Initial data commit

Task/Babbage-problem/Python/babbage-problem-4.py

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+'''Babbage problem'''
+
+from math import (floor, sqrt)
+from itertools import (islice)
+
+
+# squaresWithSuffix :: Int -> Gen [Int]
+def squaresWithSuffix(n):
+    '''Non finite stream of squares with a given suffix.'''
+    stem = 10 ** len(str(n))
+    i = 0
+    while True:
+        i = until(lambda x: isPerfectSquare(n + (stem * x)))(
+            succ
+        )(i)
+        yield n + (stem * i)
+        i = succ(i)
+
+
+# isPerfectSquare :: Int -> Bool
+def isPerfectSquare(n):
+    '''True if n is a perfect square.'''
+    r = sqrt(n)
+    return r == floor(r)
+
+
+# TEST ----------------------------------------------------
+
+# main :: IO ()
+def main():
+    '''Smallest positive integers whose squares end in the digits 269,696'''
+    print(
+        fTable(main.__doc__ + ':\n')(
+            lambda n: str(int(sqrt(n))) + '^2'
+        )(repr)(identity)(
+            take(10)(squaresWithSuffix(269696))
+        )
+    )
+
+
+# GENERIC -------------------------------------------------
+
+# identity :: a -> a
+def identity(x):
+    '''The identity function.'''
+    return x
+
+
+# succ :: Enum a => a -> a
+def succ(x):
+    '''The successor of a value.
+       For numeric types, (1 +).
+    '''
+    return 1 + x if isinstance(x, int) else (
+        chr(1 + ord(x))
+    )
+
+
+# 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, tuple))
+        else list(islice(xs, n))
+    )
+
+
+# until :: (a -> Bool) -> (a -> a) -> a -> a
+def until(p):
+    '''The result of repeatedly applying f until p holds.
+       The initial seed value is x.
+    '''
+    def go(f, x):
+        v = x
+        while not p(v):
+            v = f(v)
+        return v
+    return lambda f: lambda x: go(f, x)
+
+
+# FORMATTING ----------------------------------------------
+# fTable :: String -> (a -> String) ->
+#                     (b -> String) -> (a -> b) -> [a] -> String
+def fTable(s):
+    '''Heading -> x display function -> fx display function ->
+                     f -> xs -> tabular string.
+    '''
+    def go(xShow, fxShow, f, xs):
+        ys = [xShow(x) for x in xs]
+        w = max(map(len, ys))
+        return s + '\n' + '\n'.join(map(
+            lambda x, y: y.rjust(w, ' ') + ' -> ' + fxShow(f(x)),
+            xs, ys
+        ))
+    return lambda xShow: lambda fxShow: lambda f: lambda xs: go(
+        xShow, fxShow, f, xs
+    )
+
+
+# MAIN ---
+if __name__ == '__main__':
+    main()