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Pascal's triangle: Difference between revisions

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Pascal's triangle (view source)

Revision as of 23:04, 28 July 2021

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→‎Functional Python: Tidied
m (Updated description and link for Fōrmulæ solution)
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===Functional===
 
With a scanl and a zipWith to hand, we can derive bothDeriving finite and non-finite lists of pascal rows from a simple '''nextPascal''' step function:▼
The itertools module yields a simple functional definition of '''scanl''' in terms of '''accumulate''', and '''zipWith''' can be defined in terms either of '''itertools.starmap''', or the base '''map'''.
 
▲With a scanl and a zipWith to hand, we can derive both finite and non-finite lists of pascal rows from a simple '''nextPascal''' step function:
 
{{Works with|Python|3.7}}
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'''A row of Pascal's triangle
derived from a preceding row.'''
return zipWithlist(add)([0] + xs)(xs + [0])
list(map(fadd, [0] + xs, ys)xs + [0])▼
)▼
 
 
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def go(a, _):
return nextPascal(a)
 
return scanl(go)([1])(
return rangeaccumulate(1, n)
accumulate(chain([a[1]], xs)range(1, fn)),▼
xs[0:n]go▼
)
 
 
# TESTS -------------------------- TESTS -------------------------
# main :: IO ()
def main():
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- taking from a non-finite stream of rows,
- or constructing a finite list of rows.'''
print(unlines'\n'.join(map(
showPascal,
[
take(7)islice(
pascalTriangle() , # Non finite,
7
),
finitePascalRows(7) # finite.
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# GENERIC ------------------------- GENERIC ------------------------
 
 
# center :: Int -> Char -> String -> String
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# iterate :: (a -> a) -> a -> Gen [a]
def iterate(f):
'''An infinite list of repeated applications of f to x.'''
applications of f to x.
)'''▼
def go(x):
v = x
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yield v
v = f(v)
return lambda x: go(x)
 
 
# scanl :: (b -> a -> b) -> b -> [a] -> [b]
def scanl(f):
'''scanl is like reduce, but returns a succession of
intermediate values, building from the left.'''
return lambda a: lambda xs: (
▲ accumulate(chain([a], xs), f)
▲ )
 
 
# take :: Int -> [a] -> [a]
# take :: Int -> String -> String
def take(n):
'''The prefix of xs of length n,
or xs itself if n > length xs.'''
return lambda xs: (
▲ xs[0:n]
if isinstance(xs, list)
else list(islice(xs, n))
▲ )
 
 
# unlines :: [String] -> String
def unlines(xs):
'''A single string derived by the intercalation
of a list of strings with the newline character.'''
return '\n'.join(xs)
 
 
# zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
def zipWith(f):
'''A list constructed by zipping with a
custom function, rather than with the
default tuple constructor.'''
return lambda xs: lambda ys: (
▲ list(map(f, xs, ys))
)
 
 
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