Solution to Project Euler problem 31

extra/project-euler/031/031.factor

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+! Copyright (c) 2007 Aaron Schaefer.
+! See http://factorcode.org/license.txt for BSD license.
+USING: kernel math ;
+IN: project-euler.031
+
+! http://projecteuler.net/index.php?section=problems&id=31
+
+! DESCRIPTION
+! -----------
+
+! In England the currency is made up of pound, £, and pence, p, and there are
+! eight coins in general circulation:
+
+!     1p, 2p, 5p, 10p, 20p, 50p, £1 (100p) and £2 (200p).
+
+! It is possible to make £2 in the following way:
+
+!     1×£1 + 1×50p + 2×20p + 1×5p + 1×2p + 3×1p
+
+! How many different ways can £2 be made using any number of coins?
+
+
+
+! SOLUTION
+! --------
+
+<PRIVATE
+
+: 1p ( m -- n )
+    drop 1 ;
+
+: 2p ( m -- n )
+    dup 0 >= [ [ 2 - 2p ] keep 1p + ] [ drop 0 ] if ;
+
+: 5p ( m -- n )
+    dup 0 >= [ [ 5 - 5p ] keep 2p + ] [ drop 0 ] if ;
+
+: 10p ( m -- n )
+    dup 0 >= [ [ 10 - 10p ] keep 5p + ] [ drop 0 ] if ;
+
+: 20p ( m -- n )
+    dup 0 >= [ [ 20 - 20p ] keep 10p + ] [ drop 0 ] if ;
+
+: 50p ( m -- n )
+    dup 0 >= [ [ 50 - 50p ] keep 20p + ] [ drop 0 ] if ;
+
+: 100p ( m -- n )
+    dup 0 >= [ [ 100 - 100p ] keep 50p + ] [ drop 0 ] if ;
+
+: 200p ( m -- n )
+    dup 0 >= [ [ 200 - 200p ] keep 100p + ] [ drop 0 ] if ;
+
+PRIVATE>
+
+: euler031 ( -- answer )
+    200 200p ;
+
+! [ euler031 ] 100 ave-time
+! 4 ms run / 0 ms GC ave time - 100 trials
+
+! TODO: generalize to eliminate duplication; use a sequence to specify denominations?
+
+MAIN: euler031