From 09e59b202823092cbe7a974f25edf0224af0b042 Mon Sep 17 00:00:00 2001
From: "Casper V. Kristensen" <c@spervk.com>
Date: Mon, 8 Oct 2018 18:31:00 +0200
Subject: [PATCH] Make progress on MbC; 1DLP working with unittests. Still
 working on the real problem: 2DLP.

---
 h2/mbc.py | 62 ++++++++++++++++++++++++++++++++++++++++++++++++++++++-
 1 file changed, 61 insertions(+), 1 deletion(-)

diff --git a/h2/mbc.py b/h2/mbc.py
index 3994aba..cf3ef5e 100644
--- a/h2/mbc.py
+++ b/h2/mbc.py
@@ -2,7 +2,8 @@ import random
 import statistics
 from collections import namedtuple
 from enum import Enum, auto
-from typing import Set
+from math import inf
+from typing import Set, List, Tuple
 
 import matplotlib.pyplot as plt
 import numpy as np
@@ -68,6 +69,65 @@ def sidedness(slope: int, intersection: int, p3: Point, linprog_flipper: callabl
     return Side.BELOW
 
 
+def solve_1dlp(c: float, constraints: List[Tuple[float, float]]):
+    """
+    :param c: c1
+    :param constraints: [(ai, bi), ...]
+    :return: x1
+    """
+    if c > 0:
+        return max(b/a for a, b in constraints if a < 0)
+    return min(b/a for a, b in constraints if a > 0)
+
+
+assert solve_1dlp(1, [(-1, -2)]) == 2
+assert solve_1dlp(1, [(-1, -2), (-1, -3)]) == 3
+assert solve_1dlp(1, [(-1, -3), (-1, -2)]) == 3
+assert solve_1dlp(-1, [(1, 3), (1, 2)]) == 2
+assert solve_1dlp(1, [(-1, 3), (-1, 2)]) == -2
+
+
+def solve_2dlp(c: Tuple[float, float], constraints: List[Tuple[Tuple[float, float], float]]):
+    """
+    :param c: (c1, c2)
+    :param constraints: [(ai1, ai2, bi), ...]
+    :return: x1, x2
+    """
+    x1, x2 = -inf, -inf  # TODO: something other than -inf (?)
+    our_constraints = []
+    for (a1, a2), b in constraints:  # TODO: random.shuffle()
+        if not a1*x1 + a2*x2 <= b:
+            our_constraints.append(((a1, a2), b))
+
+            new_obj = c[0] + (b/a2 - a1/a2)
+
+            constraint_for_1d = []
+            for constraint in our_constraints:
+                (old_a1, old_a2), old_b = constraint
+                new_a1 = old_a1 + ((old_b/old_a2) - (old_a1/old_a2))
+
+                constraint_for_1d.append((new_a1, old_b))
+
+            x1 = solve_1dlp(new_obj, constraint_for_1d)
+            x2 = ((b/a2) - (a1/a2))*x1
+    return x1, x2
+
+
+# TODO: assert solve_2dlp((-3, -2), [((-1, 3), 12), ((1, 1), 8), ((2, -1), 10)]) == (6, 2)
+
+c = (-3, -2)
+constraints = [
+    ((-1, 3), 12),
+    ((1, 1), 8),
+    ((2, -1), 10),
+]
+# = (6.0, 2.0)
+
+result = solve_2dlp(c, constraints)
+print(result)
+exit()
+
+
 def mbc_ch(points: Set[Point], linprog_flipper: callable) -> Set[Point]:
     if len(points) <= 2:
         return points