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43 lines
1.3 KiB
43 lines
1.3 KiB
4 years ago
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input = ARGF.read.split("\n")
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depart_time = input.shift.to_i
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buses = input.shift.split(?,).map {|b| b != ?x ? b.to_i : nil }
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# p buses.compact.map {|bus|
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# d = bus * ((depart_time / bus) + 1)
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# [bus, d - depart_time]
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# }.min_by(&:last).inject {|a,b| a * b }
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# shamelessly copied from https://rosettacode.org/wiki/Chinese_remainder_theorem#Ruby
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def extended_gcd(a, b)
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last_remainder, remainder = a.abs, b.abs
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x, last_x, y, last_y = 0, 1, 1, 0
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while remainder != 0
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last_remainder, (quotient, remainder) = remainder, last_remainder.divmod(remainder)
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x, last_x = last_x - quotient*x, x
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y, last_y = last_y - quotient*y, y
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end
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return last_remainder, last_x * (a < 0 ? -1 : 1)
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end
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def invmod(e, et)
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g, x = extended_gcd(e, et)
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if g != 1
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raise 'Multiplicative inverse modulo does not exist!'
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end
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x % et
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end
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def chinese_remainder(mods, remainders)
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max = mods.inject( :* ) # product of all moduli
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series = remainders.zip(mods).map{ |r,m| (r * max * invmod(max/m, m) / m) }
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series.inject( :+ ) % max
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end
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buses = buses.map.with_index.select {|b,_| b }
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# p 0.step(by: buses[0][0]).lazy.find {|depart_time|
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# buses.all? {|b,i| (depart_time + i) % b == 0 }
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# }
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mods, remainders = buses.map {|b,i| [b, b-i] }.transpose
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p chinese_remainder(mods, remainders)
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