diff --git a/lib.py b/lib.py
index 4e5956d..102846a 100644
--- a/lib.py
+++ b/lib.py
@@ -2,11 +2,18 @@
 
 import itertools
 from collections import deque
+from enum import Enum
 
 # Iterator recipes ----------------------------------------
 def last(iterator):
+    """Exhausts an iterator and returns its last element."""
     return deque(iterator, maxlen=1)[0]
 
+def exhaust(iterator):
+    """Exhausts an iterator."""
+    deque(iterator, maxlen=0)
+
+# Custom collections --------------------------------------
 class defaultlist(list):
     """Default list class. Allows writing and reading out of bounds."""
     def __init__(self, lst, val_factory):
@@ -23,17 +30,56 @@ class defaultlist(list):
             return self.val_factory() 
         return super().__getitem__(i)
 
+# Basic linear algebra ------------------------------------
+class vector(tuple):
+    """Vector class. Convert iterator to vector."""
+    def __neg__(self):
+        return vector(-x for x in self)
 
-def memoize(f):
-    cache = dict()
-    def memf(*args):
-        key = tuple(args)
-        if key not in cache:
-            cache[key] = f(*args)
-        return cache[key]
-    return memf
+    def __add__(self, other):
+        o = tuple(other)
+        if len(self) != len(o):
+            raise ValueError("vectors have different lengths")
+        return vector(x + y for x, y in zip(self, o))
 
+    def __sub__(self, other):
+        return self + (- vector(other)) 
 
+    def __mul__(self, other):
+        if type(other) == int:
+            return vector(other * x for x in self)
+        o = tuple(other)
+        if len(o) != len(self):
+            raise ValueError("vectors have different lengths")
+        return sum(x * y for x, y in zip(self, o))
+
+    def __truediv__(self, d):
+        return vector(x/d for x in self)
+
+    __radd__ = __add__
+    __rmul__ = __mul__
+
+    def __rsub__(self, other):
+        return other + (-self)
+
+def rotate90pos(v):
+    """Rotates vector v by 90 degrees in positive direction."""
+    x, y = v
+    return vector((-y, x))
+
+def rotate90neg(v):
+    """Rotates vector v by 90 degrees in negative direction."""
+    x, y = v
+    return vector((x, -y))
+
+class Cardinals(Enum):
+    UP     = vector((0, 1))
+    DOWN   = vector((0, -1))
+    LEFT   = vector((-1, 0))
+    RIGHT  = vector((1, 0))
+    ORIGIN = vector((0, 0))
+
+# Graphs ---------------------------------------------------
 class Graph(dict):
     nodes = dict.keys