I have some number of arrays which is unknown at programming time, maybe it is 3 or 4 or 7 ... each array has some elements, i.e,
a={1 2 3 4}
b={6 7 5 2 1}
c={22 4 6 8 4 8 5 4}
d={....}
e, f, g, ...
I want to get get all possible combinations by sampling one number from each array for example one case is that I pick up "1" from a, "7" from b, first "8" from c, d[3], e[5],... to make "1,7,8,d[3],e[5],...". It's not possible to use nested for loops because I don't know the number of arrays at compile time. If it was known for example 4 arrays (a,b,c,d) I could use 4 loops:
for (int i = 0; i <= a.Length-1; i++)
{
for (int j = 0; i <= b.Length-1; j++)
{
for (int k = 0; i <= c.Length-1; k++)
{
for (int m = 0; i <= d.Length-1; m++)
{
Response[f++] = a[i].toString()+","+b[j].toString()+","+c[k].toString()+","+d[m].toString();
}
}
}
}
but for different number of arrays, I don't have any idea.
Let the input array be {1, 2, 3, 4, 5} and r be 3. We first fix 1 at index 0 in data[], then recur for remaining indexes, then we fix 2 at index 0 and recur. Finally, we fix 3 and recur for remaining indexes. When number of elements in data[] becomes equal to r (size of a combination), we print data[].
C = combntns( v , k ) returns all possible combinations of the set of values v , given combinations of length k .
This works:
Func<
IEnumerable<IEnumerable<int>>,
IEnumerable<IEnumerable<int>>> f0 = null;
f0 = xss =>
{
if (!xss.Any())
{
return new [] { Enumerable.Empty<int>() };
}
else
{
var query =
from x in xss.First()
from y in f0(xss.Skip(1))
select new [] { x }.Concat(y);
return query;
}
};
Func<IEnumerable<IEnumerable<int>>, IEnumerable<string>> f =
xss => f0(xss).Select(xs => String.Join(",", xs));
So if I have this input:
var input = new []
{
new [] { 1, 2, 3, 4, },
new [] { 6, 7, 5, 2, 1, },
new [] { 22, 4, 6, 8, 4, 8, 5, 4, },
};
I can get the results this way:
var results = f(input);
Here's a version which simply sums the results, as per the request in the comments:
Func<IEnumerable<IEnumerable<int>>, IEnumerable<int>> f = null;
f = xss =>
{
if (!xss.Any())
{
return new [] { 0 };
}
else
{
var query =
from x in xss.First()
from y in f(xss.Skip(1))
select x + y;
return query;
}
};
var input = new []
{
new [] { 1, 2, 3, 4, },
new [] { 6, 7, 5, 2, 1, },
new [] { 22, 4, 6, 8, 4, 8, 5, 4, },
};
var results = f(input);
I think the linq version looks awesome:
from i in a
from j in b
from k in c
from m in d
select String.Join(",", i, j, k, m)
But the answer to your question is not easy. Eric Lippert wrote about it on his blog:
http://blogs.msdn.com/b/ericlippert/archive/2010/06/28/computing-a-cartesian-product-with-linq.aspx
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