Add shell sort (#154)

* add shell sort * updating DIRECTORY.md * rename shell sort test class * updating DIRECTORY.md --------- Co-authored-by: dongio99 <[email protected]>
TheAlgorithms · Jul 25, 2024 · e679135 · e679135
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diff --git a/DIRECTORY.md b/DIRECTORY.md
@@ -83,6 +83,7 @@
   * [Quicksort](./Sorting/QuickSort.php)
   * [Radixsort](./Sorting/RadixSort.php)
   * [Selectionsort](./Sorting/SelectionSort.php)
+  * [Shellsort](./Sorting/ShellSort.php)
 
 ## Strings
   * [Checkanagram](./Strings/CheckAnagram.php)
@@ -123,6 +124,7 @@
   * Sorting
     * [Arraykeyssorttest](./tests/Sorting/ArrayKeysSortTest.php)
     * [Gnomesorttest](./tests/Sorting/GnomeSortTest.php)
+    * [Shellsorttest](./tests/Sorting/ShellSortTest.php)
     * [Sortingtest](./tests/Sorting/SortingTest.php)
   * Strings
     * [Stringstest](./tests/Strings/StringsTest.php)

diff --git a/Sorting/ShellSort.php b/Sorting/ShellSort.php
@@ -0,0 +1,53 @@
+<?php
+
+/**
+ * Shell Sort
+ * This function sorts an array in ascending order using the Shell Sort algorithm.
+ * Time complexity of the Shell Sort algorithm depends on the gap sequence used.
+ * With Knuth's sequence, the time complexity is O(n^(3/2)).
+ *
+ *
+ * @param array $array
+ * @return array
+ */
+
+function shellSort(array $array): array
+{
+    $length = count($array);
+    $series = calculateKnuthSeries($length);
+
+    foreach ($series as $gap) {
+        for ($i = $gap; $i < $length; $i++) {
+            $temp = $array[$i];
+            $j = $i;
+
+            while ($j >= $gap && $array[$j - $gap] > $temp) {
+                $array[$j] = $array[$j - $gap];
+                $j -= $gap;
+            }
+
+            $array[$j] = $temp;
+        }
+    }
+
+    return $array;
+}
+
+/**
+ * Calculate Knuth's series
+ *
+ * @param int $n Size of the array
+ * @return array
+ */
+function calculateKnuthSeries(int $n): array
+{
+    $h = 1;
+    $series = [];
+
+    while ($h < $n) {
+        array_unshift($series, $h);
+        $h = 3 * $h + 1;
+    }
+
+    return $series;
+}
diff --git a/tests/Sorting/ShellSortTest.php b/tests/Sorting/ShellSortTest.php
@@ -0,0 +1,80 @@
+<?php
+
+namespace Sorting;
+
+use PHPUnit\Framework\TestCase;
+
+require_once __DIR__ . '/../../vendor/autoload.php';
+require_once __DIR__ . '/../../Sorting/ShellSort.php';
+
+class ShellSortTest extends TestCase
+{
+    public function testShellSort()
+    {
+        $array = [
+            51158, 1856, 8459, 67957, 59748, 58213, 90876, 39621, 66570, 64204, 79935, 27892, 47615, 94706, 34201,
+            74474, 63968, 4337, 43688, 42685, 31577, 5239, 25385, 56301, 94083, 23232, 67025, 44044, 74813, 34671,
+            90235, 65764, 49709, 12440, 21165, 20620, 38265, 12973, 25236, 93144, 13720, 4204, 77026, 42348, 19756,
+            97222, 78828, 73437, 48208, 69858, 19713, 29411, 49809, 66174, 5257, 43340, 40565, 9592, 52328, 16677,
+            38386, 55416, 99519, 13732, 84076, 52905, 47662, 31805, 46184, 2811, 35374, 50800, 53635, 51886, 49052,
+            75197, 3720, 75045, 28309, 63771, 71526, 16122, 36625, 44654, 86814, 98845, 44637, 54955, 24714, 81960,
+            78095, 49048, 99711, 272, 45755, 31919, 8181, 1392, 15352, 82656, 27760, 18362, 43780, 50209, 51433, 2847,
+            62310, 87450, 22874, 40789, 56841, 52928, 5523, 76474, 8935, 63245, 16387, 21746, 47596, 84402, 49168,
+            58223, 26993, 55908, 92837, 64208, 86309, 30819, 83638, 9508, 44628, 10786, 68125, 14123, 70474, 50596,
+            44518, 74872, 61968, 36828, 17860, 4605, 68756, 86070, 52068, 51830, 56992, 45799, 42422, 68514, 92559,
+            40206, 31263, 71774, 14202, 94807, 25774, 15003, 54211, 18708, 32074, 43836, 48964, 40742, 26281, 67338,
+            75786, 34925, 34649, 45519, 72472, 80188, 40858, 83246, 92215, 66178, 67452, 86198, 82300, 45894, 97156,
+            73907, 31159, 7018, 55549, 35245, 68975, 88246, 14098, 59973, 7762, 40459, 86358, 63178, 47489, 55515,
