minor tweaks

Author: pa-kh039

dynamic_programming/largest_divisible_subset.py

@@ -1,10 +1,10 @@
 from __future__ import annotations
 
 
-def largest_divisible_subset(array):
+def largest_divisible_subset(array: list[int]) -> list[int]:
     """
-    Algorithm to find the biggest subset 
-    in the given array such that for any 
+    Algorithm to find the biggest subset
+    in the given array such that for any
     2 elements x and y in the subset,
     either x divides y or y divides x
     >>> largest_divisible_subset([1,16,7,8,4])
@@ -14,48 +14,49 @@ def largest_divisible_subset(array):
     >>> largest_divisible_subset([1, 2, 4, 8])
     [8, 4, 2, 1]
     """
-    n = len(array)
+    array_size = len(array)
 
     # Sort the array in ascending order
-    # as the sequence does not matter 
+    # as the sequence does not matter
     # we only have to pick up a subset
     array.sort()
 
-    # Initialize dp and hash arrays with 1s
-    dp = [1] * n
-    hash_arr = list(range(n))
+    # Initialize memo and hash arrays with 1s
+    memo = [1] * array_size
+    hash_array = list(range(array_size))
 
     # Iterate through the array
-    for i in range(n):
+    for i in range(array_size):
         for prev_index in range(i):
-            if array[i] % array[prev_index] == 0 and 1 + dp[prev_index] > dp[i]:
-                dp[i] = 1 + dp[prev_index]
-                hash_arr[i] = prev_index
+            if array[i] % array[prev_index] == 0 and 1 + memo[prev_index] > memo[i]:
+                memo[i] = 1 + memo[prev_index]
+                hash_array[i] = prev_index
 
     ans = -1
     last_index = -1
 
     # Find the maximum length and its corresponding index
-    for i in range(n):
-        if dp[i] > ans:
-            ans = dp[i]
+    for i in range(array_size):
+        if memo[i] > ans:
+            ans = memo[i]
             last_index = i
 
     # Reconstruct the divisible subset
     result = [array[last_index]]
-    while hash_arr[last_index] != last_index:
-        last_index = hash_arr[last_index]
+    while hash_array[last_index] != last_index:
+        last_index = hash_array[last_index]
         result.append(array[last_index])
 
     return result
 
+
 if __name__ == "__main__":
     from doctest import testmod
 
     testmod()
 
     array = [1, 16, 7, 8, 4]
 
-    ans = largest_divisible_subset(array)
+    answer = largest_divisible_subset(array)
 
-    print("The longest divisible subset elements are:", ans)
+    print("The longest divisible subset elements are:", answer)