Merge branch 'master' of http://factorforge.org/glguy.factor

extra/project-euler/116/116.factor

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+! Copyright (c) 2008 Eric Mertens
+! See http://factorcode.org/license.txt for BSD license.
+USING: kernel math math.ranges sequences sequences.lib ;
+
+IN: project-euler.116
+
+! http://projecteuler.net/index.php?section=problems&id=116
+
+! DESCRIPTION
+! -----------
+
+! A row of five black square tiles is to have a number of its tiles replaced
+! with coloured oblong tiles chosen from red (length two), green (length
+! three), or blue (length four).
+
+! If red tiles are chosen there are exactly seven ways this can be done.
+! If green tiles are chosen there are three ways.
+! And if blue tiles are chosen there are two ways.
+
+! Assuming that colours cannot be mixed there are 7 + 3 + 2 = 12 ways of
+! replacing the black tiles in a row measuring five units in length.
+
+! How many different ways can the black tiles in a row measuring fifty units in
+! length be replaced if colours cannot be mixed and at least one coloured tile
+! must be used?
+
+! SOLUTION
+! --------
+
+! This solution uses a simple dynamic programming approach using the
+! following recurence relation
+
+! ways(n,_) = 0   | n < 0
+! ways(0,_) = 1
+! ways(n,i) = ways(n-i,i) + ways(n-1,i)
+! solution(n) = ways(n,1) - 1 + ways(n,2) - 1 + ways(n,3) - 1
+
+<PRIVATE
+
+: nth* ( n seq -- elt/0 )
+    [ length swap - 1- ] keep ?nth 0 or ;
+
+: next ( colortile seq -- )
+     [ nth* ] [ peek + ] [ push ] tri ;
+
+: ways ( length colortile -- permutations )
+    V{ 1 } clone [ [ next ] 2curry times ] keep peek 1- ;
+
+PRIVATE>
+
+: (euler116) ( length -- permutations )
+    3 [1,b] [ ways ] with sigma ;
+
+: euler116 ( -- permutations )
+    50 (euler116) ;

extra/project-euler/117/117.factor

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+! Copyright (c) 2008 Eric Mertens
+! See http://factorcode.org/license.txt for BSD license.
+USING: kernel math splitting sequences ;
+
+IN: project-euler.117
+
+! http://projecteuler.net/index.php?section=problems&id=117
+
+! DESCRIPTION
+! -----------
+
+! Using a combination of black square tiles and oblong tiles chosen
+! from: red tiles measuring two units, green tiles measuring three
+! units, and blue tiles measuring four units, it is possible to tile a
+! row measuring five units in length in exactly fifteen different ways.
+
+!  How many ways can a row measuring fifty units in length be tiled?
+
+! SOLUTION
+! --------
+
+! This solution uses a simple dynamic programming approach using the
+! following recurence relation
+
+! ways(i) = 1 | i <= 0
+! ways(i) = ways(i-4) + ways(i-3) + ways(i-2) + ways(i-1)
+
+<PRIVATE
+
+: short ( seq n -- seq n )
+    over length min ;
+
+: next ( seq -- )
+    [ 4 short tail* sum ] keep push ;
+
+PRIVATE>
+
+: (euler117) ( n -- m )
+    V{ 1 } clone tuck [ next ] curry times peek ;
+
+: euler117 ( -- m )
+    50 (euler117) ;

extra/project-euler/150/150.factor

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+! Copyright (c) 2008 Eric Mertens
+! See http://factorcode.org/license.txt for BSD license.
+USING: kernel math sequences locals ;
+IN: project-euler.150
+
+<PRIVATE
+
+! sequence helper functions
+
+: partial-sums ( seq -- seq )
+    0 [ + ] accumulate swap suffix ; inline
+
+: generate ( n quot -- seq )
+    [ drop ] swap compose map ; inline
+
+: map-infimum ( seq quot -- min )
+    [ min ] compose 0 swap reduce ; inline
+
+
+! triangle generator functions
+
+: next ( t -- new-t s )
+    615949 * 797807 + 1 20 shift mod dup 1 19 shift - ; inline
+
+: sums-triangle ( -- seq )
+    0 1000 [ 1+ [ next ] generate partial-sums ] map nip ;
+
+PRIVATE>
+
+:: (euler150) ( m -- n )
+    [let | table [ sums-triangle ] |
+        m [| x |
+            x 1+ [| y |
+                m x - [| z |
+                    x z + table nth
+                    [ y z + 1+ swap nth ]
+                    [ y        swap nth ] bi -
+                ] map partial-sums infimum
+            ] map-infimum
+        ] map-infimum
+    ] ;
+
+: euler150 ( -- n )
+    1000 (euler150) ;