Update beautiful_arrangement.py

Author: zirea3l

dynamic_programming/beautiful_arrangement.py

@@ -10,18 +10,20 @@
 """
 # Solution using Backtracking
 
-class beautifulArrange:
+class beautifularrange:
     # funtion call; n is the size of the permutation (numbers 1..n)
-    def countArrangement(self, n: int) -> int:
+    def countarrangement(self, n: int) -> int:
 
         self.count = 0
         """
         We initialize a counter to record how many valid arrangements we find. 
-        Using self.count lets the nested function modify it without nonlocal."""
+        Using self.count lets the nested function modify it without nonlocal.
+        """
 
         used = [False] * (n + 1)
         """
-        A boolean list to mark which numbers have already been placed in the permutation.
+        A boolean list to mark which numbers have 
+        already been placed in the permutation.
         """
 
         def backtrack(pos):
@@ -32,16 +34,19 @@ def backtrack(pos):
             """
             if pos > n:
 
-                self.count += 1 # We found a complete valid arrangement, so increment the total count.
+                self.count += 1 
+                # We found a complete valid arrangement, so increment the total count.
                 return
-            for num in range(1, n + 1): # Try every candidate number num for the current position pos.
+            for num in range(1, n + 1): 
+                # Try every candidate number num for the current position pos.
 
 
                 """
                 Two checks in one:
                 1. not used[num] — the number num has not been placed yet (we can use it).
-                2. (num % pos == 0 or pos % num == 0) — the beautiful-arrangement condition: 
-                number num is compatible with position pos (either num divides pos or pos divides num).
+                2. (num % pos == 0 or pos % num == 0) — the 
+                    beautiful-arrangement condition: 
+                    either num divides pos or pos divides num.
                 If both are true, num is a valid choice for pos.
             
                 """