From 320f8f2d8c482f8a8084c0e162c69c1af90298e4 Mon Sep 17 00:00:00 2001
From: kosuri-indu <kosurilindu@gmail.com>
Date: Sun, 1 Oct 2023 09:33:46 +0530
Subject: [PATCH 01/12] Project euler 95

---
 project_euler/problem_095/__init__.py |  0
 project_euler/problem_095/sol1.py     | 38 +++++++++++++++++++++++++++
 2 files changed, 38 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..54f2ba687def
--- /dev/null
+++ b/project_euler/problem_095/sol1.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)}")

From 9ab8052b9c4b5e570ba674846aa0e69fc2c3ad89 Mon Sep 17 00:00:00 2001
From: kosuri-indu <kosurilindu@gmail.com>
Date: Sun, 1 Oct 2023 09:39:10 +0530
Subject: [PATCH 02/12] adding doctests

---
 project_euler/problem_095/sol1.py | 7 +++++--
 1 file changed, 5 insertions(+), 2 deletions(-)

diff --git a/project_euler/problem_095/sol1.py b/project_euler/problem_095/sol1.py
index 54f2ba687def..85e85e9ed5a3 100644
--- a/project_euler/problem_095/sol1.py
+++ b/project_euler/problem_095/sol1.py
@@ -2,7 +2,7 @@
 Problem 95
 Url: https://projecteuler.net/problem=95
 """
-def find_smallest_member(n: int) -> int:
+def solution(n: int = 10**6) -> int:
     """
     Returns the smallest member of the longest amicable chain with no element exceeding one million
     >> 14316
@@ -35,4 +35,7 @@ def find_smallest_member(n: int) -> int:
 
 
 if __name__ == "__main__":
-    print(f"Solution : {find_smallest_member(10**6)}")
+    import doctest
+
+    doctest.testmod()
+    print(f"{solution() = }")

From a3638197c7f5e48e6d933ec8d250fda240d0f20a Mon Sep 17 00:00:00 2001
From: kosuri-indu <kosurilindu@gmail.com>
Date: Sun, 1 Oct 2023 09:40:40 +0530
Subject: [PATCH 03/12] adding doctests

---
 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 85e85e9ed5a3..f2a290331304 100644
--- a/project_euler/problem_095/sol1.py
+++ b/project_euler/problem_095/sol1.py
@@ -4,7 +4,7 @@
 """
 def solution(n: int = 10**6) -> int:
     """
-    Returns the smallest member of the longest amicable chain with no element exceeding one million
+    Returns the smallest member when n = 1000000
     >> 14316
     """
 

From 6d688122d3b7094ce464061435313168238cdb41 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Sun, 1 Oct 2023 04:11:39 +0000
Subject: [PATCH 04/12] [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, 2 insertions(+)

diff --git a/project_euler/problem_095/sol1.py b/project_euler/problem_095/sol1.py
index f2a290331304..a76f249d139d 100644
--- a/project_euler/problem_095/sol1.py
+++ b/project_euler/problem_095/sol1.py
@@ -2,6 +2,8 @@
 Problem 95
 Url: https://projecteuler.net/problem=95
 """
+
+
 def solution(n: int = 10**6) -> int:
     """
     Returns the smallest member when n = 1000000

From 51a626b7b3ba19aadb5c37310f61490d6e58f828 Mon Sep 17 00:00:00 2001
From: kosuri-indu <kosurilindu@gmail.com>
Date: Sun, 1 Oct 2023 09:44:17 +0530
Subject: [PATCH 05/12] descriptive names

---
 project_euler/problem_095/sol1.py | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/project_euler/problem_095/sol1.py b/project_euler/problem_095/sol1.py
index a76f249d139d..1f7dc5489ade 100644
--- a/project_euler/problem_095/sol1.py
+++ b/project_euler/problem_095/sol1.py
@@ -4,28 +4,28 @@
 """
 
 
-def solution(n: int = 10**6) -> int:
+def solution(number : 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 = [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] * (n + 1)
+    checked = [False] * (number + 1)
     max_len_of_chain = 0
     result = 0
-    for i in range(2, n + 1):
+    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 > n:
+            if j > number:
                 break
             if j in possible_chain:
                 len_of_chain = len(possible_chain) - possible_chain.index(j)

