80 lines
1.9 KiB
Python
80 lines
1.9 KiB
Python
'''Van Eck series by map-accumulation'''
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from functools import reduce
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from itertools import repeat
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# vanEck :: Int -> [Int]
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def vanEck(n):
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'''First n terms of the vanEck sequence.'''
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def go(xns, i):
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x, ns = xns
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prev = ns[x]
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v = i - prev if 0 is not prev else 0
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return (
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(v, insert(ns, x, i)),
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v
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)
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return [0] + mapAccumL(go)((0, list(repeat(0, n))))(
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range(1, n)
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)[1]
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# -------------------------- TEST --------------------------
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# main :: IO ()
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def main():
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'''The last 10 of the first N vanEck terms'''
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print(
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fTable(main.__doc__ + ':\n')(
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lambda m: 'N=' + str(m), repr,
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lambda n: vanEck(n)[-10:], [10, 1000, 10000]
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)
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)
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# ----------------------- FORMATTING -----------------------
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# fTable :: String -> (a -> String) ->
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# (b -> String) -> (a -> b) -> [a] -> String
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def fTable(s):
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'''Heading -> x display function -> fx display function ->
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f -> xs -> tabular string.
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'''
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def go(xShow, fxShow, f, xs):
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ys = [xShow(x) for x in xs]
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w = max(map(len, ys))
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return s + '\n' + '\n'.join(map(
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lambda x, y: y.rjust(w, ' ') + ' -> ' + fxShow(f(x)),
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xs, ys
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))
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return go
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# ------------------------ GENERIC -------------------------
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# insert :: Array Int -> Int -> Int -> Array Int
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def insert(xs, i, v):
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'''An array updated at position i with value v.'''
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xs[i] = v
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return xs
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# mapAccumL :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])
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def mapAccumL(f):
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'''A tuple of an accumulation and a list derived by a
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combined map and fold,
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with accumulation from left to right.
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'''
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def go(a, x):
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tpl = f(a[0], x)
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return (tpl[0], a[1] + [tpl[1]])
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return lambda acc: lambda xs: (
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reduce(go, xs, (acc, []))
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)
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# MAIN ---
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if __name__ == '__main__':
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main()
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