tuple-gen (empty) → 1.0

raw patch · 4 files changed

+207/−0 lines, 4 filesdep +basesetup-changed

Dependencies added: base

Files

LICENSE +11/−0
Setup.hs +3/−0
src/Data/Tuple/Gen.hs +175/−0
tuple-gen.cabal +18/−0

+ LICENSE view

@@ -0,0 +1,11 @@+Copyright (c) 2010, Tillmann Vogt
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
+Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
+Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
+The names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+

+ Setup.hs view

@@ -0,0 +1,3 @@+#!/usr/bin/env runhaskell
+import Distribution.Simple
+main = defaultMain

+ src/Data/Tuple/Gen.hs view

@@ -0,0 +1,175 @@+module Data.Tuple.Gen(all2s, all3s, all4s, all5s, all6s, all7s, all8s, all9s, all10s,
+   all2sFrom, all3sFrom, all4sFrom, all5sFrom, all6sFrom, all7sFrom, all8sFrom, all9sFrom, all10sFrom)
+where
+
+-- | generate all 2-tuples so that the sum of all digits is monotonic increasing
+all2s :: Integral a => [(a,a)]
+all2s = all2sFrom (1,0)
+
+-- | generate all 3-tuples so that the sum of all digits is monotonic increasing
+all3s :: Integral a => [(a,a,a)]
+all3s = all3sFrom (1,0,0)
+
+-- | generate all 4-tuples so that the sum of all digits is monotonic increasing
+all4s :: Integral a => [(a,a,a,a)]
+all4s = all4sFrom (1,0,0,0)
+
+-- | generate all 5-tuples so that the sum of all digits is monotonic increasing
+all5s :: Integral a => [(a,a,a,a,a)]
+all5s = all5sFrom (1,0,0,0,0)
+
+-- | generate all 6-tuples so that the sum of all digits is monotonic increasing
+all6s :: Integral a => [(a,a,a,a,a,a)]
+all6s = all6sFrom (1,0,0,0,0,0)
+
+-- | generate all 7-tuples so that the sum of all digits is monotonic increasing
+all7s :: Integral a => [(a,a,a,a,a,a,a)]
+all7s = all7sFrom (1,0,0,0,0,0,0)
+
+-- | generate all 8-tuples so that the sum of all digits is monotonic increasing
+all8s :: Integral a => [(a,a,a,a,a,a,a,a)]
+all8s = all8sFrom (1,0,0,0,0,0,0,0)
+
+-- | generate all 9-tuples so that the sum of all digits is monotonic increasing
+all9s :: Integral a => [(a,a,a,a,a,a,a,a,a)]
+all9s = all9sFrom (1,0,0,0,0,0,0,0,0)
+
+-- | generate all 10-tuples so that the sum of all digits is monotonic increasing
+all10s :: Integral a => [(a,a,a,a,a,a,a,a,a,a)]
+all10s = all10sFrom (1,0,0,0,0,0,0,0,0,0)
+
+
+all2sFrom :: Integral a => (a,a) -> [(a,a)]
+all2sFrom start = s_A [start]
+ where
+  s_A ((a,b):is)  = (a,b) : (s_B ((a-1,b+1):is))
