From 1d93eb3c8b6d9ed024c3cbfff040b587e264e6d7 Mon Sep 17 00:00:00 2001
From: kosuri-indu <kosurilindu@gmail.com>
Date: Sat, 7 Oct 2023 13:15:27 +0530
Subject: [PATCH 1/2] to add the program

---
 project_euler/problem_095/__init__.py |  0
 project_euler/problem_095/sol1.py     | 59 +++++++++++++++++++++++++++
 2 files changed, 59 insertions(+)
 create mode 100644 project_euler/problem_095/__init__.py
 create mode 100644 project_euler/problem_095/sol1.py

diff --git a/project_euler/problem_095/__init__.py b/project_euler/problem_095/__init__.py
new file mode 100644
index 000000000000..e69de29bb2d1
diff --git a/project_euler/problem_095/sol1.py b/project_euler/problem_095/sol1.py
new file mode 100644
index 000000000000..e98bf72aa613
--- /dev/null
+++ b/project_euler/problem_095/sol1.py
@@ -0,0 +1,59 @@
+"""
+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() = }")
\ No newline at end of file

From ea33d4501e3aacad99c7208753512dab338cc379 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Sat, 7 Oct 2023 07:47:45 +0000
Subject: [PATCH 2/2] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 project_euler/problem_095/sol1.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/project_euler/problem_095/sol1.py b/project_euler/problem_095/sol1.py
index e98bf72aa613..c1ba1749e2c3 100644
--- a/project_euler/problem_095/sol1.py
+++ b/project_euler/problem_095/sol1.py
@@ -56,4 +56,4 @@ def solution(number: int = 10**6) -> int:
     import doctest
 
     doctest.testmod()
-    print(f"{solution() = }")
\ No newline at end of file
+    print(f"{solution() = }")