From 93648c6bfda392eb721c1c863e9e42a6adc40b27 Mon Sep 17 00:00:00 2001
From: William Boyles <40878829+wmboyles@users.noreply.github.com>
Date: Sun, 8 Jul 2018 15:06:56 -0400
Subject: [PATCH 01/16] Python implementation from Graham Scan

---
 .../graham_scan/code/python/grahamScan.py     | 57 +++++++++++++++++++
 1 file changed, 57 insertions(+)
 create mode 100644 chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py

diff --git a/chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py b/chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py
new file mode 100644
index 000000000..35c7a113d
--- /dev/null
+++ b/chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py
@@ -0,0 +1,57 @@
+from math import atan2
+
+#Is the turn counter clockwise?
+def CCW(p1, p2, p3):
+    return (p3[1]-p1[1])*(p2[0]-p1[0]) >= (p2[1]-p1[1])*(p3[0]-p1[0])
+
+
+#Find the point with least y-value. If tie, use point with least x-value.
+def minYPoint(points):
+    minYPt = points[0]
+    
+    for point in points[1:]:
+        if point[1] < minYPt[1]:
+            minYPt = point
+        elif point[1] == minYPt[1] and point[0]<minYPt[0]:
+            minYPt = point
+            
+    return minYPt
+
+
+#Find the polar angle of each point in list relative to a reference point
+def polarAngles(ref, points):
+    return [atan2(point[1]-ref[0],point[0]-ref[0]) for point in points]
+
+
+#Sort the list of point by their polar angle
+def sortByPolar(ref, points):
+    return [x for _,x in sorted(zip(polarAngles(ref,points),points))]
+
+
+def grahamScan(gift):
+    start = minYPoint(gift) #Must be in hull
+    gift.remove(start)
+
+    S = sortByPolar(start,gift)
+    hull = [start,S[0],S[1]]
+
+    #Remove points from hull that make the hull concave
+    for pt in S[2:]:
+        while not CCW(hull[-2],hull[-1],pt):
+            del hull[-1]
+        hull.append(pt)
+
+    return hull
+
+
+def main():
+    testGift = [(-5,2),(5,7),(-6,-12),(-14,-14),(9,9),
+                (-1,-1),(-10,11),(-6,15),(-6,-8),(15,-9),
+                (7,-7),(-2,-9),(6,-5),(0,14),(2,8)]
+    hull = grahamScan(testGift)
+
+    print("The points in the hull are:")
+    for point in hull:
+        print(point)
+
+main()

From 37d5cb34da4f7953ab1e9fd12c0739b9b6c3adb9 Mon Sep 17 00:00:00 2001
From: William Boyles <40878829+wmboyles@users.noreply.github.com>
Date: Sun, 8 Jul 2018 15:23:42 -0400
Subject: [PATCH 02/16] Included Python code in .md

---
 .../gift_wrapping/graham_scan/graham_scan.md                  | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/chapters/computational_geometry/gift_wrapping/graham_scan/graham_scan.md b/chapters/computational_geometry/gift_wrapping/graham_scan/graham_scan.md
index 877e8111c..346adedbd 100644
--- a/chapters/computational_geometry/gift_wrapping/graham_scan/graham_scan.md
+++ b/chapters/computational_geometry/gift_wrapping/graham_scan/graham_scan.md
@@ -20,6 +20,8 @@ We can find whether a rotation is counter-clockwise with trigonometric functions
 [import:24-26, lang:"c_cpp"](code/c/graham.c)
 {% sample lang="js" %}
 [import:36-38, lang:"javascript"](code/javascript/graham-scan.js)
+{% sample lang="py" %}
+[import3-5, lang:"python"](code/python/grahamScan.py)
 {% endmethod %}
 
 If the output of this function is 0, the points are collinear.
@@ -42,6 +44,8 @@ In the end, the code should look something like this:
 [import:65-95, lang:"c_cpp"](code/c/graham.c)
 {% sample lang="js" %}
 [import:1-30, lang:"javascript"](code/javascript/graham-scan.js)
+{% sample lang="py" %}
+[import31-44, lang:"python"](code/python/grahamScan.py)
 {% endmethod %}
 
