Create cycle_Sort.dart

sort/cycle_Sort.dart

@@ -0,0 +1,54 @@
+void cycleSort(List<int> arr) {
+  int n = arr.length;
+
+  for (int cycleStart = 0; cycleStart < n - 1; cycleStart++) {
+    int item = arr[cycleStart];
+    int pos = cycleStart;
+
+    // Find the position to place the current item
+    for (int i = cycleStart + 1; i < n; i++) {
+      if (arr[i] < item) {
+        pos++;
+      }
+    }
+
+    // Skip if the item is already in its correct position
+    if (pos == cycleStart) {
+      continue;
+    }
+
+    // Place the item in its correct position
+    while (item == arr[pos]) {
+      pos++;
+    }
+    int temp = arr[pos];
+    arr[pos] = item;
+    item = temp;
+
+    // Rotate the rest of the cycle
+    while (pos != cycleStart) {
+      pos = cycleStart;
+      for (int i = cycleStart + 1; i < n; i++) {
+        if (arr[i] < item) {
+          pos++;
+        }
+      }
+
+      while (item == arr[pos]) {
+        pos++;
+      }
+      temp = arr[pos];
+      arr[pos] = item;
+      item = temp;
+    }
+  }
+}
+
+void main() {
+  List<int> arr = [64, 34, 25, 12, 22, 11, 90];
+  print("Original List: $arr");
+
+  cycleSort(arr);
+
+  print("Sorted List: $arr");
+}