Initial data commit

Task/Van-Eck-sequence/Python/van-eck-sequence-4.py

@@ -0,0 +1,79 @@
+'''Van Eck series by map-accumulation'''
+
+from functools import reduce
+from itertools import repeat
+
+
+# vanEck :: Int -> [Int]
+def vanEck(n):
+    '''First n terms of the vanEck sequence.'''
+    def go(xns, i):
+        x, ns = xns
+
+        prev = ns[x]
+        v = i - prev if 0 is not prev else 0
+        return (
+            (v, insert(ns, x, i)),
+            v
+        )
+
+    return [0] + mapAccumL(go)((0, list(repeat(0, n))))(
+        range(1, n)
+    )[1]
+
+
+# -------------------------- TEST --------------------------
+# main :: IO ()
+def main():
+    '''The last 10 of the first N vanEck terms'''
+    print(
+        fTable(main.__doc__ + ':\n')(
+            lambda m: 'N=' + str(m), repr,
+            lambda n: vanEck(n)[-10:], [10, 1000, 10000]
+        )
+    )
+
+
+# ----------------------- 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 go
+
+
+# ------------------------ GENERIC -------------------------
+
+# insert :: Array Int -> Int -> Int -> Array Int
+def insert(xs, i, v):
+    '''An array updated at position i with value v.'''
+    xs[i] = v
+    return xs
+
+
+# mapAccumL :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])
+def mapAccumL(f):
+    '''A tuple of an accumulation and a list derived by a
+       combined map and fold,
+       with accumulation from left to right.
+    '''
+    def go(a, x):
+        tpl = f(a[0], x)
+        return (tpl[0], a[1] + [tpl[1]])
+    return lambda acc: lambda xs: (
+        reduce(go, xs, (acc, []))
+    )
+
+
+# MAIN ---
+if __name__ == '__main__':
+    main()