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+/*
+📘 Shell Sort Algorithm
+
+✍️ Description:
+Shell Sort is an optimization over Insertion Sort that allows the exchange of far-apart elements.
+It works by sorting elements that are a certain 'gap' apart, reducing the gap in each iteration until it becomes 1.
+At that point, the algorithm becomes a regular Insertion Sort, but since the array is already mostly sorted,
+it performs much faster.
+
+💡 Use Cases / Applications:
+- Useful for medium-sized datasets
+- Works well when memory is limited (in-place sorting)
+- Suitable when a simple but efficient improvement over insertion sort is needed
+
+📊 Complexity Analysis:
+Time Complexity:
+    • Best Case: O(n log n)
+    • Average Case: O(n^(3/2))
+    • Worst Case: O(n²)
+Space Complexity: O(1)
+    • Only a few temporary variables are used — no extra data structures.
+
+*/
+
+#include <iostream>
+#include <vector>
+using namespace std;
+
+/*
+🔹 Function: shellSort
+🔹 Parameters:
+    arr — reference to the vector of integers to be sorted
+🔹 Description:
+    Performs Shell Sort on the input array.
+*/
+void shellSort(vector<int> &arr) {
+    int n = arr.size();
+
+    // Start with a large gap and reduce it each iteration
+    for (int gap = n / 2; gap > 0; gap /= 2) {
+
+        // Perform a gapped insertion sort for this gap size
+        for (int i = gap; i < n; i++) {
+            int temp = arr[i];
+            int j;
+
+            // Shift earlier gap-sorted elements until correct location for arr[i] is found
+            for (j = i; j >= gap && arr[j - gap] > temp; j -= gap) {
+                arr[j] = arr[j - gap]; // Move element ahead by gap
+            }
+
+            arr[j] = temp; // Insert temp at correct position
+        }
+    }
+}
+
+/*
+✅ Test Cases / Examples
+Demonstrates sorting functionality on multiple inputs
+*/
+int main() {
+    // Example 1: Random elements
+    vector<int> arr1 = {12, 34, 54, 2, 3};
+    shellSort(arr1);
+    cout << "Sorted Array 1: ";
+    for (int x : arr1) cout << x << " ";
+    cout << endl;
+
+    // Example 2: Already sorted array
+    vector<int> arr2 = {1, 2, 3, 4, 5};
+    shellSort(arr2);
+    cout << "Sorted Array 2: ";
+    for (int x : arr2) cout << x << " ";
+    cout << endl;
+
+    // Example 3: Reverse order
+    vector<int> arr3 = {9, 8, 7, 6, 5};
+    shellSort(arr3);
+    cout << "Sorted Array 3: ";
+    for (int x : arr3) cout << x << " ";
+    cout << endl;
+
+    // Example 4: Single element (edge case)
+    vector<int> arr4 = {42};
+    shellSort(arr4);
+    cout << "Sorted Array 4: ";
+    for (int x : arr4) cout << x << " ";
+    cout << endl;
+
+    return 0;
+}