 ### Bibliography

From 781e986d05a870770dd149b7d9e39fcc54cfe4af Mon Sep 17 00:00:00 2001
From: William Boyles <40878829+wmboyles@users.noreply.github.com>
Date: Sun, 8 Jul 2018 17:54:41 -0400
Subject: [PATCH 03/16] Compliance with pep8

This should make the code follow pep-8 standards.
---
 .../graham_scan/code/python/grahamScan.py     | 35 +++++++------------
 1 file changed, 12 insertions(+), 23 deletions(-)

diff --git a/chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py b/chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py
index 35c7a113d..401cfc695 100644
--- a/chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py
+++ b/chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py
@@ -1,43 +1,31 @@
 from math import atan2
 
+
 #Is the turn counter clockwise?
-def CCW(p1, p2, p3):
+def counter_Clockwise(p1, p2, p3):
     return (p3[1]-p1[1])*(p2[0]-p1[0]) >= (p2[1]-p1[1])*(p3[0]-p1[0])
 
 
-#Find the point with least y-value. If tie, use point with least x-value.
-def minYPoint(points):
-    minYPt = points[0]
-    
-    for point in points[1:]:
-        if point[1] < minYPt[1]:
-            minYPt = point
-        elif point[1] == minYPt[1] and point[0]<minYPt[0]:
-            minYPt = point
-            
-    return minYPt
-
-
 #Find the polar angle of each point in list relative to a reference point
-def polarAngles(ref, points):
+def polar_Angles(ref, points):
     return [atan2(point[1]-ref[0],point[0]-ref[0]) for point in points]
 
 
 #Sort the list of point by their polar angle
-def sortByPolar(ref, points):
-    return [x for _,x in sorted(zip(polarAngles(ref,points),points))]
+def sort_By_Polar(ref, points):
+    return [x for _,x in sorted(zip(polar_Angles(ref,points),points))]
 
 
-def grahamScan(gift):
-    start = minYPoint(gift) #Must be in hull
+def graham_Scan(gift):
+    start = min(gift, key=lambda pL (p[1],p[0])) #Must be in hull
     gift.remove(start)
 
-    S = sortByPolar(start,gift)
+    S = sort_By_Polar(start,gift)
     hull = [start,S[0],S[1]]
 
     #Remove points from hull that make the hull concave
     for pt in S[2:]:
-        while not CCW(hull[-2],hull[-1],pt):
+        while not counter_Clockwise(hull[-2],hull[-1],pt):
             del hull[-1]
         hull.append(pt)
 
@@ -45,13 +33,14 @@ def grahamScan(gift):
 
 
 def main():
-    testGift = [(-5,2),(5,7),(-6,-12),(-14,-14),(9,9),
+    test_Gift = [(-5,2),(5,7),(-6,-12),(-14,-14),(9,9),
                 (-1,-1),(-10,11),(-6,15),(-6,-8),(15,-9),
                 (7,-7),(-2,-9),(6,-5),(0,14),(2,8)]
-    hull = grahamScan(testGift)
+    hull = graham_Scan(test_Gift)
 
     print("The points in the hull are:")
     for point in hull:
         print(point)
 
+        
 main()

From e944e1fe24b0779fc31f524933e9e71cf9aac742 Mon Sep 17 00:00:00 2001
From: William Boyles <40878829+wmboyles@users.noreply.github.com>
Date: Sun, 8 Jul 2018 17:57:39 -0400
Subject: [PATCH 04/16] Updated .md to reflect code changes

