Added Graham Scan Algorithm ( a new algorithm )

algorithms/computational-geometry/graham_scan.py

@@ -0,0 +1,68 @@
+'''
+Layout: algorithms
+Title : Graham Scan Algorithm
+Author: RadientBrain
+'''
+
+
+from random import randint
+import matplotlib.pyplot as plt
+
+
+def orientation(m, n, o):
+    val = ((n[1]-m[1])*(o[0]-n[0])) - ((o[1]-n[1])*(n[0]-m[0]))
+    if val > 0:
+        return 1
+    elif val < 0:
+        return -1
+    else:   
+        return 0
+
+def distance(m, n):
+    return (n[0]-m[0])**2 + (n[1]-m[1])**2
+
+def Sorting_with_bubble(coordinates, b):
+    for coord_ith in range(len(coordinates)):
+        for j in range(len(coordinates)-coord_ith-1):
+            if (orientation(b, coordinates[j], coordinates[j+1]) > 0) or (orientation(b, coordinates[j], coordinates[j+1])==0 and (distance(b, coordinates[j]) > distance(b, coordinates[j+1]))):
+                temp = coordinates[j+1]
+                coordinates[j+1] = coordinates[j]
+                coordinates[j] = temp
+
+    return coordinates
+
+
+def Convex_hull_through_graham(coordinates):
+    b = min(coordinates, key= lambda coord: (coord[1], coord[0]))
+    coord_ith = coordinates.index(b)
+    coordinates[coord_ith]=coordinates[0]
+    coordinates[0] = b
+    coordinates = [b] + Sorting_with_bubble(coordinates[1:], b)
+    size_triplet = [coordinates[0], coordinates[1], coordinates[2]]
+    for coord_ith in range(3, len(coordinates)):
+        while len(size_triplet)>=3 and orientation(size_triplet[-2], size_triplet[-1], coordinates[coord_ith]) >= 0:
+            size_triplet.pop()            
+        size_triplet.append(coordinates[coord_ith])
+    return size_triplet+[size_triplet[0]]
+
+
+def random_points(n=30):
+    coordinates = [(randint(0, n), randint(0, n)) for _ in range(n)]
+    print (coordinates)
+    return coordinates
+
+
+if __name__ == "__main__":
+    coordinates = random_points(120)
+
+    X = [coord[0] for coord in coordinates]
+    Y = [coord[1] for coord in coordinates]
+    plt.plot(X, Y, '.b')
+
+    boundary_poly = Convex_hull_through_graham(coordinates)
+
+    X = [coord[0] for coord in boundary_poly]
+    Y = [coord[1] for coord in boundary_poly]
+    plt.plot(X, Y, '-og')
+
+    plt.show()