utils: Point2D and related functions

4 files changed, 109 insertions, 55 deletions

diff --git a/15.py b/15.py
index ab369f5..231f5e8 100644
--- a/15.py
+++ b/15.py
@@ -1,21 +1,34 @@
 from collections import defaultdict
-from utils import open_day
+from utils import open_day, Point2D, adjacent_bounded
 from heapq import heappop, heappush
 
 def a_star(start, goal, neighbours, h, d):
+    vtoi = dict()
+    itov = dict()
+    i = 0
+    def intern(v):
+        nonlocal i
+        ret = vtoi.get(v)
+        if ret is None:
+            ret = i
+            vtoi[v] = i
+            itov[i] = v
+            i += 1
+        return ret
     open_set = {start}
-    open_heapq = [(0, start)]
+    open_heapq = [(0, intern(start))]
     came_from = dict()
     g_score = defaultdict(lambda: float('inf'))
     g_score[start] = 0
     f_score = defaultdict(lambda: float('inf'))
     f_score[start] = h(start)
-
     while open_set:
-        f, current = open_heapq[0]
+        while True:
+            f, current = heappop(open_heapq)
+            current = itov[current]
+            if current in open_set: break
         if current == goal:
             return f
-        heappop(open_heapq)
         open_set.remove(current)
         for neighbour in neighbours(current):
             tentative_g = g_score[current] + d(current, neighbour)
@@ -23,31 +36,22 @@ def a_star(start, goal, neighbours, h, d):
                 came_from[neighbour] = current
                 g_score[neighbour] = tentative_g
                 f_score[neighbour] = tentative_g + h(neighbour)
-                if neighbour not in open_set:
-                    open_set.add(neighbour)
-                    heappush(open_heapq, (f_score[neighbour], neighbour))
+                open_set.add(neighbour)
+                heappush(open_heapq, (f_score[neighbour], intern(neighbour)))
     return None
 
 with open_day(15) as f:
     inp = [[int(c) for c in l.rstrip()] for l in f]
 
-def neighbours(p, dim):
-    for dx, dy in ((-1, 0), (1, 0), (0, -1), (0, 1)):
-        px, py = p[0] + dx, p[1] + dy
-        if px < 0 or py < 0 or px >= dim[0] or py >= dim[1]: continue
-        yield px, py
-
-def manhattan(a, b): return abs(a[0] - b[0]) + abs(a[1] - b[1])
 def d(a, b):
-    x, y = b
-    add = x // len(inp[0]) + y // len(inp)
-    x, y = x % len(inp[0]), y % len(inp)
+    add = b.x // len(inp[0]) + b.y // len(inp)
+    x, y = b.x % len(inp[0]), b.y % len(inp)
     return (inp[y][x] + add - 1) % 9 + 1
 
-start = (0, 0)
-goal1 = (len(inp[0]) - 1, len(inp) - 1)
-neighbours1 = lambda p: neighbours(p, (len(inp[0]), len(inp)))
-print(a_star(start, goal1, neighbours1, lambda p: manhattan(p, goal1), d))
-goal2 = (len(inp[0]) * 5 - 1, len(inp) * 5 - 1)
-neighbours2 = lambda p: neighbours(p, (len(inp[0]) * 5, len(inp) * 5))
-print(a_star(start, goal2, neighbours2, lambda p: manhattan(p, goal2), d))
+start = Point2D(0, 0)
+goal1 = Point2D(len(inp[0]) - 1, len(inp) - 1)
+neighbours1 = lambda p: adjacent_bounded(p, Point2D(len(inp[0]), len(inp)), False)
+print(a_star(start, goal1, neighbours1, lambda p: 0, d))
+goal2 = Point2D(len(inp[0]) * 5 - 1, len(inp) * 5 - 1)
+neighbours2 = lambda p: adjacent_bounded(p, Point2D(len(inp[0]) * 5, len(inp) * 5), False)
+print(a_star(start, goal2, neighbours2, lambda p: 0, d))
diff --git a/5.py b/5.py
index 1e61efb..802ccc7 100644
--- a/5.py
+++ b/5.py
@@ -1,11 +1,9 @@
 from collections import defaultdict, namedtuple
-from utils import open_day
-
-Pos = namedtuple('Pos', ['x', 'y'])
+from utils import open_day, Point2D
 
 vents = [
     tuple(
-        Pos(*map(int, h.split(',')))
+        Point2D(*map(int, h.split(',')))
         for h in l.rstrip().split(' -> ')
     )
     for l in open_day(5).read().rstrip().split('\n')
diff --git a/9.py b/9.py
index d1a63b9..0db75b1 100644
--- a/9.py
+++ b/9.py
@@ -1,45 +1,43 @@
 from functools import reduce
-from utils import open_day
+from utils import open_day, Point2D, adjacent_bounded
 from collections import deque
 
 heatmap = [[int(c) for c in l.rstrip()] for l in open_day(9)]
+bounds = Point2D(len(heatmap[0]), len(heatmap))
 adj = [(1, 0), (0, 1), (-1, 0), (0, -1)]
 