---
 .../gift_wrapping/graham_scan/graham_scan.md                  | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/chapters/computational_geometry/gift_wrapping/graham_scan/graham_scan.md b/chapters/computational_geometry/gift_wrapping/graham_scan/graham_scan.md
index 346adedbd..fdd6bdfcc 100644
--- a/chapters/computational_geometry/gift_wrapping/graham_scan/graham_scan.md
+++ b/chapters/computational_geometry/gift_wrapping/graham_scan/graham_scan.md
@@ -21,7 +21,7 @@ We can find whether a rotation is counter-clockwise with trigonometric functions
 {% sample lang="js" %}
 [import:36-38, lang:"javascript"](code/javascript/graham-scan.js)
 {% sample lang="py" %}
-[import3-5, lang:"python"](code/python/grahamScan.py)
+[import:20, lang:"python"](code/python/grahamScan.py)
 {% endmethod %}
 
 If the output of this function is 0, the points are collinear.
@@ -45,7 +45,7 @@ In the end, the code should look something like this:
 {% sample lang="js" %}
 [import:1-30, lang:"javascript"](code/javascript/graham-scan.js)
 {% sample lang="py" %}
-[import31-44, lang:"python"](code/python/grahamScan.py)
+[import19-32, lang:"python"](code/python/grahamScan.py)
 {% endmethod %}
 
 ### Bibliography

From 494d0832571aba64d76f305123514e99effad1a2 Mon Sep 17 00:00:00 2001
From: William Boyles <40878829+wmboyles@users.noreply.github.com>
Date: Sun, 8 Jul 2018 17:59:31 -0400
Subject: [PATCH 05/16]  fixed missing ":"

---
 .../gift_wrapping/graham_scan/graham_scan.md                    | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/chapters/computational_geometry/gift_wrapping/graham_scan/graham_scan.md b/chapters/computational_geometry/gift_wrapping/graham_scan/graham_scan.md
index fdd6bdfcc..638b3633b 100644
--- a/chapters/computational_geometry/gift_wrapping/graham_scan/graham_scan.md
+++ b/chapters/computational_geometry/gift_wrapping/graham_scan/graham_scan.md
@@ -45,7 +45,7 @@ In the end, the code should look something like this:
 {% sample lang="js" %}
 [import:1-30, lang:"javascript"](code/javascript/graham-scan.js)
 {% sample lang="py" %}
-[import19-32, lang:"python"](code/python/grahamScan.py)
+[import:19-32, lang:"python"](code/python/grahamScan.py)
 {% endmethod %}
 
 ### Bibliography

From 4839e221170a6119013df8da24cf37c211f0a963 Mon Sep 17 00:00:00 2001
From: William Boyles <40878829+wmboyles@users.noreply.github.com>
Date: Sun, 8 Jul 2018 18:01:34 -0400
Subject: [PATCH 06/16] Added full example to .md

---
 .../gift_wrapping/graham_scan/graham_scan.md                  | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/chapters/computational_geometry/gift_wrapping/graham_scan/graham_scan.md b/chapters/computational_geometry/gift_wrapping/graham_scan/graham_scan.md
index 638b3633b..e541e6555 100644
--- a/chapters/computational_geometry/gift_wrapping/graham_scan/graham_scan.md
+++ b/chapters/computational_geometry/gift_wrapping/graham_scan/graham_scan.md
@@ -65,7 +65,11 @@ In the end, the code should look something like this:
 ### C
 [import, lang:"c_cpp"](code/c/graham.c)
 {% sample lang="js" %}
+### Javascript
 [import, lang:"javascript"](code/javascript/graham-scan.js)
+{% sample lang="py" %}
+### Python
+[import, lang:"python"](code/python/grahamScan.py)
 {% endmethod %}
 
 <script>

From 132b0b0dfa53c92cba7021264060757643770a88 Mon Sep 17 00:00:00 2001
From: William Boyles <40878829+wmboyles@users.noreply.github.com>
Date: Sun, 8 Jul 2018 18:06:41 -0400
Subject: [PATCH 07/16] Fixed incorrect code reference

