add : Project Euler 95 solution

project_euler/problem_095/sol1.py

@@ -0,0 +1,41 @@
+"""
+Problem 95
+Url: https://projecteuler.net/problem=95
+"""
+def solution(n: int = 10**6) -> int:
+    """
+    Returns the smallest member when n = 1000000
+    >> 14316
+    """
+
+    sum_of_div = [0] * (n + 1)
+    for i in range(1, n // 2 + 1):
+        for j in range(i * 2, n + 1, i):
+            sum_of_div[j] += i
+
+    checked = [False] * (n + 1)
+    max_len_of_chain = 0
+    result = 0
+    for i in range(2, n + 1):
+        possible_chain = []
+        j = i
+        while not checked[j]:
+            checked[j] = True
+            possible_chain.append(j)
+            j = sum_of_div[j]
+            if j > n:
+                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() = }")