75 lines
1.8 KiB
Python
75 lines
1.8 KiB
Python
from math import sqrt
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sample = {
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"time": [7, 15, 30],
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"distance": [9, 40, 200],
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}
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input = {
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"time": [ 48, 87, 69, 81,],
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"distance": [ 255, 1288, 1117, 1623,],
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}
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def solve(data):
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time = data["time"]
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dist = data["distance"]
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part1 = 1
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for t, best in zip(time, dist):
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ways = 0
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for i in range(t):
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v = i
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d = (t-i)*v
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if d > best:
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ways += 1
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part1 *= ways
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return part1
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def fancy_solve(data):
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time = data["time"]
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dist = data["distance"]
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for t, best in zip(time, dist):
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# the distance traveled if the boat is released at time i
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# is equal to (t-i)*i
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# we want to know the range of values of i for which this
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# exceeds the best time
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# (t-i)*i > best
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# a little rearranging gets us the quadratic equation
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# i^2 - ti + best <= 0
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# which we can determine the crossing points for
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# using the quadratic formula (the good one, not the
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# one you learned in school)
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h = t/2
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s = sqrt(h*h - best)
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#print(h-s, h+s)
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# in general these will not be at integer values,
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# so we probe the floor and ceiling of each crossing
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# point to determine exactly where the condition is met
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a = int(h-s)
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b = int(h+s)
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if (t-a)*a <= best:
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a += 1
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if (t-b)*b > best:
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b += 1
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ways = b - a
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return ways
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print(solve(sample))
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print(solve(input))
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def part2(data):
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return {"time": [int("".join(str(x) for x in data["time"]))],
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"distance": [int("".join(str(x) for x in data["distance"]))]}
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print(solve(part2(sample)))
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print(fancy_solve(part2(sample)))
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print(fancy_solve(part2(input)))
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