day6

Author: shuckc

2023/day6.py

@@ -0,0 +1,62 @@
+from common import ai
+from math import sqrt, ceil, floor
+
+inp = """
+Time:      7  15   30
+Distance:  9  40  200
+"""
+
+def parse_p1(inp):
+    res = []
+    for l in inp.strip().split("\n"):
+        a,ns = l.split(':')
+        res.append(list(map(int, ns.strip().split())))
+    assert len(res) == 2
+    return res
+
+def p1(inp):
+    ts, ds = inp
+    ways = 1
+    for t,d in zip(ts, ds):
+        print(f"race t {t} record d {d}")
+
+        # known t,d  unknown time charging, tc
+        # d = ts*speed   where ts=t-tc, speed=tc
+        #   = (t-tc)*tc
+        #   = t*tc - tc*tc
+        # 0 = -1*tc^2 +t*tc -d
+        # solve roots by quadratic eqn a=-1, b=t, c=-d, x=tc
+        # tc = (-b +- sqrt(bb - 4ac)))/2a
+        # tc = (-t +- sqrt(tt - 4*d))/-2
+        # tc = (t +- sqrt(tt - 4d)) /2
+        tc_p = (t + sqrt(t*t - 4*d))/2
+        tc_m = (t - sqrt(t*t - 4*d))/2
+        tc_m = ceil(tc_m)
+        tc_p = floor(tc_p)
+        print(f"tc={tc_m}  tc={tc_p}")
+
+        # need to beat the record, not match it exactly.
+        # nudge by 1 more towards max distance
+        while tc_m * (t-tc_m) <= d:
+            tc_m += 1
+        while tc_p * (t-tc_p) <= d:
+            tc_p -= 1
+        print(f"after inequality adjustment {tc_m} - {tc_p}")
+        ways = ways * (tc_p - tc_m + 1)
+    return ways
+
+ai(p1(parse_p1(inp)), 288)
+ai(p1(parse_p1(open("day6.txt").read())), 1710720)
+
+# stupid part2 parser without spaces
+def parse_p2(inp):
+    res = []
+    for l in inp.strip().split("\n"):
+        a,ns = l.split(':')
+        ns = ns.replace(" ", "")
+        res.append(list(map(int, ns.strip().split())))
+    assert len(res) == 2
+    return res
+
+ai(p1(parse_p2(inp)), 71503)
+ai(p1(parse_p2(open("day6.txt").read())), 35349468)

2023/day6.txt

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+Time:        56     97     77     93
+Distance:   499   2210   1097   1440