add : Project Euler 95 solution

project_euler/problem_095/sol1.py

@@ -0,0 +1,61 @@
+"""
+Problem 95
+Url: https://projecteuler.net/problem=95
+Statement:
+The proper divisors of a number are all the divisors excluding the number itself.
+For example, the proper divisors of  28 is 1,2,4,7 and 14.
+As the sum of these divisors is equal to 28, we call it a perfect number.
+
+Interestingly the sum of the proper divisors of 220 is 284.
+The sum of the proper divisors of 284 is 220 forming a chain of two numbers.
+For this reason, 220 and 284 are called an amicable pair.
+Perhaps less well known are longer chains.
+For example, starting with 12496, we form a chain of five numbers:
+12496 -> 14288 -> 15472 -> 14536 -> 14264(->12496 -> ....)
+Since this chain returns to its starting point, it is called an amicable chain.
+
+Find the smallest member of the longest amicable chain with ..
+no element exceeding one million.
+"""
+
+
+def solution(number: int = 10**6) -> int:
+    """
+    Returns the smallest member when n = 1000000
+    >>> solution(1000000)
+    14316
+    >>> solution(5000)
+    220
+    """
+
+    sum_of_div = [0] * (number + 1)
+    for i in range(1, number // 2 + 1):
+        for j in range(i * 2, number + 1, i):
+            sum_of_div[j] += i
+
+    checked = [False] * (number + 1)
+    max_len_of_chain = 0
+    result = 0
+    for i in range(2, number + 1):
+        possible_chain = []
+        j = i
+        while not checked[j]:
+            checked[j] = True
+            possible_chain.append(j)
+            j = sum_of_div[j]
+            if j > number:
+                break
+            if j in possible_chain:
+                len_of_chain = len(possible_chain) - possible_chain.index(j)
+                if len_of_chain > max_len_of_chain:
+                    max_len_of_chain = len_of_chain
+                    result = min(possible_chain[-len_of_chain:])
+                break
+    return result
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+    print(f"{solution() = }")