+  s_B ((0,b):is)  = (0,b) : (s_A ((b+1, 0 ):is))
+  s_B ((a,b):is)  = (a,b) : (s_B ((a-1,b+1):is))
+
+all3sFrom :: Integral a => (a,a,a) -> [(a,a,a)]
+all3sFrom start = s_A [start]
+ where
+  s_A ((a,b,c):is)  = (a,b,c) : (s_B ((a-1,b+1,c):is))
+  s_B ((a,b,c):is)  = (a,b,c) : (s_C ((a,b-1,c+1):is))
+  s_C ((0,0,c):is)  = (0,0,c) : (s_A ((c+1, 0 ,0):is))
+  s_C ((a,0,c):is)  = (a,0,c) : (s_B ((a-1,c+1,0):is))
+  s_C ((a,b,c):is)  = (a,b,c) : (s_C ((a,b-1,c+1):is))
+
+all4sFrom :: Integral a => (a,a,a,a) -> [(a,a,a,a)]
+all4sFrom start = s_A [start]
+ where
+  s_A ((a,b,c,d):is)  = (a,b,c,d) : (s_B ((a-1,b+1,c,d):is))
+  s_B ((a,b,c,d):is)  = (a,b,c,d) : (s_C ((a,b-1,c+1,d):is))
+  s_C ((a,b,c,d):is)  = (a,b,c,d) : (s_D ((a,b,c-1,d+1):is))
+  s_D ((0,0,0,d):is)  = (0,0,0,d) : (s_A ((d+1, 0 ,0,0):is))
+  s_D ((a,0,0,d):is)  = (a,0,0,d) : (s_B ((a-1,d+1,0,0):is))
+  s_D ((a,b,0,d):is)  = (a,b,0,d) : (s_C ((a,b-1,d+1,0):is))
+  s_D ((a,b,c,d):is)  = (a,b,c,d) : (s_D ((a,b,c-1,d+1):is))
+
+all5sFrom :: Integral a => (a,a,a,a,a) -> [(a,a,a,a,a)]
+all5sFrom start = s_A [start]
+ where
+  s_A ((a,b,c,d,e):is)  = (a,b,c,d,e) : (s_B ((a-1,b+1,c,d,e):is))
+  s_B ((a,b,c,d,e):is)  = (a,b,c,d,e) : (s_C ((a,b-1,c+1,d,e):is))
+  s_C ((a,b,c,d,e):is)  = (a,b,c,d,e) : (s_D ((a,b,c-1,d+1,e):is))
+  s_D ((a,b,c,d,e):is)  = (a,b,c,d,e) : (s_E ((a,b,c,d-1,e+1):is))
+  s_E ((0,0,0,0,e):is)  = (0,0,0,0,e) : (s_A ((e+1, 0 ,0,0,0):is))
+  s_E ((a,0,0,0,e):is)  = (a,0,0,0,e) : (s_B ((a-1,e+1,0,0,0):is))
+  s_E ((a,b,0,0,e):is)  = (a,b,0,0,e) : (s_C ((a,b-1,e+1,0,0):is))
+  s_E ((a,b,c,0,e):is)  = (a,b,c,0,e) : (s_D ((a,b,c-1,e+1,0):is))
+  s_E ((a,b,c,d,e):is)  = (a,b,c,d,e) : (s_E ((a,b,c,d-1,e+1):is))
+
+all6sFrom :: Integral a => (a,a,a,a,a,a) -> [(a,a,a,a,a,a)]
+all6sFrom start = s_A [start]
+ where
+  s_A ((a,b,c,d,e,f):is)  = (a,b,c,d,e,f) : (s_B ((a-1,b+1,c,d,e,f):is))
+  s_B ((a,b,c,d,e,f):is)  = (a,b,c,d,e,f) : (s_C ((a,b-1,c+1,d,e,f):is))
+  s_C ((a,b,c,d,e,f):is)  = (a,b,c,d,e,f) : (s_D ((a,b,c-1,d+1,e,f):is))
+  s_D ((a,b,c,d,e,f):is)  = (a,b,c,d,e,f) : (s_E ((a,b,c,d-1,e+1,f):is))
+  s_E ((a,b,c,d,e,f):is)  = (a,b,c,d,e,f) : (s_F ((a,b,c,d,e-1,f+1):is))
+  s_F ((0,0,0,0,0,f):is)  = (0,0,0,0,0,f) : (s_A ((f+1, 0 ,0,0,0,0):is))
+  s_F ((a,0,0,0,0,f):is)  = (a,0,0,0,0,f) : (s_B ((a-1,f+1,0,0,0,0):is))
+  s_F ((a,b,0,0,0,f):is)  = (a,b,0,0,0,f) : (s_C ((a,b-1,f+1,0,0,0):is))
