Initial data commit

Task/Pascals-triangle/Python/pascals-triangle-3.py

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+'''Pascal's triangle'''
+
+from itertools import (accumulate, chain, islice)
+from operator import (add)
+
+
+# nextPascal :: [Int] -> [Int]
+def nextPascal(xs):
+    '''A row of Pascal's triangle
+       derived from a preceding row.'''
+    return list(
+        map(add, [0] + xs, xs + [0])
+    )
+
+
+# pascalTriangle :: Generator [[Int]]
+def pascalTriangle():
+    '''A non-finite stream of
+       Pascal's triangle rows.'''
+    return iterate(nextPascal)([1])
+
+
+# finitePascalRows :: Int -> [[Int]]
+def finitePascalRows(n):
+    '''The first n rows of Pascal's triangle.'''
+    return accumulate(
+        chain(
+            [[1]], range(1, n)
+        ),
+        lambda a, _: nextPascal(a)
+    )
+
+
+# ------------------------ TESTS -------------------------
+# main :: IO ()
+def main():
+    '''Test of two different approaches:
+        - taking from a non-finite stream of rows,
+        - or constructing a finite list of rows.'''
+    print('\n'.join(map(
+        showPascal,
+        [
+            islice(
+                pascalTriangle(),       # Non finite,
+                7
+            ),
+            finitePascalRows(7)         # finite.
+        ]
+    )))
+
+
+# showPascal :: [[Int]] -> String
+def showPascal(xs):
+    '''Stringification of a list of
+       Pascal triangle rows.'''
+    ys = list(xs)
+
+    def align(w):
+        return lambda ns: center(w)(
+            ' '
+        )('   '.join(map(str, ns)))
+
+    w = len('   '.join((map(str, ys[-1]))))
+    return '\n'.join(map(align(w), ys))
+
+
+# ----------------------- GENERIC ------------------------
+
+# center :: Int -> Char -> String -> String
+def center(n):
+    '''String s padded with c to approximate centre,
+       fitting in but not truncated to width n.'''
+    def go(c, s):
+        qr = divmod(n - len(s), 2)
+        q = qr[0]
+        return (q * c) + s + ((q + qr[1]) * c)
+
+    return lambda c: lambda s: go(c, s)
+
+
+# iterate :: (a -> a) -> a -> Gen [a]
+def iterate(f):
+    '''An infinite list of repeated
+       applications of f to x.
+    '''
+    def go(x):
+        v = x
+        while True:
+            yield v
+            v = f(v)
+
+    return go
+
+
+# MAIN ---
+if __name__ == '__main__':
+    main()