In Euler 98, there is a need to see if words are permutations of each other.
I thought that rather than make permutation signatures, I would sort the
words, because a sorted word should equal a sorted word when they are
permutations, and, well, I can probably make permutation indexes allowing 4
unsigned bits for characters, but that would require 104 bits for 26
letters. Even 3 bits requires 78 bits. So 64 bit permutation indexes fail.
So I tried to sort the words. Observe:
]S:_1]0{boxwords
A
/:~L:_1 boxwords
┌─┬───────┬────┬─────┬─────┬───────┬──────────┬────────┬──────┬──────┬────────┬─────────┬─────────┬───────┬───────┬───────────┬────┬───────┬──────┬───┬──────┬──────┬────────┬──────┬────────┬───┬────────┬──────────┬───────┬──────────────┬─────┬─────┬─────┬─...
│
│ABIILTY│ABEL│ABOTU│ABEOV│ABCEENS│ABELLOSTUY│AACCDEIM│ACCEPT│ACCESS│ACCDEINT│AACCMNOPY│ACCDGINOR│ACCNOTU│ACEEHIV│ACEEEHIMNTV│ACDI│ACEIQRU│ACORSS│ACT│ACINOT│ACEITV│ACIITTVY│AACLTU│AACLLTUY│ADD│ADDIINOT│AADDIILNOT│ADDERSS│AADIIIMNNORSTT│ADIMT│ADOPT│ADLTU│A...
└─┴───────┴────┴─────┴─────┴───────┴──────────┴────────┴──────┴──────┴────────┴─────────┴─────────┴───────┴───────┴───────────┴────┴───────┴──────┴───┴──────┴──────┴────────┴──────┴────────┴───┴────────┴──────────┴───────┴──────────────┴─────┴─────┴─────┴─...
0{boxwords
┌─┐
│A│
└─┘
/:~L:_1]0{boxwords
┌─┐
│ │
└─┘
This is the story.
The first element in the boxed list of words is the single letter word A.
When you try to sort it, it vanishes, but other letters do not. This is a
more visible example, limited to 5 words:
(i.5){boxwords
┌─┬───────┬────┬─────┬─────┐
│A│ABILITY│ABLE│ABOUT│ABOVE│
└─┴───────┴────┴─────┴─────┘
/:~L:_1(i.5){boxwords
┌─┬───────┬────┬─────┬─────┐
│ │ABIILTY│ABEL│ABOTU│ABEOV│
└─┴───────┴────┴─────┴─────┘
See? Other lists are sorted properly. This one list fails.
/:~'a'
shows the same failure.
Now, I finally see this, which is even weirder.
/:~@,L:_1(i.5){boxwords
┌─┬───────┬────┬─────┬─────┐
│A│ABIILTY│ABEL│ABOTU│ABEOV│
└─┴───────┴────┴─────┴─────┘
Is it as simple as the 'A' is a scalar and that you can't sort a scalar, but
raveling it turns it into a one element vector that can be sorted?
--
Of course I can ride in the carpool lane, officer. Jesus is my constant
companion.
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