Insertion Sort - Implementation in PHP

This section provides a tutorial on how to implement the Insertion Sort algorithm with the binary search method in PHP.

Insertion Sort is a simple and slow sorting algorithm that repeatedly takes the next element from the un-sorted section and inserts it into the sorted section at the correct position.

The basic idea of Insertion 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. Take an element from the un-sorted section.

3. Insert the element into the sorted section at the correct position based on the comparable property.

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

The idea of insertion sort comes from our daily life experiences. For example, when you play cards with your friends, you will insert the next card you pick into the sorted cards in your hand.

Here is my PHP implementation of the Insertion Sort algorithm in the Sort_Functions.php script. The binary search method was used to find the target of the insertiong in the sorted section.

<?php
#- Sort_Functions.php
#- Copyright (c) HerongYang.com. All Rights Reserved.
#-
function insertionSort(&$a, $fromIndex, $toIndex) {
  for ($i=$fromIndex+1; $i<$toIndex; $i++) {
    $d = $a[$i];
    $jLeft = $fromIndex; # left index of the target range for insertion
    $jRight = $i-1;      # right index of the target range for insertion
    if ($a[$jRight]>$d) { # insertion is needed
      while ($jRight-$jLeft>=2) { # bring the target range to 1 or 2
        $jMiddle = intval(($jRight-$jLeft)/2) + $jLeft - 1;
        if (($a[$jMiddle])>$d) {
          $jRight = $jMiddle;
        } else {
          $jLeft = $jMiddle + 1;
        }
      }
      if ($jRight-$jLeft==1) { # bring the target range to 1
        $jMiddle = $jLeft;
        if (($a[$jMiddle])>$d) {
           $jRight = $jMiddle;
        } else {
           $jLeft = $jMiddle + 1;
        }
      }
      for ($j=$i; $j>$jLeft; $j--) { # the target of insertion is jLeft
        $a[$j] = $a[$j-1];
      }
      $a[$j] = $d;
    }
  }
}

# Functions for other sorting algorithms ...
?>

The following diagram illustrates how this implementation works:

                             ----------24   4  53   ...            42
                            |               |   |                   |
        +-----------+---+---+---+---+---+---+---+-------------------+
        |           |   |    /   /   /
        5   ...    17  20  29  36  39
        |           |   |   |           |                           |
fromIndex             j-1   j           i                   toIndex-1

Note that:

Here are the performance test results of insertionSort() function using PHP 5.6. The execution of insertionSort() is so slow. I have to reduce the number of tests to 10 to avoid long waiting time.

Array size: 10000
Average sorting time: 2212.8 milliseconds
Number of tests: 10
Performance: 221.28 O(N) microseconds
Performance: 16.652979360131 O(N*Log2(N)) microseconds
Performance: 0.022128 O(N*N) microseconds

Array size: 20000
Average sorting time: 9484.1 milliseconds
Number of tests: 10
Performance: 474.205 O(N) microseconds
Performance: 33.189707869452 O(N*Log2(N)) microseconds
Performance: 0.02371025 O(N*N) microseconds

Array size: 30000
Average sorting time: 23328.8 milliseconds
Number of tests: 10
Performance: 777.62666666667 O(N) microseconds
Performance: 52.285595760466 O(N*Log2(N)) microseconds
Performance: 0.025920888888889 O(N*N) microseconds

The results showed us that the performance of insertion method is O(N*N), because the last performance line gave me a constant, when I increased the array size.

Here is the comparison of insertionSort() performance with 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

Table of Contents

 About This Book

 Introduction of Sorting Algorithms

 Java API for Sorting Algorithms

 Insertion Sort Algorithm and Java Implementation

 Selection Sort Algorithm and Java Implementation

 Bubble Sort Algorithm and Java Implementation

 Quicksort Algorithm and Java Implementation

 Merge Sort Algorithm and Java Implementation

 Heap Sort Algorithm and Java Implementation

 Shell Sort Algorithm and Java Implementation

Sorting Algorithms Implementations in PHP

 Sort_Test.php - Sorting Performance Test

Insertion Sort - Implementation in PHP

 Selection Sort - Implementation in PHP

 Bubble Sort - Implementation in PHP

 Quicksort - Implementation in PHP

 Merge Sort - Implementation in PHP

 Heap Sort - Implementation in PHP

 Shell Sort - Implementation in PHP

 Sorting Algorithms Implementations in Perl

 Sorting Algorithms Implementations in Python

 Performance Summary of All Implementations

 References

 Full Version in PDF/EPUB