Python implementation for Graham Scan (#238)

* Python implementation of Graham Scan

Author: wmboyles

contents/graham_scan/code/python/grahamScan.py

@@ -0,0 +1,42 @@
+from math import atan2
+
+
+#Is the turn counter clockwise?
+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):
+    return atan2(point[1]-ref[1],point[0]-ref[0])
+
+
+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)
+
+    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):
+            del hull[-1]
+        hull.append(pt)
+
+    return hull
+
+
+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)
+
+    print("The points in the hull are:")
+    for point in hull:
+        print(point)
+
+        
+main()

contents/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" %}
+[import:4-6, 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" %}
+[import:14-27, lang:"python"](code/python/grahamScan.py)
 {% endmethod %}
 
 ### Bibliography
@@ -59,6 +63,8 @@ In the end, the code should look something like this:
 [import, lang:"c_cpp"](code/c/graham.c)
 {% sample lang="js" %}
 [import, lang:"javascript"](code/javascript/graham-scan.js)
+{% sample lang="py" %}
+[import, lang:"python"](code/python/grahamScan.py)
 {% endmethod %}
 
 <script>