From 77660a8cf9264db955b35801272386e7d6f68fdd Mon Sep 17 00:00:00 2001
From: Tomasz Kramkowski <tk@the-tk.com>
Date: Sat, 18 Dec 2021 00:24:20 +0000
Subject: day 17: now faster with a list of intervals

---
 17.py | 71 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++-----------
 1 file changed, 60 insertions(+), 11 deletions(-)

diff --git a/17.py b/17.py
index ebe3116..88665b3 100644
--- a/17.py
+++ b/17.py
@@ -1,7 +1,33 @@
+from __future__ import annotations
 from math import sqrt, ceil, floor
 from utils import parse_day
-from collections import defaultdict
-from itertools import chain
+from functools import cache, total_ordering
+from enum import Enum, auto
+from dataclasses import dataclass
+
+@total_ordering
+@dataclass(frozen=True)
+class Interval:
+    class Type(Enum):
+        START = auto()
+        END = auto()
+
+    class Axis(Enum):
+        Y = auto()
+        X = auto()
+
+    time: int
+    type: Interval.Type
+    axis: Interval.Axis
+    value: int
+
+    def __lt__(self, other: Interval) -> bool:
+        def cmptuple(o: Interval) -> tuple[int, bool, bool]:
+            is_end: bool = o.type == Interval.Type.END
+            return o.time, is_end, (o.axis == Interval.Axis.Y) ^ is_end, o.value
+        if not isinstance(other, Interval):
+            return NotImplemented
+        return cmptuple(self) < cmptuple(other)
 
 tx_min, tx_max, ty_min, ty_max = \
     map(int, parse_day(17, r'.* x=(-?\d+)..(-?\d+), y=(-?\d+)..(-?\d+)'))
@@ -11,16 +37,19 @@ vx_max = tx_max
 vy_min = ty_min
 vy_max = abs(ty_min) - 1
 
+@cache
 def sum_n(n):
     return n * (n + 1) // 2
 
 print(sum_n(vy_max))
 
+@cache
 def time_at_pos(v, d):
     """d = -t(t - 2v - 1) / 2 solved for t"""
     middle = sqrt((2 * v + 1) ** 2 - 8 * d)
     return (-middle + 2 * v + 1) / 2, (middle + 2 * v + 1) / 2
 
+@cache
 def time_at_xpos(v, d):
     if d > sum_n(v): return float('inf')
     return time_at_pos(v, d)[0]
@@ -32,18 +61,38 @@ def y_times(vy0):
 
 def x_times(vx0):
     start = time_at_xpos(vx0, tx_min)
+    if start != float('inf'): start = ceil(start)
     end = time_at_xpos(vx0, tx_max)
+    if end != float('inf'): end = floor(end)
     return start, end
 
-times = defaultdict(set)
+intervals = []
+for vx0 in range(vx_min, vx_max + 1):
+    start, end = x_times(vx0)
+    if end < start: continue
+    intervals.append(Interval(start, Interval.Type.START, Interval.Axis.X, vx0))
+    intervals.append(Interval(end,   Interval.Type.END,   Interval.Axis.X, vx0))
 for vy0 in range(vy_min, vy_max + 1):
-    tmin, tmax = y_times(vy0)
-    for t in range(tmin, tmax + 1):
-        times[t].add(vy0)
+    start, end = y_times(vy0)
+    if end < start: continue
+    intervals.append(Interval(start, Interval.Type.START, Interval.Axis.Y, vy0))
+    intervals.append(Interval(end,   Interval.Type.END,   Interval.Axis.Y, vy0))
+intervals.sort()
+active_vx0 = set()
+active_vy0 = set()
 count = 0
-for vx0 in range(vx_min, vx_max + 1):
-    tmin, tmax = x_times(vx0)
-    count += len(set(chain.from_iterable(
-        vy0set for t, vy0set in times.items() if tmin <= t <= tmax
-    )))
+for interval in intervals:
+    match interval:
+        case Interval(type=Interval.Type.END, axis=axis, value=value):
+            match axis:
+                case Interval.Axis.X: active_vx0.remove(value)
+                case Interval.Axis.Y: active_vy0.remove(value)
+        case Interval(type=Interval.Type.START, axis=axis, value=value):
+            match axis:
+                case Interval.Axis.X:
+                    count += len(active_vy0)
+                    active_vx0.add(value)
+                case Interval.Axis.Y:
+                    count += len(active_vx0)
+                    active_vy0.add(value)
 print(count)
-- 
cgit v1.2.3-54-g00ecf