First question: The j essays present many algorithms solving the same
problem. It would be nice if these could be ordered by efficiency.
Granted, the specific j implementation, the problem size, or much else
might affect the result making this request unreasonable. For instance,
is the structural odometer that a non-mathematician might prefer less
efficient than base representation?
odometer =: #: i.@(*/) NB. mathematician's version perhaps
odometer2=: [: |: */ $&> */\...@}.@(,&1) #&.> i.&.> NB. Structural
Second question: What is a more efficient expression?
NB. characterize the input, b
$b NB. b is a vector of 3 million integers
2857143
*./2(</)\b NB. b is monotonic.
1
0 _1{b NB. from 10 to 150 million
10 149999980
diff=.2(-~/)\b NB. successive differences of b
(+/ % #)diff NB. mean of differences
52.5
m28 diff NB. Standard deviation, from phrases
20.4634
27+*:0 _1{b NB. ok without extended precision
127 22499994000000427
1 p: 1 3 7 9 13 27+"_ 0*:0 _1{b NB. example, an island of primes?
1 1 1 1 1 1
0 0 0 0 0 0
b#~(*./"1)1 p: 1 3 7 9 13 27+"_ 0*:b NB. THE PROBLEM
What is an efficient way to arrange this search for islands of prime
numbers? In c I wouldn't bother to add 3 and test for primality having
determined that 1+n*n is composite. *./ should not "short circuit" on
zero as would && in c, since
*./1 0 _
|NaN error
| *./1 0 _
Thanks,
Dave.
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