day 17

1 files changed, 37 insertions, 0 deletions

diff --git a/17.py b/17.py
new file mode 100644
index 0000000..fa426d4
--- /dev/null
+++ b/17.py
@@ -0,0 +1,37 @@
+from math import sqrt, ceil, floor
+from utils import parse_day
+
+tx_min, tx_max, ty_min, ty_max = \
+    map(int, parse_day(17, r'.* x=(-?\d+)..(-?\d+), y=(-?\d+)..(-?\d+)'))
+
+vx_min = int(sqrt(tx_min * 2) - 1)
+vx_max = tx_max
+vy_min = ty_min
+vy_max = abs(ty_min) - 1
+
+def sum_n(n):
+    return n * (n + 1) // 2
+
+print(sum_n(vy_max))
+
+def time_at_pos(v, d):
+    """d = - (t + 1)(t - 2v) / 2 solved for t"""
+    return (sqrt((2 * v + 1) ** 2 - 8 * d) + 2 * v - 1) / 2 + 1
+
+def y_times(vy0):
+    start = time_at_pos(vy0, ty_max)
+    end = time_at_pos(vy0, ty_min)
+    return range(ceil(start), floor(end) + 1)
+
+def x_at(vx0, t):
+    assert(t >= 0)
+    return sum_n(vx0) - sum_n(max(vx0 - t, 0))
+
+count = 0
+for vy0 in range(vy_min, vy_max + 1):
+    for vx0 in range(vx_min, vx_max + 1):
+        for t in y_times(vy0):
+            if tx_min <= x_at(vx0, t) <= tx_max:
+                count += 1
+                break
+print(count)