1 files changed, 57 insertions, 1 deletions
diff --git a/utils.py b/utils.py
index 91b90ff..83a54c1 100644
--- a/utils.py
+++ b/utils.py
@@ -1,8 +1,64 @@
 from collections import deque
 from collections.abc import Iterable, Iterator, Generator
+from dataclasses import dataclass
 from itertools import islice
+from math import sqrt
 from sys import argv
-from typing import TypeVar
+from typing import TypeVar, Generic, Union, Optional, cast
+
+Numeric = Union[int, float]
+
+T = TypeVar('T', bound=Numeric)
+@dataclass(frozen=True)
+class Point2D(Generic[T]):
+    x: T
+    y: T
+
+    def __str__(self) -> str:
+        return f'({self.x}, {self.y})'
+
+    def __add__(self, other: 'Point2D') -> Union['Point2D', bool]:
+        if isinstance(other, Point2D):
+            return Point2D(self.x + other.x, self.y + other.y)
+        return NotImplemented
+
+    def __sub__(self, other: 'Point2D') -> Union['Point2D', bool]:
+        if isinstance(other, Point2D):
+            return Point2D(self.x - other.x, self.y - other.y)
+        return NotImplemented
+
+    def __abs__(self) -> 'Point2D':
+        return Point2D(abs(self.x), abs(self.y))
+
+T = TypeVar('T', bound=Numeric)
+def norm_1(p: Point2D[T]) -> T:
+    return abs(p.x) + abs(p.y)
+
+def norm_2(p: Point2D) -> float:
+    return sqrt(p.x ** 2 + p.y ** 2)
+
+T = TypeVar('T', bound=Numeric)
+def norm_inf(p: Point2D[T]) -> T:
+    return max(abs(p.x), abs(p.y))
+
+T = TypeVar('T', bound=Numeric)
+def inbounds(p: Point2D[T], a: Point2D[T], b: Optional[Point2D[T]] = None) -> bool:
+    if b is None and isinstance(a.x, int):
+        b = a
+        a = cast(Point2D[T], Point2D(0, 0))
+    return p.x >= a.x and p.y >= a.y and p.x < b.x and p.y < b.y
+
+def adjacent(p: Point2D[int], diagonal: bool = True) \
+        -> Generator[Point2D[int], None, None]:
+    for dx in range(-1, 2):
+        for dy in range(-1, 2):
+            if dx == 0 and dy == 0: continue
+            if dx != 0 and dy != 0 and not adjacent: continue
+            yield Point2D(p.x + dx, p.y + dy)
+
+def adjacent_bounded(p: Point2D[int], bound: Point2D[int], diagonal: bool = True) \
+        -> filter[Point2D[int]]: # This has to return filter[...] not Generator[...] because ???
+    return filter(lambda p: inbounds(p, bound), adjacent(p, diagonal))
 
 T = TypeVar('T')
 def sliding_window(iterable: Iterable[T], n: int) -> Generator[tuple[T, ...], None, None]: