MusingsAs part of his science fair project, my 3rd-grader needed a large number of random strings of 8 digits, in each of which “1” appears four times, and “2”–“5” appear once each.
#!/usr/bin/ruby
class Array
def scramble
p = dup
collect { p.delete_at(rand(p.length) - 1) }
end
end
100.times { puts [1,1,1,1,2,3,4,5].scramble.join }
TrackBack URL for this Entry: https://golem.ph.utexas.edu/cgi-bin/MT-3.0/dxy-tb.fcgi/2144
By the way, this is a great pedagogical example how to use FromDigits; /@ or Map; as well as Permutations. ;-)
Yes, But one neither wants, nor needs to construct the full list of such permutations, in order to draw 100 randomly-selected ones from among them.
OK, then the following code should do exactly what you wanted:
<< Combinatorica`;
Table[FromDigits[RandomPermutation[{1, 1, 1, 1, 2, 3, 4, 5}]], {100}]
But indeed using Mathematica for this kind of problem is a vast overkill.
But indeed using Mathematica for this kind of problem is a vast overkill.
I wouldn’t quite say that. Mathematica does have a built-in function
RandomPermutation[{}]
that does precisely what I needed (though I did not realize it at the time).
On the other hand, what I enjoyed was the elegantly-simple two-line implementation of that function, which I called “scramble”, as an extension to Ruby’s Array class.
Re: Haiku
Mathematica is pretty good at this kind of things. The package Combinatorica contains a wealth of combinatorial algorithms (it seems to be loaded automatically in the version 7 of Mathematica). Anyway, the full list of numbers satisfying the constraints you stated can be found by using
FromDigits /@ Permutations[{1,1,1,1,2,3,4,5}]which is very concise. There are 1680 such numbers.