From 977446f234af3dcb700fb891475a7ef0871fe13e Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Sun, 1 Oct 2023 04:14:55 +0000
Subject: [PATCH 06/12] [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 1f7dc5489ade..18b97bf9be48 100644
--- a/project_euler/problem_095/sol1.py
+++ b/project_euler/problem_095/sol1.py
@@ -4,7 +4,7 @@
 """
 
 
-def solution(number : int = 10**6) -> int:
+def solution(number: int = 10**6) -> int:
     """
     Returns the smallest member when n = 1000000
     >> 14316

From 3ddfcdc25163bae76af33e4afb67f5a92fca29a4 Mon Sep 17 00:00:00 2001
From: kosuri-indu <kosurilindu@gmail.com>
Date: Sun, 1 Oct 2023 09:47:53 +0530
Subject: [PATCH 07/12] examples

---
 project_euler/problem_095/sol1.py | 21 +++++++++++++++++++--
 1 file changed, 19 insertions(+), 2 deletions(-)

diff --git a/project_euler/problem_095/sol1.py b/project_euler/problem_095/sol1.py
index 1f7dc5489ade..82bbc0d3d68a 100644
--- a/project_euler/problem_095/sol1.py
+++ b/project_euler/problem_095/sol1.py
@@ -1,13 +1,30 @@
 """
 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 and .
+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
-    >> 14316
+    >>> solution(1000000)
+    14316
+    >>> solution(5000)
+    220
     """
 
     sum_of_div = [0] * (number + 1)

From 6f0f56305ed42e9492afdbf18c1cbf5a60704595 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Sun, 1 Oct 2023 04:18:47 +0000
Subject: [PATCH 08/12] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 project_euler/problem_095/sol1.py | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/project_euler/problem_095/sol1.py b/project_euler/problem_095/sol1.py
index 9c01113a2434..1b6a70f553c7 100644
--- a/project_euler/problem_095/sol1.py
+++ b/project_euler/problem_095/sol1.py
@@ -6,11 +6,11 @@
 For example, the proper divisors of  28 is 1,2,4,7 and 14 and .
 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 
+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. 
+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.
@@ -18,6 +18,7 @@
 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

From c19bd99827ee9224e20201f3756bd1e300448c3c Mon Sep 17 00:00:00 2001
From: kosuri-indu <kosurilindu@gmail.com>
Date: Sun, 1 Oct 2023 09:49:53 +0530
Subject: [PATCH 09/12] ruff errors sorted

---
 project_euler/problem_095/sol1.py | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/project_euler/problem_095/sol1.py b/project_euler/problem_095/sol1.py
index 1b6a70f553c7..2433191a98ff 100644
--- a/project_euler/problem_095/sol1.py
+++ b/project_euler/problem_095/sol1.py
@@ -3,13 +3,12 @@
 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 and .
+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 -> ....)

From 9d6cb8e4ded8e3c423fb54f89dc4c7ccd347170a Mon Sep 17 00:00:00 2001
From: kosuri-indu <kosurilindu@gmail.com>
Date: Sun, 1 Oct 2023 09:50:36 +0530
Subject: [PATCH 10/12] ruff errors sorted

---
 project_euler/problem_095/sol1.py | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/project_euler/problem_095/sol1.py b/project_euler/problem_095/sol1.py
index 2433191a98ff..4bffbcee7920 100644
--- a/project_euler/problem_095/sol1.py
+++ b/project_euler/problem_095/sol1.py
@@ -14,7 +14,8 @@
 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.
+Find the smallest member of the longest amicable chain with ..
+no element exceeding one million.
 """
 
 

From e652c2806970471e16be61612952197a14d31dbd Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Sun, 1 Oct 2023 04:20:43 +0000
Subject: [PATCH 11/12] [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 4bffbcee7920..36c550d0dc14 100644
--- a/project_euler/problem_095/sol1.py
+++ b/project_euler/problem_095/sol1.py
@@ -3,7 +3,7 @@
 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 
+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

From 18e2c7cf70550b26bf95d6c088eeff65012f02f1 Mon Sep 17 00:00:00 2001
From: kosuri-indu <kosurilindu@gmail.com>
Date: Sun, 1 Oct 2023 09:51:15 +0530
Subject: [PATCH 12/12] ruff errors sorted

---
 project_euler/problem_095/sol1.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/project_euler/problem_095/sol1.py b/project_euler/problem_095/sol1.py
index 4bffbcee7920..c89866cd162b 100644
--- a/project_euler/problem_095/sol1.py
+++ b/project_euler/problem_095/sol1.py
@@ -3,10 +3,10 @@
 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 
+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
+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.