/* The contents of this file are subject to the Mozilla Public License Version 1.1 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at: http://www.mozilla.org/MPL/ Software distributed under the License is distributed on an "AS IS" basis, WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License for the specific language governing rights and limitations under the License. The Original Code is the contents of this file. The Initial Developer of the Original Code is SICS, Swedish Institute of Computer Science AB (SICS). Portions created by the Initial Developer are Copyright (C) 2007 of the Initial Developer. All Rights Reserved. Contributor(s): _____Mats Carlsson _____Nicolas Beldiceanu Alternatively, if the contents of this file is included as a part of SICStus Prolog distribution by SICS, it may be used under the terms of an appropriate SICStus Prolog License Agreement (the "SICStus Prolog License"), in which case the provisions of the SICStus Prolog License are applicable instead of those above. */ :- multifile ctr_predefined/1, ctr_date/2, ctr_persons/2, ctr_origin/3, ctr_usual_name/2, ctr_synonyms/2, ctr_types/2, ctr_arguments/2, ctr_exchangeable/2, ctr_restrictions/2, ctr_typical/2, ctr_pure_functional_dependency/2, ctr_functional_dependency/3, ctr_contractible/4, ctr_extensible/4, ctr_aggregate/3, ctr_example/2, ctr_draw_example/9, ctr_cond_imply/5, ctr_see_also/2, ctr_key_words/2, ctr_derived_collections/2, ctr_graph/7, ctr_graph/9, ctr_eval/2, ctr_sol/6, ctr_logic/3, ctr_application/2. ctr_date(path,['20090101','20120219']). ctr_origin(path, 'Derived from %c.', [binary_tree]). ctr_arguments(path, ['NPATH'-dvar , 'NODES'-collection(index-int, succ-dvar)]). ctr_restrictions(path, ['NPATH' >= 1 , 'NPATH' =< size('NODES'), required('NODES',[index,succ]), size('NODES') > 0 , 'NODES'^index >= 1 , 'NODES'^index =< size('NODES'), distinct('NODES',index) , 'NODES'^succ >= 1 , 'NODES'^succ =< size('NODES')]). ctr_typical(path, ['NPATH' < size('NODES'), size('NODES') > 1 ]). ctr_functional_dependency(path, 1, [2]). ctr_exchangeable(path, [items('NODES',all)]). ctr_graph(path, ['NODES'], 2, ['CLIQUE'>>collection(nodes1,nodes2)], [nodes1^succ = nodes2^index], ['MAX_NSCC' =< 1 , 'NCC' = 'NPATH' , 'MAX_ID' =< 1 ], ['ONE_SUCC']). ctr_example(path, [path(3,[[index-1, succ-1], [index-2, succ-3], [index-3, succ-5], [index-4, succ-7], [index-5, succ-1], [index-6, succ-6], [index-7, succ-7], [index-8, succ-6]]), path(1,[[index-1, succ-8], [index-2, succ-7], [index-3, succ-6], [index-4, succ-5], [index-5, succ-5], [index-6, succ-4], [index-7, succ-3], [index-8, succ-2]]), path(8,[[index-1, succ-1], [index-2, succ-2], [index-3, succ-3], [index-4, succ-4], [index-5, succ-5], [index-6, succ-6], [index-7, succ-7], [index-8, succ-8]]) ]). ctr_draw_example(path, ['NODES'], [[[index-1, succ-1], [index-2, succ-3], [index-3, succ-5], [index-4, succ-7], [index-5, succ-1], [index-6, succ-6], [index-7, succ-7], [index-8, succ-6]]], ['CLIQUE'], [1-1,2-3,3-5,4-7,5-1,6-6,7-7,8-6], ['NCC'([[1,2,3,5],[4,7],[6,8]]), 'MAX_ID'([1])], '','MAX_NSCC=1, NCC=3\\nMAX_ID=1', [2.5,4,2.5,2.5]). ctr_see_also(path, [link('implies', binary_tree, '', []), link('generalisation', binary_tree, 'at most one child replaced by at most two children', []), link('generalisation', tree, 'at most one child replaced by no limit on the number of children', []), link('generalisation', temporal_path, 'vertices are located in time, and to each arc corresponds a precedence constraint', []), link('common keyword', circuit, '%k, %k', ['graph partitioning constraint', 'one\\_succ']), link('common keyword', proper_circuit, '%k, %k', ['graph partitioning constraint', 'one\\_succ']), link('common keyword', dom_reachability, '%k', ['path']), link('common keyword', path_from_to, '%k, select an induced subgraph so that there is a path from a given vertex to an other given vertex', ['path']), link('related', balance_path, 'counting number of paths versus controlling how balanced the paths are', [])]). ctr_key_words(path,['graph constraint' , 'graph partitioning constraint', 'connected component' , 'path' , 'tree' , 'one\\_succ' , 'DFS-bottleneck' , 'functional dependency' ]). ctr_application(path, [2]). ctr_eval(path, [reformulation(path_r),checker(path_c)]). ctr_sol(path,2,0,2,3,[1-2,2-1]). ctr_sol(path,3,0,3,13,[1-6,2-6,3-1]). ctr_sol(path,4,0,4,73,[1-24,2-36,3-12,4-1]). ctr_sol(path,5,0,5,501,[1-120,2-240,3-120,4-20,5-1]). ctr_sol(path,6,0,6,4051,[1-720,2-1800,3-1200,4-300,5-30,6-1]). ctr_sol(path,7,0,7,37633,[1-5040,2-15120,3-12600,4-4200,5-630,6-42,7-1]). ctr_sol(path,8,0,8,394353,[1-40320,2-141120,3-141120,4-58800,5-11760,6-1176,7-56,8-1]). path_r(NPATH, NODES) :- eval(tree(NPATH, NODES)), get_attr1(NODES, INDEXES), get_attr2(NODES, SUCCS), k_ary_tree(INDEXES, INDEXES, SUCCS, 1). path_c(NPATH, NODES) :- length(NODES, N), check_type(dvar(1,N), NPATH), collection(NODES, [int(1,N),dvar(1,N)]), get_attr1(NODES, IND), sort(IND, SIND), length(SIND, N), get_attr12(NODES, IND_SUCC), keysort(IND_SUCC, SIND_SUCC), remove_key_from_collection(SIND_SUCC, Succ), ( foreach(S,Succ), foreach(S-P,L1), foreach(_,Sink), % each element will get its sink count(P,1,_) do true ), keysort(L1, L2), keyclumped(L2, L3), % L3 is a list of pairs (successor-predecessors) ( foreach(Su-Ps,L3), param(Sink) do ( Ps = [Su] -> nth1(Su, Sink, Su) ; Ps = [Other] -> nth1(Su, Sink, X), nth1(Other, Sink, X) ; Ps = [Su,Other] -> nth1(Su, Sink, Su), nth1(Other, Sink, Su) ; Ps = [Other,Su] -> nth1(Su, Sink, Su), nth1(Other, Sink, Su) ) ), ground(Sink), sort(Sink, Sinks), length(Sinks, NPATH).