! Copyright (c) 2008 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: hashtables kernel math.functions math.ranges project-euler.common
    sequences ;
IN: project-euler.029

! http://projecteuler.net/index.php?section=problems&id=29

! DESCRIPTION
! -----------

! Consider all integer combinations of a^b for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:

!     2^2 = 4,  2^3 = 8,   2^4 = 16,  2^5 = 32
!     3^2 = 9,  3^3 = 27,  3^4 = 81,  3^5 = 243
!     4^2 = 16, 4^3 = 64,  4^4 = 256, 4^5 = 1024
!     5^2 = 25, 5^3 = 125, 5^4 = 625, 5^5 = 3125

! If they are then placed in numerical order, with any repeats removed, we get
! the following sequence of 15 distinct terms:

!     4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125

! How many distinct terms are in the sequence generated by a^b for 2 ≤ a ≤ 100
! and 2 ≤ b ≤ 100?


! SOLUTION
! --------

: euler029 ( -- answer )
    2 100 [a,b] dup cartesian-product [ first2 ^ ] map prune length ;

! [ euler029 ] 100 ave-time
! 951 ms run / 12 ms GC ave time - 100 trials

MAIN: euler029