Add ShellSort implementation in Java

Java/algorithms/sorting/ShellSort.java

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+/**
+ * Algorithm: Shell Sort
+ * Description: Advanced insertion sort that uses gap sequences for improved performance
+ * Time Complexity: O(n^3/2) worst case, O(n log n) average case (depends on gap sequence)
+ * Space Complexity: O(1) - in-place sorting algorithm
+ *
+ * @author Pasan Sulakshana Rathnayake
+ * @version 1.0
+ * @since 2025-10-04
+ */
+
+import java.util.*;
+
+public class ShellSort {
+
+    /**
+     * Sorts an array using shell sort algorithm with Knuth's gap sequence.
+     *
+     * @param arr the array to be sorted
+     * @throws IllegalArgumentException if array is null
+     */
+    public static void shellSort(int[] arr) {
+        if (arr == null) {
+            throw new IllegalArgumentException("Array cannot be null");
+        }
+
+        if (arr.length <= 1) {
+            return; // Already sorted
+        }
+
+        int n = arr.length;
+
+        // Start with Knuth's gap sequence: h = 3h + 1
+        // This gives us gaps like: 1, 4, 13, 40, 121, 364, ...
+        int gap = 1;
+        while (gap < n / 3) {
+            gap = 3 * gap + 1;
+        }
+
+        // Perform shell sort with decreasing gaps
+        while (gap >= 1) {
+            // Perform insertion sort for elements at gap distance
+            for (int i = gap; i < n; i++) {
+                int temp = arr[i];
+                int j;
+
+                // Shift elements that are greater than temp
+                for (j = i; j >= gap && arr[j - gap] > temp; j -= gap) {
+                    arr[j] = arr[j - gap];
+                }
+
+                // Place temp in its correct position
+                arr[j] = temp;
+            }
+
+            // Reduce gap for next iteration
+            gap = gap / 3;
+        }
+    }
+
+    /**
+     * Alternative shell sort implementation using Shell's original gap sequence.
+     * This version uses gaps: n/2, n/4, n/8, ..., 1
+     *
+     * @param arr the array to be sorted
+     * @throws IllegalArgumentException if array is null
+     */
+    public static void shellSortOriginal(int[] arr) {
+        if (arr == null) {
+            throw new IllegalArgumentException("Array cannot be null");
+        }
+
+        if (arr.length <= 1) {
+            return;
+        }
+
+        int n = arr.length;
+
+        // Start with gap = n/2 and reduce by half each time
+        for (int gap = n / 2; gap > 0; gap /= 2) {
+            // Perform insertion sort for elements at gap distance
+            for (int i = gap; i < n; i++) {
+                int temp = arr[i];
+                int j;
+
+                // Shift elements that are greater than temp
+                for (j = i; j >= gap && arr[j - gap] > temp; j -= gap) {
+                    arr[j] = arr[j - gap];
+                }
+
+                // Place temp in its correct position
+                arr[j] = temp;
+            }
+        }
+    }
+
+
+
+    /**
+     * Test the shell sort implementation.
+     */
+    public static void main(String[] args) {
+        System.out.println("SHELL SORT ALGORITHM TESTING");
+        System.out.println("=============================");
+
+        // Test case 1: Regular array
+        int[] test1 = {64, 34, 25, 12, 22, 11, 90, 88, 76, 50, 42};
+        System.out.println("\n1. Regular array test:");
+        System.out.println("Original: " + Arrays.toString(test1));
+        shellSort(test1.clone());
+        System.out.println("Sorted:   " + Arrays.toString(test1));
+        shellSort(test1);
+        System.out.println("Verified: " + Arrays.toString(test1));
+
+        // Test case 2: Already sorted
+        int[] test2 = {1, 2, 3, 4, 5, 6, 7, 8};
+        System.out.println("\n2. Already sorted array:");
+        System.out.println("Original: " + Arrays.toString(test2));
+        shellSort(test2);
+        System.out.println("Sorted:   " + Arrays.toString(test2));
+
+        // Test case 3: Reverse sorted
+        int[] test3 = {9, 8, 7, 6, 5, 4, 3, 2, 1};
+        System.out.println("\n3. Reverse sorted array:");
+        System.out.println("Original: " + Arrays.toString(test3));
+        shellSort(test3);
+        System.out.println("Sorted:   " + Arrays.toString(test3));
+
+        // Test case 4: Array with duplicates
+        int[] test4 = {5, 2, 8, 2, 9, 1, 5, 5, 2};
+        System.out.println("\n4. Array with duplicates:");
+        System.out.println("Original: " + Arrays.toString(test4));
+        shellSort(test4);
+        System.out.println("Sorted:   " + Arrays.toString(test4));
+
+        // Test case 5: Single element
+        int[] test5 = {42};
+        shellSort(test5);
+        assert test5[0] == 42;
+
+        // Test case 6: Empty array
+        int[] test6 = {};
+        shellSort(test6);
+        assert test6.length == 0;
+
+        // Test case 7: Two elements
+        int[] test7 = {9, 3};
+        System.out.println("\n5. Two elements:");
+        System.out.println("Original: " + Arrays.toString(test7));
+        shellSort(test7);
+        System.out.println("Sorted:   " + Arrays.toString(test7));
+
+        // Test case 8: Compare gap sequences
+        int[] testOriginal = {64, 34, 25, 12, 22, 11, 90, 88, 76, 50, 42};
+        int[] testKnuth = testOriginal.clone();
+
+        System.out.println("\n6. Comparing gap sequences:");
+        System.out.println("Original array: " + Arrays.toString(testOriginal));
+
+        shellSortOriginal(testOriginal);
+        System.out.println("Shell's gaps:   " + Arrays.toString(testOriginal));
+
+        shellSort(testKnuth);
+        System.out.println("Knuth's gaps:   " + Arrays.toString(testKnuth));
+
+        System.out.println("\nAll test cases passed!");
+        System.out.println("Shell Sort advantages:");
+        System.out.println("   - Better than insertion sort for larger arrays");
+        System.out.println("   - In-place sorting (O(1) space complexity)");
+        System.out.println("   - Adaptive - performs well on partially sorted data");
+        System.out.println("   - Gap sequence affects performance significantly");
+    }
+}