我编写了以下程序，它计算输入数组的最长非递减子序列。
从列表列表中查找最长列表的子程序取自stackoverflow（How do I find the longest list in a list of lists）本身。
:- dynamic lns/2.
:- retractall(lns(_, _)).
lns([], []).
lns([X|_], [X]).
lns([X|Xs], [X, Y|Ls]) :-
lns(Xs, [Y|Ls]),
X < Y,
asserta(lns([X|Xs], [X, Y|Ls])).
lns([_|Xs], [Y|Ls]) :-
lns(Xs, [Y|Ls]).
% Find the longest list from the list of lists.
lengths([], []).
lengths([H|T], [LH|LengthsT]) :-
length(H, LH),
lengths(T, LengthsT).
lengthLongest(ListOfLists, Max) :-
lengths(ListOfLists, Lengths),
max_list(Lengths, Max).
longestList(ListOfLists, Longest) :-
lengthLongest(ListOfLists, Len),
member(Longest, ListOfLists),
length(Longest, Len).
optimum_solution(List, Ans) :-
setof(A, lns(List, A), P),
longestList(P, Ans),
!.
我使用Prolog动态数据库进行记忆。 虽然带数据库的程序比没有数据库的程序运行得慢。以下是两次运行之间的比较时间。
?- time(optimum_solution([0, 8, 4, 12, 2, 10, 6, 14, 1, 9], Ans)).
% 53,397 inferences, 0.088 CPU in 0.088 seconds (100% CPU, 609577 Lips)
Ans = [0, 2, 6, 9]. %% With database
?- time(optimum_solution([0, 8, 4, 12, 2, 10, 6, 14, 1, 9], Ans)).
% 4,097 inferences, 0.002 CPU in 0.002 seconds (100% CPU, 2322004 Lips)
Ans = [0, 2, 6, 9]. %% Without database. commented out the database usage.
我想知道我是否正确使用动态数据库。谢谢！
答案 0 :(得分：2)
问题在于，当您遍历列表构建子序列时，您只需要考虑其最后一个值小于您手头值的先前子序列。问题是Prolog的第一个参数索引正在进行相等检查，而不是检查。所以Prolog必须遍历lns/2的整个商店，用一个值统一第一个参数，这样你就可以查看它是否更少，然后回溯以获得下一个。
答案 1 :(得分：2)
Earlier，我们提出了基于clpfd的简明解决方案。 现在我们的目标是普遍性和效率！
:- use_module([library(clpfd), library(lists)]). list_long_nondecreasing_subseq(Zs, Xs) :- minimum(Min, Zs), append(_, Suffix, Zs), same_length(Suffix, Xs), zs_subseq_taken0(Zs, Xs, Min). zs_subseq_taken0([], [], _). zs_subseq_taken0([E|Es], [E|Xs], E0) :- E0 #=< E, zs_subseq_taken0(Es, Xs, E). zs_subseq_taken0([E|Es], Xs, E0) :- zs_subseq_taken0_min0_max0(Es, Xs, E0, E, E). zs_subseq_taken0_min0_max0([], [], E0, _, Max) :- Max #< E0. zs_subseq_taken0_min0_max0([E|Es], [E|Xs], E0, Min, Max) :- E0 #=< E, E0 #> Min #\/ Min #> E, E0 #> Max #\/ Max #> E, zs_subseq_taken0(Es, Xs, E). zs_subseq_taken0_min0_max0([E|Es], Xs, E0, Min0, Max0) :- Min #= min(Min0,E), Max #= max(Max0,E), zs_subseq_taken0_min0_max0(Es, Xs, E0, Min, Max).
使用SICStus Prolog 4.3.2进行的示例查询（具有漂亮的答案序列）：
?- list_long_nondecreasing_subseq([0,8,4,12,2,10,6,14,1,9], Xs).
Xs = [0,8,12,14]
; Xs = [0,8,10,14]
; Xs = [0,4,12,14]
; Xs = [0,4,10,14]
; Xs = [0,4, 6,14]
; Xs = [0,4, 6, 9]
; Xs = [0,2,10,14]
; Xs = [0,2, 6,14]
; Xs = [0,2, 6, 9]
; Xs = [0,8,9]
; Xs = [0,4,9]
; Xs = [0,2,9]
; Xs = [0,1,9]
; false.
