From 1081a4fc8d59c8ed7baa558f3b433703ebc0d3a8 Mon Sep 17 00:00:00 2001
From: Bruno BELANYI <bruno@belanyi.fr>
Date: Wed, 6 Dec 2023 09:16:02 +0000
Subject: [PATCH] 2023: d06: ex1: add solution

---
 2023/d06/ex1/ex1.py | 36 ++++++++++++++++++++++++++++++++++++
 1 file changed, 36 insertions(+)
 create mode 100755 2023/d06/ex1/ex1.py

diff --git a/2023/d06/ex1/ex1.py b/2023/d06/ex1/ex1.py
new file mode 100755
index 0000000..1cbd4b7
--- /dev/null
+++ b/2023/d06/ex1/ex1.py
@@ -0,0 +1,36 @@
+#!/usr/bin/env python
+
+import math
+import sys
+
+
+def solve(input: list[str]) -> int:
+    def parse_line(line: str) -> list[int]:
+        return [int(n) for n in line.split(":")[1].split()]
+
+    def solve(time: int, distance: int) -> int:
+        # With n being the button-held-down time.
+        # We want to solve: (time - n) * n > distance
+        # So we want the number of intergers in ]n_1, n_2[, n_1 and n_2 roots of the quadratic
+        # a = -1, b = time, c = -distance
+        determinant = time**2 - 4 * distance
+        if determinant <= 0:
+            return 0
+        max = time / 2
+        delta = math.sqrt(determinant) / 2
+        n_1 = max - delta
+        n_2 = max + delta
+        return math.ceil(n_2 - 1) - math.floor(n_1 + 1) + 1
+
+    times, distances = map(parse_line, input)
+
+    return math.prod(solve(t, d) for t, d in zip(times, distances))
+
+
+def main() -> None:
+    input = sys.stdin.read().splitlines()
+    print(solve(input))
+
+
+if __name__ == "__main__":
+    main()