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A. Improved

initial writing: 2000-00-00
last updated: 2004-10-21

The dyad A. is now faster and uses less space, especially when the right argument is i.n . Time and space comparisons are as follows:

   ts=: 6!:2 , 7!:2@]
   ts '(i.!n) A. i.n'                  NB. all    permutations
   ts 'i A. i.n' [ i=: ?(!1>.n-1)$!n   NB. random permutations

All Permutations

n                         J 4.05               J 4.04
1 4.441904e_5   1.600000e3         4.693333e_5   1.664000e3
2 4.441904e_5   1.600000e3 4.860952e_5   1.728000e3
3 4.777142e_5   1.792000e3 5.699047e_5   2.176000e3
4 7.123808e_5   2.816000e3 9.638094e_5   4.352000e3
5 2.857904e_4   1.100800e4 3.595428e_4   1.971200e4
6 1.465828e_3   7.315200e4 2.392762e_3   1.694080e5
7 1.100838e_2   5.749120e5 2.038834e_2   1.245632e6
8 1.047242e_1   4.588992e6 2.015694e_1   9.957824e6
9 1.057751e0     3.670163e7 2.049871e0     8.501805e7

Random Permutations

n                         J 4.05               J 4.04
1 3.687618e_5   1.408000e3         4.190476e_5   1.536000e3        
2 3.771428e_5   1.472000e3 4.190476e_5   1.600000e3
3 3.855238e_5   1.536000e3 4.441904e_5   1.792000e3
4 4.358095e_5   1.792000e3 5.363809e_5   2.304000e3
5 7.542856e_5   3.456000e3 9.805713e_5   5.504000e3
6 3.084190e_4   1.004800e4 4.064761e_4   2.649600e4
7 1.659428e_3   6.892800e4 2.639162e_3   1.652480e5
8 1.243733e_2   5.420160e5 2.290933e_2   1.212800e6
9 1.168506e_1   4.326720e6 2.214423e_1   9.695616e6

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