From 4e1c71b221c24849e977284979085ce5f103fbff Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Mika=C3=ABl=20Capelle?= <capelle.mikael@gmail.com>
Date: Wed, 6 Dec 2023 07:13:53 +0100
Subject: [PATCH] 2023 day 6.

---
 2023/day6.py         | 49 ++++++++++++++++++++++++++++++++++++++++----
 2023/inputs/day6.txt |  2 ++
 2023/tests/day6.txt  |  2 ++
 3 files changed, 49 insertions(+), 4 deletions(-)

diff --git a/2023/day6.py b/2023/day6.py
index 992bf35..0c4a864 100644
--- a/2023/day6.py
+++ b/2023/day6.py
@@ -1,13 +1,54 @@
+import operator
 import sys
-from collections import defaultdict
-from dataclasses import dataclass
+from functools import reduce
 
 lines = sys.stdin.read().splitlines()
 
+
+def extreme_times_to_beat(time: int, distance: int) -> tuple[int, int]:
+    import math
+
+    # formula
+    # - distance = (T - t) * t
+    # - (T - t) * t >= D
+    # - T * t - t^2 - D >= 0
+
+    a = -1
+    b = time
+    c = -distance
+
+    d = b * b - 4 * a * c
+
+    t1 = math.ceil(-(b - math.sqrt(d)) / (2 * a))
+    t2 = math.floor(-(b + math.sqrt(d)) / (2 * a))
+
+    if (time - t1) * t1 == distance:
+        t1 += 1
+
+    if (time - t2) * t2 == distance:
+        t2 -= 1
+
+    return t1, t2
+
+
 # part 1
-answer_1 = ...
+times = list(map(int, lines[0].split()[1:]))
+distances = list(map(int, lines[1].split()[1:]))
+answer_1 = reduce(
+    operator.mul,
+    (
+        t2 - t1 + 1
+        for t1, t2 in (
+            extreme_times_to_beat(time, distance)
+            for time, distance in zip(times, distances)
+        )
+    ),
+)
 print(f"answer 1 is {answer_1}")
 
 # part 2
-answer_2 = ...
+time = int(lines[0].split(":")[1].strip().replace(" ", ""))
+distance = int(lines[1].split(":")[1].strip().replace(" ", ""))
+t1, t2 = extreme_times_to_beat(time, distance)
+answer_2 = t2 - t1 + 1
 print(f"answer 2 is {answer_2}")
diff --git a/2023/inputs/day6.txt b/2023/inputs/day6.txt
index e69de29..01c2b63 100644
--- a/2023/inputs/day6.txt
+++ b/2023/inputs/day6.txt
@@ -0,0 +1,2 @@
+Time:        59     79     65     75
+Distance:   597   1234   1032   1328
diff --git a/2023/tests/day6.txt b/2023/tests/day6.txt
index e69de29..28f5ae9 100644
--- a/2023/tests/day6.txt
+++ b/2023/tests/day6.txt
@@ -0,0 +1,2 @@
+Time:      7  15   30
+Distance:  9  40  200