+  s_F ((a,b,c,0,0,f):is)  = (a,b,c,0,0,f) : (s_D ((a,b,c-1,f+1,0,0):is))
+  s_F ((a,b,c,d,0,f):is)  = (a,b,c,d,0,f) : (s_E ((a,b,c,d-1,f+1,0):is))
+  s_F ((a,b,c,d,e,f):is)  = (a,b,c,d,e,f) : (s_F ((a,b,c,d,e-1,f+1):is))
+
+all7sFrom :: Integral a => (a,a,a,a,a,a,a) -> [(a,a,a,a,a,a,a)]
+all7sFrom start = s_A [start]
+ where
+  s_A ((a,b,c,d,e,f,g):is)  = (a,b,c,d,e,f,g) : (s_B ((a-1,b+1,c,d,e,f,g):is))
+  s_B ((a,b,c,d,e,f,g):is)  = (a,b,c,d,e,f,g) : (s_C ((a,b-1,c+1,d,e,f,g):is))
+  s_C ((a,b,c,d,e,f,g):is)  = (a,b,c,d,e,f,g) : (s_D ((a,b,c-1,d+1,e,f,g):is))
+  s_D ((a,b,c,d,e,f,g):is)  = (a,b,c,d,e,f,g) : (s_E ((a,b,c,d-1,e+1,f,g):is))
+  s_E ((a,b,c,d,e,f,g):is)  = (a,b,c,d,e,f,g) : (s_F ((a,b,c,d,e-1,f+1,g):is))
+  s_F ((a,b,c,d,e,f,g):is)  = (a,b,c,d,e,f,g) : (s_G ((a,b,c,d,e,f-1,g+1):is))
+  s_G ((0,0,0,0,0,0,g):is)  = (0,0,0,0,0,0,g) : (s_A ((g+1, 0 ,0,0,0,0,0):is))
+  s_G ((a,0,0,0,0,0,g):is)  = (a,0,0,0,0,0,g) : (s_B ((a-1,g+1,0,0,0,0,0):is))
+  s_G ((a,b,0,0,0,0,g):is)  = (a,b,0,0,0,0,g) : (s_C ((a,b-1,g+1,0,0,0,0):is))
+  s_G ((a,b,c,0,0,0,g):is)  = (a,b,c,0,0,0,g) : (s_D ((a,b,c-1,g+1,0,0,0):is))
+  s_G ((a,b,c,d,0,0,g):is)  = (a,b,c,d,0,0,g) : (s_E ((a,b,c,d-1,g+1,0,0):is))
+  s_G ((a,b,c,d,e,0,g):is)  = (a,b,c,d,e,0,g) : (s_F ((a,b,c,d,e-1,g+1,0):is))
+  s_G ((a,b,c,d,e,f,g):is)  = (a,b,c,d,e,f,g) : (s_G ((a,b,c,d,e,f-1,g+1):is))
+
+all8sFrom :: Integral a => (a,a,a,a,a,a,a,a) -> [(a,a,a,a,a,a,a,a)]
+all8sFrom start = s_A [start]
+ where
+  s_A ((a,b,c,d,e,f,g,h):is)  = (a,b,c,d,e,f,g,h) : (s_B ((a-1,b+1,c,d,e,f,g,h):is))
+  s_B ((a,b,c,d,e,f,g,h):is)  = (a,b,c,d,e,f,g,h) : (s_C ((a,b-1,c+1,d,e,f,g,h):is))
+  s_C ((a,b,c,d,e,f,g,h):is)  = (a,b,c,d,e,f,g,h) : (s_D ((a,b,c-1,d+1,e,f,g,h):is))
+  s_D ((a,b,c,d,e,f,g,h):is)  = (a,b,c,d,e,f,g,h) : (s_E ((a,b,c,d-1,e+1,f,g,h):is))
+  s_E ((a,b,c,d,e,f,g,h):is)  = (a,b,c,d,e,f,g,h) : (s_F ((a,b,c,d,e-1,f+1,g,h):is))
+  s_F ((a,b,c,d,e,f,g,h):is)  = (a,b,c,d,e,f,g,h) : (s_G ((a,b,c,d,e,f-1,g+1,h):is))
+  s_G ((a,b,c,d,e,f,g,h):is)  = (a,b,c,d,e,f,g,h) : (s_H ((a,b,c,d,e,f,g-1,h+1):is))
+  s_H ((0,0,0,0,0,0,0,h):is)  = (0,0,0,0,0,0,0,h) : (s_A ((h+1, 0 ,0,0,0,0,0,0):is))
+  s_H ((a,0,0,0,0,0,0,h):is)  = (a,0,0,0,0,0,0,h) : (s_B ((a-1,h+1,0,0,0,0,0,0):is))
+  s_H ((a,b,0,0,0,0,0,h):is)  = (a,b,0,0,0,0,0,h) : (s_C ((a,b-1,h+1,0,0,0,0,0):is))
+  s_H ((a,b,c,0,0,0,0,h):is)  = (a,b,c,0,0,0,0,h) : (s_D ((a,b,c-1,h+1,0,0,0,0):is))
