4, 9, -4);
$n = sizeof($MyArray); 
echo "Original Array\n";
PrintArray($MyArray, $n);

bubblesort($MyArray, $n);
echo "\nSorted Array\n";
PrintArray($MyArray, $n);
?>

The above code will give the following output:

Original Array
1 10 23 50 4 9 -4 

Sorted Array
-4 1 4 9 10 23 50

Time Complexity:

The time complexity of bubble sort is Θ(N²) in all cases even if the whole array is sorted because the entire array need to be iterated for every element and it contains two nested loops.