---
 .../gift_wrapping/graham_scan/graham_scan.md                    | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/chapters/computational_geometry/gift_wrapping/graham_scan/graham_scan.md b/chapters/computational_geometry/gift_wrapping/graham_scan/graham_scan.md
index e541e6555..80f47cbca 100644
--- a/chapters/computational_geometry/gift_wrapping/graham_scan/graham_scan.md
+++ b/chapters/computational_geometry/gift_wrapping/graham_scan/graham_scan.md
@@ -21,7 +21,7 @@ We can find whether a rotation is counter-clockwise with trigonometric functions
 {% sample lang="js" %}
 [import:36-38, lang:"javascript"](code/javascript/graham-scan.js)
 {% sample lang="py" %}
-[import:20, lang:"python"](code/python/grahamScan.py)
+[import:5-6, lang:"python"](code/python/grahamScan.py)
 {% endmethod %}
 
 If the output of this function is 0, the points are collinear.

From 5febc4b4c45b9e46a697336111dc8217cf675b00 Mon Sep 17 00:00:00 2001
From: William Boyles <40878829+wmboyles@users.noreply.github.com>
Date: Sun, 8 Jul 2018 21:47:48 -0400
Subject: [PATCH 08/16] fixed fatal typo

---
 .../gift_wrapping/graham_scan/code/python/grahamScan.py         | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py b/chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py
index 401cfc695..56cc83739 100644
--- a/chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py
+++ b/chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py
@@ -17,7 +17,7 @@ def sort_By_Polar(ref, points):
 
 
 def graham_Scan(gift):
-    start = min(gift, key=lambda pL (p[1],p[0])) #Must be in hull
+    start = min(gift, key=lambda p (p[1],p[0])) #Must be in hull
     gift.remove(start)
 
     S = sort_By_Polar(start,gift)

From 4c14dd458a6307acf6433ca62d3a36bcfa27e25f Mon Sep 17 00:00:00 2001
From: William Boyles <40878829+wmboyles@users.noreply.github.com>
Date: Sun, 8 Jul 2018 22:32:55 -0400
Subject: [PATCH 09/16] Condensed sorting functions

---
 .../graham_scan/code/python/grahamScan.py              | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py b/chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py
index 56cc83739..4beac4a38 100644
--- a/chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py
+++ b/chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py
@@ -6,9 +6,9 @@ def counter_Clockwise(p1, p2, p3):
     return (p3[1]-p1[1])*(p2[0]-p1[0]) >= (p2[1]-p1[1])*(p3[0]-p1[0])
 
 
-#Find the polar angle of each point in list relative to a reference point
-def polar_Angles(ref, points):
-    return [atan2(point[1]-ref[0],point[0]-ref[0]) for point in points]
+#Find the polar angle of a point relative to a reference point
+def polar_Angle(ref, point):
+    return atan2(point[1]-ref[0],point[0]-ref[0])
 
 
 #Sort the list of point by their polar angle
@@ -17,10 +17,10 @@ def sort_By_Polar(ref, points):
 
 
 def graham_Scan(gift):
-    start = min(gift, key=lambda p (p[1],p[0])) #Must be in hull
+    start = min(gift, key=lambda p: (p[1],p[0])) #Must be in hull
     gift.remove(start)
 
-    S = sort_By_Polar(start,gift)
+    S = sorted(gift,key=lambda point: polar_Angle(start,point))
     hull = [start,S[0],S[1]]
 
     #Remove points from hull that make the hull concave

From e4ee29c90d1a1f81718835166f508647738e6b19 Mon Sep 17 00:00:00 2001
From: William Boyles <40878829+wmboyles@users.noreply.github.com>
Date: Sun, 8 Jul 2018 22:36:00 -0400
Subject: [PATCH 10/16] Removed unneeded sorting function

---
 .../gift_wrapping/graham_scan/code/python/grahamScan.py      | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py b/chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py
index 4beac4a38..1cc38e0df 100644
--- a/chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py
+++ b/chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py
@@ -11,11 +11,6 @@ def polar_Angle(ref, point):
     return atan2(point[1]-ref[0],point[0]-ref[0])
 
