Project euler 95

Author: kosuri-indu

project_euler/problem_095/__init__.py

@@ -0,0 +1,38 @@
+"""
+Problem 95
+Url: https://projecteuler.net/problem=95
+"""
+def find_smallest_member(n: int) -> int:
+    """
+    Returns the smallest member of the longest amicable chain with no element exceeding one million
+    >> 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__":
+    print(f"Solution : {find_smallest_member(10**6)}")