feat: add algorithm 95 to find the longest amicable chain

Author: gaye-lamine

project_euler/problem_095/sol1.py

@@ -11,31 +11,43 @@
 chain.
 """
 
-
-def sum_of_proper_divisors(n):
-    """Calculate the sum of proper divisors of n."""
-    if n < 2:
+def sum_of_proper_divisors(number: int) -> int:
+    """Calculate the sum of proper divisors of the given number.
+
+    >>> sum_of_proper_divisors(6)
+    6
+    >>> sum_of_proper_divisors(28)
+    28
+    >>> sum_of_proper_divisors(12)
+    16
+    >>> sum_of_proper_divisors(1)
+    0
+    """
+    if number < 2:
         return 0  # Proper divisors of 0 and 1 are none.
-    total = 1  # Start with 1, since it is a proper divisor of any n > 1
-    sqrt_n = int(n**0.5)  # Calculate the integer square root of n.
+    total = 1  # Start with 1, since it is a proper divisor of any number > 1
+    sqrt_n = int(number**0.5)  # Calculate the integer square root of number.
 
-    # Loop through possible divisors from 2 to the square root of n
+    # Loop through possible divisors from 2 to the square root of number
     for i in range(2, sqrt_n + 1):
-        if n % i == 0:  # Check if i is a divisor of n
+        if number % i == 0:  # Check if i is a divisor of number
             total += i  # Add the divisor
-            if i != n // i:  # Avoid adding the square root twice
-                total += n // i  # Add the corresponding divisor (n/i)
+            if i != number // i:  # Avoid adding the square root twice
+                total += number // i  # Add the corresponding divisor (number/i)
 
     return total
 
+def find_longest_amicable_chain(limit: int) -> int:
+    """Find the smallest member of the longest amicable chain under a given limit.
 
-def find_longest_amicable_chain(limit):
-    """Find the smallest member of the longest amicable chain under a given limit."""
+    >>> find_longest_amicable_chain(10**3)
+    624
+    >>> find_longest_amicable_chain(10**6)
+    14316
+    """
     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
@@ -50,9 +62,7 @@ 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:
@@ -63,16 +73,16 @@ 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() -> int:
+    """Return the smallest member of the longest amicable chain under one million.
 
-def solution():
-    """Return the smallest member of the longest amicable chain under one million."""
+    >>> solution()
+    14316
+    """
     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