From f28efd6cdbe9928966018f68f11e4b0b20565974 Mon Sep 17 00:00:00 2001
From: Sanders Lin <45224617+SandersLin@users.noreply.github.com>
Date: Thu, 11 Jul 2019 01:34:17 +0800
Subject: [PATCH 1/4] Update 3n+1.py

Made variable names more meaningful and removed nested functions.
---
 maths/3n+1.py | 30 +++++++++++++++---------------
 1 file changed, 15 insertions(+), 15 deletions(-)

diff --git a/maths/3n+1.py b/maths/3n+1.py
index 6424fe0d8f15..ef897fa40b18 100644
--- a/maths/3n+1.py
+++ b/maths/3n+1.py
@@ -1,19 +1,19 @@
-def main():
-    def n31(a):# a = initial number
-        c = 0
-        l = [a]
-        while a != 1:
-            if a % 2 == 0:#if even divide it by 2
-                a = a // 2
-            elif a % 2 == 1:#if odd 3n+1
-                a = 3*a +1
-            c += 1#counter
-            l += [a]
+def n31(a):# a = initial number
+    counter = 0
+    path = [a]
+    while a != 1:
+        if a % 2 == 0:
+            a = a // 2
+        else:
+            a = 3*a +1
+        counter += 1
+        path += [a]
+    return path , counter
 
-        return l , c
-    print(n31(43))
-    print(n31(98)[0][-1])# = a
-    print("It took {0} steps.".format(n31(13)[1]))#optional finish
+def main():
+    num = 43
+    path , length = n31(num)
+    print("The Collatz sequence of {0} took {1} steps. \nPath: {2}".format(num,length, path))
 
 if __name__ == '__main__':
     main()

From 81962a31b8443ceb70fa468fc1f1a1c301f20bd8 Mon Sep 17 00:00:00 2001
From: Sanders Lin <45224617+SandersLin@users.noreply.github.com>
Date: Thu, 11 Jul 2019 03:07:55 +0800
Subject: [PATCH 2/4] Update 3n+1.py

---
 maths/3n+1.py | 9 ++++++++-
 1 file changed, 8 insertions(+), 1 deletion(-)

diff --git a/maths/3n+1.py b/maths/3n+1.py
index ef897fa40b18..f5749464f4a9 100644
--- a/maths/3n+1.py
+++ b/maths/3n+1.py
@@ -1,4 +1,11 @@
-def n31(a):# a = initial number
+def n31(a):
+    """
+    Returns Collatz sequence of number a
+    
+    >>> n31(4)
+    ([4,2,1],3)
+    
+    """
     counter = 0
     path = [a]
     while a != 1:

From 79ddd13a4a86080c3c082176dfe6e9bf1b6f0dff Mon Sep 17 00:00:00 2001
From: Sanders Lin <45224617+SandersLin@users.noreply.github.com>
Date: Thu, 11 Jul 2019 11:34:42 +0800
Subject: [PATCH 3/4] Update 3n+1.py

---
 maths/3n+1.py | 20 +++++++++++++-------
 1 file changed, 13 insertions(+), 7 deletions(-)

diff --git a/maths/3n+1.py b/maths/3n+1.py
index f5749464f4a9..a4f9d056fcbf 100644
--- a/maths/3n+1.py
+++ b/maths/3n+1.py
@@ -1,11 +1,17 @@
-def n31(a):
+from typing import Tuple, List
+
+def n31(a: int) -> Tuple[List[int], int]: 
     """
-    Returns Collatz sequence of number a
-    
+    Returns Collatz sequence of a number 
     >>> n31(4)
-    ([4,2,1],3)
-    
+    ([4, 2, 1], 3)
     """
+
+    if not isinstance(a, int):
+        raise TypeError('Must be int, not {0}'.format(type(a).__name__))
+    if a < 1: 
+        raise ValueError('Given integer must be greater than 1, not {0}'.format(a))
+
     counter = 0
     path = [a]
     while a != 1:
@@ -15,10 +21,10 @@ def n31(a):
             a = 3*a +1
         counter += 1
         path += [a]
-    return path , counter
+    return path, counter + 1
 
 def main():
-    num = 43
+    num = 4
     path , length = n31(num)
     print("The Collatz sequence of {0} took {1} steps. \nPath: {2}".format(num,length, path))
 

From 9f220f133b13c6910668552b8f6fbcbf7aae15e8 Mon Sep 17 00:00:00 2001
From: Sanders Lin <45224617+SandersLin@users.noreply.github.com>
Date: Thu, 11 Jul 2019 13:27:37 +0800
Subject: [PATCH 4/4] Update 3n+1.py

---
 maths/3n+1.py | 8 +++-----
 1 file changed, 3 insertions(+), 5 deletions(-)

diff --git a/maths/3n+1.py b/maths/3n+1.py
index a4f9d056fcbf..d6c14ff0f47d 100644
--- a/maths/3n+1.py
+++ b/maths/3n+1.py
@@ -2,7 +2,7 @@
 
 def n31(a: int) -> Tuple[List[int], int]: 
     """
-    Returns Collatz sequence of a number 
+    Returns the Collatz sequence and its length of any postiver integer.
     >>> n31(4)
     ([4, 2, 1], 3)
     """
@@ -11,17 +11,15 @@ def n31(a: int) -> Tuple[List[int], int]:
         raise TypeError('Must be int, not {0}'.format(type(a).__name__))
     if a < 1: 
         raise ValueError('Given integer must be greater than 1, not {0}'.format(a))
-
-    counter = 0
+    
     path = [a]
     while a != 1:
         if a % 2 == 0:
             a = a // 2
         else:
             a = 3*a +1
-        counter += 1
         path += [a]
-    return path, counter + 1
+    return path, len(path)
 
 def main():
     num = 4