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Ingy döt Net
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>>> def fiblike(start):
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addnum = len(start)
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memo = start[:]
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def fibber(n):
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try:
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return memo[n]
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except IndexError:
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ans = sum(fibber(i) for i in range(n-addnum, n))
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memo.append(ans)
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return ans
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return fibber
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>>> fibo = fiblike([1,1])
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>>> [fibo(i) for i in range(10)]
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[1, 1, 2, 3, 5, 8, 13, 21, 34, 55]
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>>> lucas = fiblike([2,1])
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>>> [lucas(i) for i in range(10)]
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[2, 1, 3, 4, 7, 11, 18, 29, 47, 76]
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>>> for n, name in zip(range(2,11), 'fibo tribo tetra penta hexa hepta octo nona deca'.split()) :
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fibber = fiblike([1] + [2**i for i in range(n-1)])
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print('n=%2i, %5snacci -> %s ...' % (n, name, ' '.join(str(fibber(i)) for i in range(15))))
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n= 2, fibonacci -> 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 ...
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n= 3, tribonacci -> 1 1 2 4 7 13 24 44 81 149 274 504 927 1705 3136 ...
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n= 4, tetranacci -> 1 1 2 4 8 15 29 56 108 208 401 773 1490 2872 5536 ...
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n= 5, pentanacci -> 1 1 2 4 8 16 31 61 120 236 464 912 1793 3525 6930 ...
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n= 6, hexanacci -> 1 1 2 4 8 16 32 63 125 248 492 976 1936 3840 7617 ...
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n= 7, heptanacci -> 1 1 2 4 8 16 32 64 127 253 504 1004 2000 3984 7936 ...
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n= 8, octonacci -> 1 1 2 4 8 16 32 64 128 255 509 1016 2028 4048 8080 ...
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n= 9, nonanacci -> 1 1 2 4 8 16 32 64 128 256 511 1021 2040 4076 8144 ...
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n=10, decanacci -> 1 1 2 4 8 16 32 64 128 256 512 1023 2045 4088 8172 ...
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>>>
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>>> class Fiblike():
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def __init__(self, start):
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self.addnum = len(start)
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self.memo = start[:]
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def __call__(self, n):
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try:
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return self.memo[n]
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except IndexError:
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ans = sum(self(i) for i in range(n-self.addnum, n))
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self.memo.append(ans)
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return ans
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>>> fibo = Fiblike([1,1])
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>>> [fibo(i) for i in range(10)]
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[1, 1, 2, 3, 5, 8, 13, 21, 34, 55]
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>>> lucas = Fiblike([2,1])
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>>> [lucas(i) for i in range(10)]
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[2, 1, 3, 4, 7, 11, 18, 29, 47, 76]
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>>> for n, name in zip(range(2,11), 'fibo tribo tetra penta hexa hepta octo nona deca'.split()) :
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fibber = Fiblike([1] + [2**i for i in range(n-1)])
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print('n=%2i, %5snacci -> %s ...' % (n, name, ' '.join(str(fibber(i)) for i in range(15))))
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n= 2, fibonacci -> 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 ...
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n= 3, tribonacci -> 1 1 2 4 7 13 24 44 81 149 274 504 927 1705 3136 ...
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n= 4, tetranacci -> 1 1 2 4 8 15 29 56 108 208 401 773 1490 2872 5536 ...
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n= 5, pentanacci -> 1 1 2 4 8 16 31 61 120 236 464 912 1793 3525 6930 ...
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n= 6, hexanacci -> 1 1 2 4 8 16 32 63 125 248 492 976 1936 3840 7617 ...
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n= 7, heptanacci -> 1 1 2 4 8 16 32 64 127 253 504 1004 2000 3984 7936 ...
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n= 8, octonacci -> 1 1 2 4 8 16 32 64 128 255 509 1016 2028 4048 8080 ...
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n= 9, nonanacci -> 1 1 2 4 8 16 32 64 128 256 511 1021 2040 4076 8144 ...
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n=10, decanacci -> 1 1 2 4 8 16 32 64 128 256 512 1023 2045 4088 8172 ...
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>>>
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from itertools import islice, cycle
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def fiblike(tail):
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for x in tail:
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yield x
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for i in cycle(xrange(len(tail))):
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tail[i] = x = sum(tail)
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yield x
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fibo = fiblike([1, 1])
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print list(islice(fibo, 10))
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lucas = fiblike([2, 1])
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print list(islice(lucas, 10))
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suffixes = "fibo tribo tetra penta hexa hepta octo nona deca"
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for n, name in zip(xrange(2, 11), suffixes.split()):
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fib = fiblike([1] + [2 ** i for i in xrange(n - 1)])
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items = list(islice(fib, 15))
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print "n=%2i, %5snacci -> %s ..." % (n, name, items)
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'''Fibonacci n-step number sequences'''
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from itertools import chain, count, islice
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# A000032 :: () -> [Int]
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def A000032():
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'''Non finite sequence of Lucas numbers.
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'''
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return unfoldr(recurrence(2))([2, 1])
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# nStepFibonacci :: Int -> [Int]
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def nStepFibonacci(n):
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'''Non-finite series of N-step Fibonacci numbers,
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defined by a recurrence relation.
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'''
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return unfoldr(recurrence(n))(
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take(n)(
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chain(
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[1],
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(2 ** i for i in count(0))
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)
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)
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)
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# recurrence :: Int -> [Int] -> Int
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def recurrence(n):
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'''Recurrence relation in Fibonacci and related series.
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'''
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def go(xs):
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h, *t = xs
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return h, t + [sum(take(n)(xs))]
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return go
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# ------------------------- TEST -------------------------
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# main :: IO ()
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def main():
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'''First 15 terms each n-step Fibonacci(n) series
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where n is drawn from [2..8]
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'''
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labels = "fibo tribo tetra penta hexa hepta octo nona deca"
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table = list(
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chain(
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[['lucas:'] + [
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str(x) for x in take(15)(A000032())]
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],
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map(
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lambda k, n: list(
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chain(
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[k + 'nacci:'],
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(
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str(x) for x
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in take(15)(nStepFibonacci(n))
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)
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)
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),
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labels.split(),
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count(2)
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)
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)
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)
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print('Recurrence relation series:\n')
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print(
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spacedTable(table)
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)
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# ----------------------- GENERIC ------------------------
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# take :: Int -> [a] -> [a]
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# take :: Int -> String -> String
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def take(n):
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'''The prefix of xs of length n,
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or xs itself if n > length xs.
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'''
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def go(xs):
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return (
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xs[0:n]
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if isinstance(xs, (list, tuple))
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else list(islice(xs, n))
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)
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return go
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# unfoldr :: (b -> Maybe (a, b)) -> b -> [a]
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def unfoldr(f):
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'''Generic anamorphism.
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A lazy (generator) list unfolded from a seed value by
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repeated application of f until no residue remains.
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Dual to fold/reduce.
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f returns either None, or just (value, residue).
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For a strict output value, wrap in list().
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'''
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def go(x):
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valueResidue = f(x)
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while None is not valueResidue:
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yield valueResidue[0]
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valueResidue = f(valueResidue[1])
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return go
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# ---------------------- FORMATTING ----------------------
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# spacedTable :: [[String]] -> String
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def spacedTable(rows):
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columnWidths = [
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max([len(x) for x in col])
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for col in zip(*rows)
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]
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return '\n'.join([
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' '.join(
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map(
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lambda x, w: x.rjust(w, ' '),
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row, columnWidths
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)
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)
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for row in rows
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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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