[Issue 6034] Handy mapping with n-adic functions

[d-bugmail at puremagic.com]

http://d.puremagic.com/issues/show_bug.cgi?id=6034



--- Comment #1 from bearophile_hugs at eml.cc 2011-05-18 18:32:21 PDT ---
An example usage for triadic map/zipWith (this is Euler problem 18,
http://projecteuler.net/index.php?section=problems&id=18 ):


import std.stdio, std.algorithm, std.range, std.array;

auto reversed(R)(R range) {
    auto result = array(range);
    result.reverse;
    return result;
}

int f(int x, int y, int z) { return x + max(y, z); }

int[] g(int[] xs, int[] ys) {
    return array(map!((t){ return f(t.tupleof); })(zip(ys, xs[0..$-1],
xs[1..$])));
}

void main() {
    auto tri = [[75],
                [95,64],
                [17,47,82],
                [18,35,87,10],
                [20, 4,82,47,65],
                [19, 1,23,75, 3,34],
                [88, 2,77,73, 7,63,67],
                [99,65, 4,28, 6,16,70,92],
                [41,41,26,56,83,40,80,70,33],
                [41,48,72,33,47,32,37,16,94,29],
                [53,71,44,65,25,43,91,52,97,51,14],
                [70,11,33,28,77,73,17,78,39,68,17,57],
                [91,71,52,38,17,14,91,43,58,50,27,29,48],
                [63,66, 4,68,89,53,67,30,73,16,69,87,40,31],
                [ 4,62,98,27,23, 9,70,98,73,93,38,53,60, 4,23]];

    writeln(reduce!g(reversed(tri))[0]);
}


In Haskell it becomes:


problem_18 = head $ foldr1 g tri
  where
    f x y z = x + max y z
    g xs ys = zipWith3 f xs ys $ tail ys
    tri = [...]



In Python2.6 (this is not pythonic code):

f = lambda x, y, z: x + max(y, z)
g = lambda xs, ys: map(f, ys, xs[:-1], xs[1:])
print reduce(g, reversed(tri))[0]


With a n-way map the function g() becomes (this uses the array version of map):

int[] g(int[] xs, int[] ys) {
    return amap!f(ys, xs[0..$-1], xs[1..$]);
}


With a zipWith the function g() becomes:

int[] g(int[] xs, int[] ys) {
    return array(zipWith!f(ys, xs[0..$-1], xs[1..$]));
}

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