Bubble Sort - Implementation in PHP

This section provides a tutorial on how to implement the Bubble Sort algorithm in PHP.

Bubble Sort is a simple and slow sorting algorithm that repeatedly steps through the collection, compares each pair of adjacent elements and swaps them if they are in the wrong order.

The basic idea of Bubble Sort algorithm can be described as these steps:

1. Data elements are grouped into two sections: a sorted section and an un-sorted section.

2. Go through every element in the un-sorted section and re-arrange its position with its neighbor to put the element with higher order on the higher position. At the end, the element with the highest order will be on top of the un-sorted section, and moved to the bottom of the sorted section.

3. Repeat step 2 until no more elements left in the un-sorted section.

In the sorting algorithm, if you watch the move of the elements with higher orders, they are like bubbles in the water, floating slowly from the bottom to the top.

Here is my PHP implementation of Bubble Sort algorithm:

```<?php
#- Sort_Functions.php
#-
function bubbleSort(&\$a, \$fromIndex, \$toIndex) {
for (\$i=\$toIndex-1; \$i>\$fromIndex; \$i--) {
\$isSorted = true;
for (\$j=\$fromIndex; \$j<\$i; \$j++) {
if ((\$a[\$j])>\$a[\$j+1]) {
\$isSorted = false;
\$d = \$a[\$j+1];
\$a[\$j+1] = \$a[\$j];
\$a[\$j] = \$d;
}
}
if (\$isSorted) break;
}
}
# Functions for other sorting algorithms ...
?>
```

The following diagram illustrates how this implementation works:

```
--17  42  53  67  ...         92
|       |   |   |               |
+---+---+---------------+---+---+---+---+---+---------------+
|   |                   |     /
29  36  11   ...        24  39
|                           |   |                           |
fromIndex                           j   i                   toIndex-1
```

Note that:

• Elements to be sorted are stored from "fromIndex" to "toIndex-1" inclusive.
• At the beginning of each iteration of loop "i", elements from "i+1" to "toIndex-1" are sorted.
• At the beginning of each iteration of loop "i", elements from "fromIndex" to "j+1" are not sorted.
• At the end of each iteration of loop "i", element at "i" will be the element with the highest order in the un-sorted section.
• The "break" statement is there just in case when the un-sorted section happen to be already sorted.

Here are the performance test results of bubbleSort() function using PHP 5.6.

```Array size: 10000
Average sorting time: 6846.6 milliseconds
Number of tests: 10
Performance: 684.66 O(N) microseconds
Performance: 51.525799207825 O(N*Log2(N)) microseconds
Performance: 0.068466 O(N*N) microseconds

Array size: 20000
Average sorting time: 28426.6 milliseconds
Number of tests: 5
Performance: 1421.33 O(N) microseconds
Performance: 99.479186187595 O(N*Log2(N)) microseconds
Performance: 0.0710665 O(N*N) microseconds

Array size: 30000
Average sorting time: 66524 milliseconds
Number of tests: 1
Performance: 2217.4666666667 O(N) microseconds
Performance: 149.09669474509 O(N*Log2(N)) microseconds
Performance: 0.073915555555556 O(N*N) microseconds
```

Here is the comparison of bubbleSort() performance with other sorting functions. As you can see, Bubble Sort is much slower than other sorting functions.

```Array Size        10000   20000   30000   100000   200000   300000
----------        -----   -----   -----   ------   ------   ------
JDK Arrays.sort                               25       66      112
PHP sort()            3       7      13       75
Insertion Sort     2213    9484   23329
Selection Sort     3580   14129   33808
Bubble Sort        6847   28427   66524
```