 
-#Sort the list of point by their polar angle
-def sort_By_Polar(ref, points):
-    return [x for _,x in sorted(zip(polar_Angles(ref,points),points))]
-
-
 def graham_Scan(gift):
     start = min(gift, key=lambda p: (p[1],p[0])) #Must be in hull
     gift.remove(start)

From cd7778f31c304a09466aba0565d6171e672ac2f5 Mon Sep 17 00:00:00 2001
From: William Boyles <40878829+wmboyles@users.noreply.github.com>
Date: Sun, 8 Jul 2018 22:36:43 -0400
Subject: [PATCH 11/16] Updated .md to match code changes

---
 .../gift_wrapping/graham_scan/graham_scan.md                  | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/chapters/computational_geometry/gift_wrapping/graham_scan/graham_scan.md b/chapters/computational_geometry/gift_wrapping/graham_scan/graham_scan.md
index 80f47cbca..e2a97473d 100644
--- a/chapters/computational_geometry/gift_wrapping/graham_scan/graham_scan.md
+++ b/chapters/computational_geometry/gift_wrapping/graham_scan/graham_scan.md
@@ -21,7 +21,7 @@ We can find whether a rotation is counter-clockwise with trigonometric functions
 {% sample lang="js" %}
 [import:36-38, lang:"javascript"](code/javascript/graham-scan.js)
 {% sample lang="py" %}
-[import:5-6, lang:"python"](code/python/grahamScan.py)
+[import:4-6, lang:"python"](code/python/grahamScan.py)
 {% endmethod %}
 
 If the output of this function is 0, the points are collinear.
@@ -45,7 +45,7 @@ In the end, the code should look something like this:
 {% sample lang="js" %}
 [import:1-30, lang:"javascript"](code/javascript/graham-scan.js)
 {% sample lang="py" %}
-[import:19-32, lang:"python"](code/python/grahamScan.py)
+[import:14-27, lang:"python"](code/python/grahamScan.py)
 {% endmethod %}
 
 ### Bibliography

From 5fa8fecfcb6a77363d431ee857ebcc856e567a03 Mon Sep 17 00:00:00 2001
From: William Boyles <40878829+wmboyles@users.noreply.github.com>
Date: Sun, 8 Jul 2018 23:01:56 -0400
Subject: [PATCH 12/16] Fixed typo

This typo caused some points be be erroneously included in the hull.
---
 .../gift_wrapping/graham_scan/code/python/grahamScan.py         | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py b/chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py
index 1cc38e0df..c0647fee5 100644
--- a/chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py
+++ b/chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py
@@ -8,7 +8,7 @@ def counter_Clockwise(p1, p2, p3):
 
 #Find the polar angle of a point relative to a reference point
 def polar_Angle(ref, point):
-    return atan2(point[1]-ref[0],point[0]-ref[0])
+    return atan2(point[1]-ref[1],point[0]-ref[0])
 
 
 def graham_Scan(gift):

From a3dada2b3eec11f7d39124f6bd8db249aea844f9 Mon Sep 17 00:00:00 2001
From: William Boyles <40878829+wmboyles@users.noreply.github.com>
Date: Mon, 9 Jul 2018 01:10:38 -0400
Subject: [PATCH 13/16] More pep8

---
 .../graham_scan/code/python/grahamScan.py     | 24 +++++++++----------
 1 file changed, 12 insertions(+), 12 deletions(-)

diff --git a/chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py b/chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py
index c0647fee5..5bbaf4dd8 100644
--- a/chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py
+++ b/chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py
@@ -2,25 +2,25 @@
 
 
 #Is the turn counter clockwise?
-def counter_Clockwise(p1, p2, p3):
+def counter_clockwise(p1, p2, p3):
     return (p3[1]-p1[1])*(p2[0]-p1[0]) >= (p2[1]-p1[1])*(p3[0]-p1[0])
 
 
 #Find the polar angle of a point relative to a reference point
-def polar_Angle(ref, point):
+def polar_angle(ref, point):
     return atan2(point[1]-ref[1],point[0]-ref[0])
 
