Update beautiful_arrangement.py

Author: zirea3l

dynamic_programming/beautiful_arrangement.py

@@ -1,11 +1,14 @@
 """
-Suppose you have n integers labeled 1 through n. A permutation of those n integers
-perm (1-indexed) is considered a "beautiful arrangement" if for every i (1 <= i <= n),
+Suppose you have n integers labeled 1 through n. 
+A permutation of those n integers
+perm (1-indexed) is considered a 
+"beautiful arrangement" if for every i (1 <= i <= n),
 either of the following is true:
 
 -> perm[i] is divisible by i.
 -> i is divisible by perm[i].
-Given an integer n, return the number of the "beautiful arrangements" that you can construct.
+Given an integer n, return the number of the 
+"beautiful arrangements" that you can construct.
 
 """
 # Solution using Backtracking
@@ -15,8 +18,10 @@ class BeautifulArrange:
     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.
+        We initialize a counter to record how 
+            many valid arrangements we find.
+        Using self.count lets the nested 
+            function modify it without nonlocal.
         """
 
         used = [False] * (n + 1)
@@ -28,7 +33,8 @@ def countarrangement(self, n: int) -> int:
         def backtrack(pos):
             """
             Define the recursive backtracking function.
-            pos is the current position in the permutation we are filling (1-indexed).
+            pos is the current position in the 
+                permutation we are filling (1-indexed).
             We try to assign a number to position pos.
             """
             if pos > n:
@@ -40,9 +46,11 @@ def backtrack(pos):
             ):  # 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).
+                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:
+                    either num divides pos or pos divides num.
                 If both are true, num is a valid choice for pos.
 
                 """