feat: add algorithm 95 to find the longest amicable chain

Author: gaye-lamine

project_euler/problem_095/sol1.py

@@ -11,6 +11,7 @@
 chain.
 """
 
+
 def sum_of_proper_divisors(n):
     """Calculate the sum of proper divisors of n."""
     if n < 2:
@@ -27,11 +28,14 @@ def sum_of_proper_divisors(n):
 
     return total
 
+
 def find_longest_amicable_chain(limit):
     """Find the smallest member of the longest amicable chain under a given limit."""
     sum_divisors = {}  # Dictionary to store the sum of proper divisors for each number
     for i in range(1, limit + 1):
-        sum_divisors[i] = sum_of_proper_divisors(i)  # Calculate and store sum of proper divisors
+        sum_divisors[i] = sum_of_proper_divisors(
+            i
+        )  # Calculate and store sum of proper divisors
 
     longest_chain = []  # To store the longest amicable chain found
     seen = {}  # Dictionary to track numbers already processed
@@ -46,7 +50,9 @@ def find_longest_amicable_chain(limit):
         while current <= limit and current not in chain:
             chain.append(current)  # Add the current number to the chain
             seen[current] = True  # Mark this number as seen
-            current = sum_divisors.get(current, 0)  # Move to the next number in the chain
+            current = sum_divisors.get(
+                current, 0
+            )  # Move to the next number in the chain
 
         # Check if we form a cycle and validate the chain
         if current in chain and current != start:
@@ -57,12 +63,16 @@ def find_longest_amicable_chain(limit):
                 if len(chain) > len(longest_chain):
                     longest_chain = chain  # Update longest chain if this one is longer
 
-    return min(longest_chain) if longest_chain else None  # Return the smallest member of the longest chain
+    return (
+        min(longest_chain) if longest_chain else None
+    )  # Return the smallest member of the longest chain
+
 
 def solution():
     """Return the smallest member of the longest amicable chain under one million."""
     return find_longest_amicable_chain(10**6)
 
+
 if __name__ == "__main__":
     smallest_member = solution()  # Call the solution function
     print(smallest_member)  # Output the smallest member of the longest amicable chain