+  s_H ((a,b,c,d,0,0,0,h):is)  = (a,b,c,d,0,0,0,h) : (s_E ((a,b,c,d-1,h+1,0,0,0):is))
+  s_H ((a,b,c,d,e,0,0,h):is)  = (a,b,c,d,e,0,0,h) : (s_F ((a,b,c,d,e-1,h+1,0,0):is))
+  s_H ((a,b,c,d,e,f,0,h):is)  = (a,b,c,d,e,f,0,h) : (s_G ((a,b,c,d,e,f-1,h+1,0):is))
+  s_H ((a,b,c,d,e,f,g,h):is)  = (a,b,c,d,e,f,g,h) : (s_H ((a,b,c,d,e,f,g-1,h+1):is))
+
+all9sFrom :: Integral a => (a,a,a,a,a,a,a,a,a) -> [(a,a,a,a,a,a,a,a,a)]
+all9sFrom start = s_A [start]
+ where
+  s_A ((a,b,c,d,e,f,g,h,i):is)  = (a,b,c,d,e,f,g,h,i) : (s_B ((a-1,b+1,c,d,e,f,g,h,i):is))
+  s_B ((a,b,c,d,e,f,g,h,i):is)  = (a,b,c,d,e,f,g,h,i) : (s_C ((a,b-1,c+1,d,e,f,g,h,i):is))
+  s_C ((a,b,c,d,e,f,g,h,i):is)  = (a,b,c,d,e,f,g,h,i) : (s_D ((a,b,c-1,d+1,e,f,g,h,i):is))
+  s_D ((a,b,c,d,e,f,g,h,i):is)  = (a,b,c,d,e,f,g,h,i) : (s_E ((a,b,c,d-1,e+1,f,g,h,i):is))
+  s_E ((a,b,c,d,e,f,g,h,i):is)  = (a,b,c,d,e,f,g,h,i) : (s_F ((a,b,c,d,e-1,f+1,g,h,i):is))
+  s_F ((a,b,c,d,e,f,g,h,i):is)  = (a,b,c,d,e,f,g,h,i) : (s_G ((a,b,c,d,e,f-1,g+1,h,i):is))
+  s_G ((a,b,c,d,e,f,g,h,i):is)  = (a,b,c,d,e,f,g,h,i) : (s_H ((a,b,c,d,e,f,g-1,h+1,i):is))
+  s_H ((a,b,c,d,e,f,g,h,i):is)  = (a,b,c,d,e,f,g,h,i) : (s_I ((a,b,c,d,e,f,g,h-1,i+1):is))
+  s_I ((0,0,0,0,0,0,0,0,i):is)  = (0,0,0,0,0,0,0,0,i) : (s_A ((i+1, 0 ,0,0,0,0,0,0,0):is))
+  s_I ((a,0,0,0,0,0,0,0,i):is)  = (a,0,0,0,0,0,0,0,i) : (s_B ((a-1,i+1,0,0,0,0,0,0,0):is))
+  s_I ((a,b,0,0,0,0,0,0,i):is)  = (a,b,0,0,0,0,0,0,i) : (s_C ((a,b-1,i+1,0,0,0,0,0,0):is))
+  s_I ((a,b,c,0,0,0,0,0,i):is)  = (a,b,c,0,0,0,0,0,i) : (s_D ((a,b,c-1,i+1,0,0,0,0,0):is))
+  s_I ((a,b,c,d,0,0,0,0,i):is)  = (a,b,c,d,0,0,0,0,i) : (s_E ((a,b,c,d-1,i+1,0,0,0,0):is))
+  s_I ((a,b,c,d,e,0,0,0,i):is)  = (a,b,c,d,e,0,0,0,i) : (s_F ((a,b,c,d,e-1,i+1,0,0,0):is))
+  s_I ((a,b,c,d,e,f,0,0,i):is)  = (a,b,c,d,e,f,0,0,i) : (s_G ((a,b,c,d,e,f-1,i+1,0,0):is))
+  s_I ((a,b,c,d,e,f,g,0,i):is)  = (a,b,c,d,e,f,g,0,i) : (s_H ((a,b,c,d,e,f,g-1,i+1,0):is))
+  s_I ((a,b,c,d,e,f,g,h,i):is)  = (a,b,c,d,e,f,g,h,i) : (s_I ((a,b,c,d,e,f,g,h-1,i+1):is))
+
+all10sFrom :: Integral a => (a,a,a,a,a,a,a,a,a,a) -> [(a,a,a,a,a,a,a,a,a,a)]
+all10sFrom start = s_A [start]
+ where
+  s_A ((a,b,c,d,e,f,g,h,i,j):is)  = (a,b,c,d,e,f,g,h,i,j) : (s_B ((a-1,b+1,c,d,e,f,g,h,i,j):is))
+  s_B ((a,b,c,d,e,f,g,h,i,j):is)  = (a,b,c,d,e,f,g,h,i,j) : (s_C ((a,b-1,c+1,d,e,f,g,h,i,j):is))
