Added cyclic sort

Author: Kartikay

CPP/basic_programs/cyclic_sort.cpp

@@ -2,35 +2,72 @@
 #include <vector>
 using namespace std;
 
+/*
+-----------------------------------------------------
+🌀 Cyclic Sort Algorithm
+-----------------------------------------------------
+📌 Description:
+Cyclic Sort is an in-place algorithm used to sort an
+array containing numbers in the range [1...n] (or [0...n-1])
+without duplicates. The idea is to place each element
+at its correct index (index = value - 1) by swapping
+until the array is sorted.
+
+📊 Complexity Analysis:
+- Time Complexity: O(n)
+  Each element is swapped at most once to its correct position.
+- Space Complexity: O(1)
+  No extra data structures are used, sorting is in-place.
+
+✅ Applications:
+- Sorting numbers in the range [1...n]
+- Finding missing or duplicate numbers in arrays
+- Common in coding interview problems
+-----------------------------------------------------
+*/
+
+// Function to perform cyclic sort
 void cyclicSort(vector<int>& nums) {
     int i = 0;
     int n = nums.size();
     while (i < n) {
-        int correctIndex = nums[i] - 1;
+        int correctIndex = nums[i] - 1; // correct index for current element
+
+        // Swap only if element is in range and not at the right place
         if (nums[i] >= 1 && nums[i] <= n && nums[i] != nums[correctIndex]) {
             swap(nums[i], nums[correctIndex]);
         } else {
-            i++;
+            i++; // move to next index if already in correct position
         }
     }
 }
 
-void print(vector<int>& nums){
-    cout<<"Sorted array is:"<<endl;
-
-    for(auto i:nums){
-        cout<<i<<" "<<endl;
+// Utility function to print array
+void print(vector<int>& nums) {
+    cout << "Sorted array is:" << endl;
+    for (auto i : nums) {
+        cout << i << " ";
     }
+    cout << endl;
 }
+
+// Driver function
 int main() {
-    cout<<"This is cyclic sort code. Cyclic sort works from 1 to n or 0 to n-1 without duplicates."<<endl;
+    cout << "This is Cyclic Sort implementation." << endl;
+    cout << "Cyclic Sort works efficiently when numbers are in the range [1...n] or [0...n-1] without duplicates." << endl;
+
     int n;
-    cout<<"Enter value of n"<<endl;
-    cin>>n;
-    vector<int> nums(n,0);
-    for(int i=0;i<n;i++)
-    cin>>nums[i];
+    cout << "Enter value of n: ";
+    cin >> n;
+
+    vector<int> nums(n, 0);
+    cout << "Enter " << n << " elements:" << endl;
+    for (int i = 0; i < n; i++) {
+        cin >> nums[i];
+    }
+
     cyclicSort(nums);
     print(nums);
+
     return 0;
 }