请注意list_long_nondecreasing_subseq/2的答案序列
可能很多小于list_nondecreasing_subseq/2给出的。
以上列表[0,8,4,12,2,10,6,14,1,9]有 9 长度 4 -all的非降序子序列 - ＆＃34;返回＆＃34;由list_nondecreasing_subseq/2 和组成
list_long_nondecreasing_subseq/2。
然而，相应的答案序列大小差别很大：（65 + 9 = 74 ）vs（4 + 9 = 13 ）。
答案 2 :(得分：1)
<强> TL; DR： 在这个答案中，我们实现了一个基于clpfd的非常通用的方法。
:- use_module(library(clpfd)). list_nondecreasing_subseq(Zs, Xs) :- append(_, Suffix, Zs), same_length(Suffix, Xs), chain(Xs, #=<), list_subseq(Zs, Xs). % a.k.a. subset/2 by @gusbro
使用SWI-Prolog 7.3.16的示例查询：
?- list_nondecreasing_subseq([0,8,4,12,2,10,6,14,1,9], Zs). Zs = [0,8,12,14] ; Zs = [0,8,10,14] ; Zs = [0,4,12,14] ; Zs = [0,4,10,14] ; Zs = [0,4,6,14] ; Zs = [0,4,6,9] ; Zs = [0,2,10,14] ; Zs = [0,2,6,14] ; Zs = [0,2,6,9] ; Zs = [0,8,12] ... ; Zs = [9] ; Zs = [] ; false.
请注意答案序列的特定顺序！ 最长的列表首先出现，然后是更小的列表......一直到单例列表和空列表。
答案 3 :(得分：0)
持续变得更好！
在这个答案中，我们提供了list_long_nondecreasing_subseq__NEW/2，list_long_nondecreasing_subseq/2的简略替换 - 提交了in this earlier answer。
让我们切入追逐并定义list_long_nondecreasing_subseq__NEW/2！
:- use_module([library(clpfd), library(lists), library(random), library(between)]). list_long_nondecreasing_subseq__NEW(Zs, Xs) :- minimum(Min, Zs), append(Prefix, Suffix, Zs), same_length(Suffix, Xs), zs_skipped_subseq_taken0(Zs, Prefix, Xs, Min). zs_skipped_subseq_taken0([], _, [], _). zs_skipped_subseq_taken0([E|Es], Ps, [E|Xs], E0) :- E0 #=< E, zs_skipped_subseq_taken0(Es, Ps, Xs, E). zs_skipped_subseq_taken0([E|Es], [_|Ps], Xs, E0) :- zs_skipped_subseq_taken0_min0_max0(Es, Ps, Xs, E0, E, E). zs_skipped_subseq_taken0_min0_max0([], _, [], E0, _, Max) :- Max #< E0. zs_skipped_subseq_taken0_min0_max0([E|Es], Ps, [E|Xs], E0, Min, Max) :- E0 #=< E, E0 #> Min #\/ Min #> E, E0 #> Max #\/ Max #> E, zs_skipped_subseq_taken0(Es, Ps, Xs, E). zs_skipped_subseq_taken0_min0_max0([E|Es], [_|Ps], Xs, E0, Min0, Max0) :- Min #= min(Min0,E), Max #= max(Max0,E), zs_skipped_subseq_taken0_min0_max0(Es, Ps, Xs, E0, Min, Max).
所以...它仍然像以前一样工作吗？让我们运行一些测试并比较答案序列：
| ?- setrand(random(29251,13760,3736,425005073)),
between(7, 23, N),
nl,
write(n=N),
write(' '),
length(Zs, N),
between(1, 10, _),
maplist(random(1,N), Zs),
findall(Xs1, list_long_nondecreasing_subseq( Zs,Xs1), Xss1),
findall(Xs2, list_long_nondecreasing_subseq__NEW(Zs,Xs2), Xss2),
( Xss1 == Xss2 -> true ; throw(up) ),
length(Xss2,L),
write({L}),
false.