+  s_C ((a,b,c,d,e,f,g,h,i,j):is)  = (a,b,c,d,e,f,g,h,i,j) : (s_D ((a,b,c-1,d+1,e,f,g,h,i,j):is))
+  s_D ((a,b,c,d,e,f,g,h,i,j):is)  = (a,b,c,d,e,f,g,h,i,j) : (s_E ((a,b,c,d-1,e+1,f,g,h,i,j):is))
+  s_E ((a,b,c,d,e,f,g,h,i,j):is)  = (a,b,c,d,e,f,g,h,i,j) : (s_F ((a,b,c,d,e-1,f+1,g,h,i,j):is))
+  s_F ((a,b,c,d,e,f,g,h,i,j):is)  = (a,b,c,d,e,f,g,h,i,j) : (s_G ((a,b,c,d,e,f-1,g+1,h,i,j):is))
+  s_G ((a,b,c,d,e,f,g,h,i,j):is)  = (a,b,c,d,e,f,g,h,i,j) : (s_H ((a,b,c,d,e,f,g-1,h+1,i,j):is))
+  s_H ((a,b,c,d,e,f,g,h,i,j):is)  = (a,b,c,d,e,f,g,h,i,j) : (s_I ((a,b,c,d,e,f,g,h-1,i+1,j):is))
+  s_I ((a,b,c,d,e,f,g,h,i,j):is)  = (a,b,c,d,e,f,g,h,i,j) : (s_J ((a,b,c,d,e,f,g,h,i-1,j+1):is))
+  s_J ((0,0,0,0,0,0,0,0,0,j):is)  = (0,0,0,0,0,0,0,0,0,j) : (s_A ((j+1, 0 ,0,0,0,0,0,0,0,0):is))
+  s_J ((a,0,0,0,0,0,0,0,0,j):is)  = (a,0,0,0,0,0,0,0,0,j) : (s_B ((a-1,j+1,0,0,0,0,0,0,0,0):is))
+  s_J ((a,b,0,0,0,0,0,0,0,j):is)  = (a,b,0,0,0,0,0,0,0,j) : (s_C ((a,b-1,j+1,0,0,0,0,0,0,0):is))
+  s_J ((a,b,c,0,0,0,0,0,0,j):is)  = (a,b,c,0,0,0,0,0,0,j) : (s_D ((a,b,c-1,j+1,0,0,0,0,0,0):is))
+  s_J ((a,b,c,d,0,0,0,0,0,j):is)  = (a,b,c,d,0,0,0,0,0,j) : (s_E ((a,b,c,d-1,j+1,0,0,0,0,0):is))
+  s_J ((a,b,c,d,e,0,0,0,0,j):is)  = (a,b,c,d,e,0,0,0,0,j) : (s_F ((a,b,c,d,e-1,j+1,0,0,0,0):is))
+  s_J ((a,b,c,d,e,f,0,0,0,j):is)  = (a,b,c,d,e,f,0,0,0,j) : (s_G ((a,b,c,d,e,f-1,j+1,0,0,0):is))
+  s_J ((a,b,c,d,e,f,g,0,0,j):is)  = (a,b,c,d,e,f,g,0,0,j) : (s_H ((a,b,c,d,e,f,g-1,j+1,0,0):is))
+  s_J ((a,b,c,d,e,f,g,h,0,j):is)  = (a,b,c,d,e,f,g,h,0,j) : (s_I ((a,b,c,d,e,f,g,h-1,j+1,0):is))
+  s_J ((a,b,c,d,e,f,g,h,i,j):is)  = (a,b,c,d,e,f,g,h,i,j) : (s_J ((a,b,c,d,e,f,g,h,i-1,j+1):is))

+ tuple-gen.cabal view

@@ -0,0 +1,18 @@+Name:             tuple-gen
+Version:          1.0
+Synopsis:         Generating all n-tuples without getting stuck in one infinity
+Description:      Generating tuples like this: [(x, y) | x <- [1..], y <- [1..]] generates tuples that change only in the second position. This library uses an automata to generate all tuples whose sum of digits is constant. This constant is increased and thereby all tuples are generated.+category:         Data
+License:          BSD3
+License-file:     LICENSE
+Author:           Tillmann Vogt
+Maintainer:       Tillmann.Vogt@rwth-aachen.de
+Build-Type:       Simple
+Cabal-Version:    >=1.6
++Library+    hs-source-dirs: src
+    build-depends:
+        base == 4.*
+    exposed-modules:
+        Data.Tuple.Gen