+            79488, 46528, 99272, 10867, 75190, 56963, 5520, 56494, 42310, 40171, 78105, 29724, 30110, 28493, 36141,
+            22479, 85799, 70466, 92106, 16868, 57402, 4813, 47432, 24689, 78533, 97577, 32178, 30258, 82785, 56063,
+            76277, 96407, 77849, 1807, 45344, 30298, 18158, 49935, 90728, 22192, 36852, 33982, 66206, 30948, 40372,
+            33446, 99156, 28651, 61591, 79028, 1689, 94257, 32158, 11122, 81097, 57981, 26277, 7515, 7873, 8350, 28229,
+            24105, 76818, 86897, 18456, 29373, 7853, 24932, 93070, 4696, 63015, 9358, 28302, 3938, 11754, 33679, 18492,
+            91503, 63395, 12029, 23954, 27230, 58336, 16544, 23606, 61349, 37348, 78629, 96145, 57954, 32392, 76201,
+            54616, 59992, 5676, 97799, 47910, 98758, 75043, 72849, 6466, 68831, 2246, 69091, 22296, 6506, 93729, 86968,
+            39583, 46186, 96782, 19074, 46574, 46704, 99211, 55295, 33963, 77977, 86805, 72686
+        ];
+        $sorted = shellSort($array);
+        $this->assertEquals([
+            272, 1392, 1689, 1807, 1856, 2246, 2811, 2847, 3720, 3938, 4204, 4337, 4605, 4696, 4813, 5239, 5257, 5520,
+            5523, 5676, 6466, 6506, 7018, 7515, 7762, 7853, 7873, 8181, 8350, 8459, 8935, 9358, 9508, 9592, 10786,
+            10867, 11122, 11754, 12029, 12440, 12973, 13720, 13732, 14098, 14123, 14202, 15003, 15352, 16122, 16387,
+            16544, 16677, 16868, 17860, 18158, 18362, 18456, 18492, 18708, 19074, 19713, 19756, 20620, 21165, 21746,
+            22192, 22296, 22479, 22874, 23232, 23606, 23954, 24105, 24689, 24714, 24932, 25236, 25385, 25774, 26277,
+            26281, 26993, 27230, 27760, 27892, 28229, 28302, 28309, 28493, 28651, 29373, 29411, 29724, 30110, 30258,
+            30298, 30819, 30948, 31159, 31263, 31577, 31805, 31919, 32074, 32158, 32178, 32392, 33446, 33679, 33963,
+            33982, 34201, 34649, 34671, 34925, 35245, 35374, 36141, 36625, 36828, 36852, 37348, 38265, 38386, 39583,
+            39621, 40171, 40206, 40372, 40459, 40565, 40742, 40789, 40858, 42310, 42348, 42422, 42685, 43340, 43688,
+            43780, 43836, 44044, 44518, 44628, 44637, 44654, 45344, 45519, 45755, 45799, 45894, 46184, 46186, 46528,
+            46574, 46704, 47432, 47489, 47596, 47615, 47662, 47910, 48208, 48964, 49048, 49052, 49168, 49709, 49809,
+            49935, 50209, 50596, 50800, 51158, 51433, 51830, 51886, 52068, 52328, 52905, 52928, 53635, 54211, 54616,
+            54955, 55295, 55416, 55515, 55549, 55908, 56063, 56301, 56494, 56841, 56963, 56992, 57402, 57954, 57981,
+            58213, 58223, 58336, 59748, 59973, 59992, 61349, 61591, 61968, 62310, 63015, 63178, 63245, 63395, 63771,
+            63968, 64204, 64208, 65764, 66174, 66178, 66206, 66570, 67025, 67338, 67452, 67957, 68125, 68514, 68756,
+            68831, 68975, 69091, 69858, 70466, 70474, 71526, 71774, 72472, 72686, 72849, 73437, 73907, 74474, 74813,
+            74872, 75043, 75045, 75190, 75197, 75786, 76201, 76277, 76474, 76818, 77026, 77849, 77977, 78095, 78105,
+            78533, 78629, 78828, 79028, 79488, 79935, 80188, 81097, 81960, 82300, 82656, 82785, 83246, 83638, 84076,
+            84402, 85799, 86070, 86198, 86309, 86358, 86805, 86814, 86897, 86968, 87450, 88246, 90235, 90728, 90876,
+            91503, 92106, 92215, 92559, 92837, 93070, 93144, 93729, 94083, 94257, 94706, 94807, 96145, 96407, 96782,
+            97156, 97222, 97577, 97799, 98758, 98845, 99156, 99211, 99272, 99519, 99711
+        ], $sorted);
+    }
+
+    public function testShellSortWithEmptyInput()
+    {
+        $array = [];
+        $sorted = shellSort($array);
+        $this->assertEmpty($sorted);
+    }
+
+    public function testShellSortPerformance()
+    {
+        $array = range(1, 10000);
+        $n = count($array);
+        shuffle($array);  // Randomize the order
+        $start = microtime(true);
+        shellSort($array);
+        $end = microtime(true);
+        $this->assertLessThan(pow($n, 3 / 2), $end - $start);
+    }
+}