## digitalmars.D.bugs - [Issue 6034] New: Handy mapping with n-adic functions

d-bugmail puremagic.com writes:
```http://d.puremagic.com/issues/show_bug.cgi?id=6034

Summary: Handy mapping with n-adic functions
Product: D
Version: D2
Platform: All
OS/Version: All
Status: NEW
Severity: enhancement
Priority: P2
Component: Phobos
AssignedTo: nobody puremagic.com
ReportedBy: bearophile_hugs eml.cc

--- Comment #0 from bearophile_hugs eml.cc 2011-05-18 18:20:16 PDT ---
A very common operation is to map a n-adic function (like a triadic one) on n
iterables. To do it in Haskell you use zipWith, example:

Prelude> let arr1 = [1, 2, 3]
Prelude> let arr2 = [10, 20, 30]
Prelude> let arr3 = [100, 200, 300]
Prelude> let foo x y z = x + y * z
Prelude> zipWith3 foo arr1 arr2 arr3
[1001,4002,9003]

In Python2.6 the normal map function is enough, it optionally accepts more than
one iterable (in Python3 map does the same, but it's lazy):

def foo(x, y, z):
return x + y * z

arr1 = [1, 2, 3]
arr2 = [10, 20, 30]
arr3 = [100, 200, 300]
print map(foo, arr1, arr2, arr3)

But in D2+Phobos you need to write awkward code:

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

int foo(int x, int y, int z) {
return x + y * z;
}

void main() {
auto arr1 = [1, 2, 3];
auto arr2 = [10, 20, 30];
auto arr3 = [100, 200, 300];
auto r = map!((t){ return foo(t.tupleof); })(zip(arr1, arr2, arr3));
writeln(r);
}

Output:
[1001, 4002, 9003]

Unlike Python currently std.algorithm.map() is designed to optionally accept
more than one function, and return a tuple. It's sometimes useful to do this,
but in my experience the semantics of the Python map is useful more often. So
I'd like the semantics of D map to become similar to the semantics of the
Python3 map. In this case the D code becomes something like:

auto r = map!foo(arr1, arr2, arr3);

If this is not possible, or not desired (or it leads to too much complex Phobos
code), then I suggest to introduce a new function in std.algorithm (or even in
std.range) that acts like the Haskell zipWith. In this case the D code becomes
something like:

auto r = zipWith!foo(arr1, arr2, arr3);

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May 18 2011
d-bugmail puremagic.com writes:
```http://d.puremagic.com/issues/show_bug.cgi?id=6034

--- Comment #1 from bearophile_hugs 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]);
}

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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May 18 2011