-def is_low(x, y):
-    risk = heatmap[y][x]
-    for dx, dy in adj:
-        nx = x + dx
-        ny = y + dy
-        if nx >= 0 and nx < len(heatmap[0]) and ny >= 0 and ny < len(heatmap):
-            if heatmap[y+dy][x+dx] <= risk:
-                return False
+def is_low(p):
+    risk = heatmap[p.y][p.x]
+    for n in adjacent_bounded(p, bounds, False):
+        if heatmap[n.y][n.x] <= risk:
+            return False
     return True
 
-def basin_size(x, y):
+def basin_size(p):
     seen = set()
-    queue = deque(((x, y),))
+    queue = deque((p,))
     size = 0
     while queue:
-        x, y = queue.popleft()
-        if (x, y) in seen:
+        p = queue.popleft()
+        if p in seen:
             continue
-        if x < 0 or x >= len(heatmap[0]) or y < 0 or y >= len(heatmap):
-            continue
-        seen.add((x, y))
-        if heatmap[y][x] == 9:
+        seen.add(p)
+        if heatmap[p.y][p.x] == 9:
             continue
         size += 1
-        for dx, dy in adj:
-            queue.append((x + dx, y + dy))
+        for n in adjacent_bounded(p, bounds, False):
+            # print(p, n)
+            queue.append(n)
     return size
 
 totrisk = 0
 lows = []
-for y in range(len(heatmap)):
-    for x in range(len(heatmap[y])):
-        if is_low(x, y):
+for y in range(bounds.y):
+    for x in range(bounds.x):
+        p = Point2D(x, y)
+        if is_low(p):
             totrisk += 1 + heatmap[y][x]
-            lows.append(basin_size(x, y))
+            lows.append(basin_size(p))
 print(totrisk)
 lows.sort()
 print(reduce(lambda x, y: x * y, lows[-3:], 1))
diff --git a/utils.py b/utils.py
index 91b90ff..00d0d60 100644
--- a/utils.py
+++ b/utils.py
@@ -1,11 +1,65 @@
+from __future__ import annotations
 from collections import deque
-from collections.abc import Iterable, Iterator, Generator
+from collections.abc import Iterable, Iterator
+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
+
+NumT = TypeVar('NumT', float, int)
+
+@dataclass(frozen=True)
+class Point2D(Generic[NumT]):
+    x: NumT
+    y: NumT
+
+    def __str__(self) -> str:
+        return f'({self.x}, {self.y})'
+
+    def __add__(self, other: Point2D[NumT]) -> Union[Point2D[NumT], bool]:
+        if isinstance(other, Point2D):
+            return Point2D(self.x + other.x, self.y + other.y)
+        return NotImplemented
+
+    def __sub__(self, other: Point2D[NumT]) -> Union[Point2D[NumT], bool]:
+        if isinstance(other, Point2D):
+            return Point2D(self.x - other.x, self.y - other.y)
+        return NotImplemented
+
+    def __abs__(self) -> Point2D[NumT]:
+        return Point2D(cast(NumT, abs(self.x)), cast(NumT, abs(self.y)))
+
+def norm_1(p: Point2D[NumT]) -> NumT:
+    return cast(NumT, abs(p.x) + abs(p.y))
+
+def norm_2(p: Point2D) -> float:
+    return sqrt(p.x ** 2 + p.y ** 2)
+
+def norm_inf(p: Point2D[NumT]) -> NumT:
+    return cast(NumT, max(abs(p.x), abs(p.y)))
+
+def inbounds(p: Point2D[NumT], a: Point2D[NumT], _b: Optional[Point2D[NumT]] = None) -> bool:
+    if isinstance(_b, Point2D):
+        b = _b
+    else:
+        b = a
+        a = cast(Point2D[NumT], Point2D(0, 0) if isinstance(a.x, int) else Point2D(0.0, 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) -> Iterator[Point2D[int]]:
+    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) \
+        -> Iterator[Point2D[int]]:
+    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]:
+def sliding_window(iterable: Iterable[T], n: int) -> Iterator[tuple[T, ...]]:
     # sliding_window('ABCDEFG', 4) -> ABCD BCDE CDEF DEFG
     it: Iterator[T] = iter(iterable)
     window: deque[T] = deque(islice(it, n), maxlen=n)