 
-def graham_Scan(gift):
-    start = min(gift, key=lambda p: (p[1],p[0])) #Must be in hull
+def graham_scan(gift):
+    start = min(gift, key=lambda p: (p[1], p[0])) #Must be in hull
     gift.remove(start)
 
-    S = sorted(gift,key=lambda point: polar_Angle(start,point))
-    hull = [start,S[0],S[1]]
+    s = sorted(gift,key=lambda point: polar_angle(start, point))
+    hull = [start,s[0],s[1]]
 
     #Remove points from hull that make the hull concave
-    for pt in S[2:]:
-        while not counter_Clockwise(hull[-2],hull[-1],pt):
+    for pt in s[2:]:
+        while not counter_clockwise(hull[-2], hull[-1], pt):
             del hull[-1]
         hull.append(pt)
 
@@ -28,10 +28,10 @@ def graham_Scan(gift):
 
 
 def main():
-    test_Gift = [(-5,2),(5,7),(-6,-12),(-14,-14),(9,9),
-                (-1,-1),(-10,11),(-6,15),(-6,-8),(15,-9),
-                (7,-7),(-2,-9),(6,-5),(0,14),(2,8)]
-    hull = graham_Scan(test_Gift)
+    test_gift = [(-5, 2), (5, 7), (-6, -12), (-14, -14), (9, 9),
+                (-1, -1), (-10, 11), (-6, 15), (-6, -8), (15, -9),
+                (7, -7), (-2, -9), (6, -5), (0, 14), (2, 8)]
+    hull = graham_scan(test_gift)
 
     print("The points in the hull are:")
     for point in hull:

From 388d3a681a94ca3d1ad7925d43e1c66276e1e610 Mon Sep 17 00:00:00 2001
From: William Boyles <40878829+wmboyles@users.noreply.github.com>
Date: Fri, 20 Jul 2018 17:25:29 -0400
Subject: [PATCH 14/16] Remove Duplicate Points

---
 .../gift_wrapping/graham_scan/code/python/grahamScan.py          | 1 +
 1 file changed, 1 insertion(+)

diff --git a/chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py b/chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py
index 5bbaf4dd8..cea09a72c 100644
--- a/chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py
+++ b/chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py
@@ -12,6 +12,7 @@ def polar_angle(ref, point):
 
 
 def graham_scan(gift):
+    gift = list(set(gift)) #Remove duplicate points
     start = min(gift, key=lambda p: (p[1], p[0])) #Must be in hull
     gift.remove(start)
 

From 34a0f516fb35e806dc5bcc0f40acbbbaa9e96062 Mon Sep 17 00:00:00 2001
From: William Boyles <40878829+wmboyles@users.noreply.github.com>
Date: Fri, 20 Jul 2018 17:29:05 -0400
Subject: [PATCH 15/16] Driectory Change from .py file

---
 .../graham_scan/code/python/grahamScan.py                         | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 rename {chapters/computational_geometry/gift_wrapping => contents}/graham_scan/code/python/grahamScan.py (100%)

diff --git a/chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py b/contents/graham_scan/code/python/grahamScan.py
similarity index 100%
rename from chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py
rename to contents/graham_scan/code/python/grahamScan.py

From 675fd8ed5df81a98c3ab15a3a99cbc29473e4478 Mon Sep 17 00:00:00 2001
From: William Boyles <40878829+wmboyles@users.noreply.github.com>
Date: Fri, 20 Jul 2018 17:30:58 -0400
Subject: [PATCH 16/16] Directory change for .md file

---
 .../gift_wrapping => contents}/graham_scan/graham_scan.md         | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 rename {chapters/computational_geometry/gift_wrapping => contents}/graham_scan/graham_scan.md (100%)

diff --git a/chapters/computational_geometry/gift_wrapping/graham_scan/graham_scan.md b/contents/graham_scan/graham_scan.md
similarity index 100%
rename from chapters/computational_geometry/gift_wrapping/graham_scan/graham_scan.md
rename to contents/graham_scan/graham_scan.md