Fix.

h2/MBC_carlsen.py

@@ -1,10 +1,10 @@
-
 import matplotlib.pyplot as plt
 import collections
 from enum import Enum, auto
 from random import randint
 
-Point = collections.namedtuple("Point", "x y")
+Point = collections.namedtuple("Point", ("x", "y"))
+
 
 class Side(Enum):
     ON = auto()
@@ -14,13 +14,14 @@ class Side(Enum):
 
 def sidedness(slope, intersection, p3, eps=0.0000001):
     print(slope * p3[0] + intersection )
-    """ finds where a point is in regards to a line """
+    # finds where a point is in regards to a line
     if p3[1] - eps <= slope * p3[0] + intersection <= p3[1] + eps or p3[0] - eps <= (p3[1] - intersection)/slope <= p3[0] + eps:
         return Side.ON
     elif p3[1] > slope * p3[0] + intersection:
         return Side.ABOVE
     return Side.BELOW
 
+
 def diplay_prune_points(points, p1, p2):
     xs = [p[0] for p in points]
     ys = [p[1] for p in points]
@@ -90,7 +91,6 @@ def solve1D(points, xm, iteration_num):
     return v
 
 
-
 def findBridge(points, xm):
     if xm > 0:
         v = (-float('Inf'), -float('Inf'))
@@ -190,5 +190,3 @@ res_ys = [p[1] for p in result]
 plt.plot(res_xs, res_ys)
 plt.plot(xs, ys, 'ro')
 plt.show()
-
- 

h2/howto

@@ -0,0 +1,56 @@
+---- MbC ---
+MbC(P: l, r):   (finds UH of P from x-coordinates l to r)
+    Find median x-coordinate x_m
+    Partition points on x_m into Pl and Pr
+    Find bridge uv over x_m
+    Remove points below bridge
+    Recurse MbC(Pl: l, u.x) and MbC(Pr: v.x, r)
+
+Find bridge is finding the line (y=ax+b) such that:
+    1) passes above all the points
+    2) has the lowest intersection point with the median line
+
+
+
+---- 1D ----
+Unknown x1
+Minimize c1*x1
+such that
+a1*x1 \leq b1
+a2*x1 \leq b2
+...
+an*x1 \leq bn
+
+for each of the constraints:
+    ai*x1 \leq bi
+    =>
+    if ai > 0: x1 <= bi/ai
+    if ai < 0: x1 >= bi/ai
+    if ai = 0:
+        if bi < 0: impossible
+        if bi \geq 0: always satisfied
+
+this means that each constraint half of the real line
+therefore run for-loop on bi/ai and check the ifs
+
+
+when we have feasible region/interval:
+    if c1 > 0: choose minimum of interval
+    if c1 < 0: choose maximum of interval
+    if c1 = 0: degenerate
+
+
+
+---- 2D ----
+a and b are unknowns
+minimize ax_m + b
+such that y_i \leq ax_i + b, for every input point (x_i, y_i)
+where x_m is given (median)
+
+Algorithm:
+    Initialise v
+    Randomly shuffle constraints
+    for i=1 to n:
+        if constraint i does not violate v, do nothing
+        else solve 1d LP on boundary of constraint i
+