n=7 {3}{8}{3}{7}{2}{5}{4}{4}{8}{4}
n=8 {9}{9}{9}{8}{4}{4}{7}{5}{6}{9}
n=9 {9}{8}{5}{7}{10}{7}{9}{4}{5}{4}
n=10 {7}{12}{7}{14}{13}{19}{13}{17}{10}{7}
n=11 {14}{17}{7}{9}{17}{21}{14}{10}{10}{21}
n=12 {25}{18}{20}{10}{32}{35}{7}{30}{15}{11}
n=13 {37}{19}{18}{22}{20}{14}{10}{11}{8}{14}
n=14 {27}{9}{18}{10}{20}{29}{69}{28}{10}{33}
n=15 {17}{24}{13}{26}{32}{14}{22}{28}{32}{41}
n=16 {41}{55}{35}{73}{44}{22}{46}{47}{26}{23}
n=17 {54}{43}{38}{110}{50}{33}{48}{64}{33}{56}
n=18 {172}{29}{79}{36}{32}{99}{55}{48}{83}{37}
n=19 {225}{83}{119}{61}{27}{67}{48}{65}{90}{96}
n=20 {58}{121}{206}{169}{111}{66}{233}{57}{110}{146}
n=21 {44}{108}{89}{99}{149}{148}{92}{76}{53}{47}
n=22 {107}{137}{221}{79}{172}{156}{184}{78}{162}{112}
n=23 {163}{62}{76}{192}{133}{372}{101}{290}{84}{378}
no
所有答案序列完全相同！ ......那么，运行时怎么样？
让我们使用SICStus Prolog 4.3.2运行更多查询并打印出答案！
?- member(N, [15,20,25,30,35,40,45,50]), length(Zs, N), _NN #= N*N, maplist(random(1,_NN), Zs), call_time(once(list_long_nondecreasing_subseq( Zs, Xs )), T1), call_time(once(list_long_nondecreasing_subseq__NEW(Zs,_Xs2)), T2), Xs == _Xs2, length(Xs,L). N = 15, L = 4, T1 = 20, T2 = 0, Zs = [224,150,161,104,134,43,9,111,76,125,50,68,202,178,148], Xs = [104,111,125,202] ; N = 20, L = 6, T1 = 60, T2 = 10, Zs = [71,203,332,366,350,19,241,88,370,100,288,199,235,343,181,90,63,149,215,285], Xs = [71,88,100,199,235,343] ; N = 25, L = 7, T1 = 210, T2 = 20, Zs = [62,411,250,222,141,292,276,94,548,322,13,317,68,488,137,33,80,167,101,475,475,429,217,25,477], Xs = [62,250,292,322,475,475,477] ; N = 30, L = 10, T1 = 870, T2 = 30, Zs = [67,175,818,741,669,312,99,23,478,696,63,793,280,364,677,254,530,216,291,660,218,664,476,556,678,626,75,834,578,850], Xs = [67,175,312,478,530,660,664,678,834,850] ; N = 35, L = 7, T1 = 960, T2 = 120, Zs = [675,763,1141,1070,299,650,1061,1184,512,905,139,719,844,8,1186,1006,400,690,29,791,308,1180,819,331,482,982,81,574,1220,431,416,357,1139,636,591], Xs = [299,650,719,844,1006,1180,1220] ; N = 40, L = 9, T1 = 5400, T2 = 470, Zs = [958,1047,132,1381,22,991,701,1548,470,1281,358,32,605,1270,692,1020,350,794,1451,11,985,1196,504,1367,618,1064,961,463,736,907,1103,719,1385,1026,935,489,1053,380,637,51], Xs = [132,470,605,692,794,985,1196,1367,1385] ; N = 45, L = 10, T1 = 16570, T2 = 1580, Zs = [1452,171,442,1751,160,1046,470,450,1245,971,1574,901,1613,1214,1849,1805,341,34,1923,698,156,1696,717,1708,1814,1548,463,421,1584,190,1195,1563,1772,1639,712,693,1848,1531,250,783,1654,1732,1333,717,1322], Xs = [171,442,1046,1245,1574,1613,1696,1708,1814,1848] ; N = 50, L = 11, T1 = 17800, T2 = 1360, Zs = [2478,2011,2411,1127,1719,1286,1081,2042,1166,86,355,894,190,7,1973,1912,753,1411,1082,70,2142,417,1609,1649,2329,2477,1324,37,1781,1897,2415,1018,183,2422,1619,1446,1461,271,56,2399,1681,267,977,826,2145,2318,2391,137,55,1995], Xs = [86,355,894,1411,1609,1649,1781,1897,2145,2318,2391] ; false.
当然，此答案中显示的baroque方法根本无法与“严重”suitable algorithms竞争以确定lis - 仍然，获得10倍加速始终感觉良好：）