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42 lines
1.2 KiB
42 lines
1.2 KiB
import math
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import re
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with open("input") as file:
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target = file.read().removesuffix("\n")
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minX, maxX, minY, maxY = [int(v) for v in re.search(r"x=(.+)\.\.(.+), y=(.+)\.\.(.+)", target).groups()]
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# minimize the set of velocities to check via bounds
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# lower x bound cant be lower than a
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# where a(a+1)/2 = minX (little gauss)
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# because posX loses 1 every step and posX must at least reach minX
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# isolating a gives -0.5 + sqrt(0.25 + 2 * minX)
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# ceiling is enough because if minX gets a bit higher then a cannot reach it anymore
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xBounds = math.ceil(-0.5 + math.sqrt(0.25 + 2 * minX)), maxX
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# yPos is symmetric on the way back down and starts with 0
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yBounds = minY, -minY
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xRange = range(xBounds[0], xBounds[1] + 1)
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yRange = range(yBounds[0], yBounds[1] + 1)
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validCount = 0
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allMaxYReached = []
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# simulate all possible velocities
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for vx, vy in [(x, y) for x in xRange for y in yRange]:
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posX, posY = 0, 0
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maxYReached = 0
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while posX <= maxX and posY >= minY:
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if posX >= minX and posY <= maxY:
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# target hit
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validCount += 1
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allMaxYReached.append(maxYReached)
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break
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posX += vx
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posY += vy
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vx -= 1 if vx > 0 else 0
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vy -= 1
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maxYReached = max(posY, maxYReached)
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print(max(allMaxYReached))
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print(validCount)
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