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Merge pull request #28 from ajfAfg/fix-solve_in_exp_time_with_c-orrec…
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…tness-output-result-to-satisfy-all2

fix solve in exp time with c orrectness output result to satisfy all 2
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@ajfAfg
ajfAfg authored Jan 3, 2024
2 parents 8739dde + a46539a commit 847a2fb
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Showing 5 changed files with 56 additions and 74 deletions.
61 changes: 9 additions & 52 deletions src/core/all_local_minimum_vertex_splitters_solver.erl
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Original file line number Diff line number Diff line change
Expand Up @@ -41,59 +41,16 @@ solve_in_exp_time_with_correctness(ConnectedDAG) ->
<- my_lists:power(
digraph:vertices(ConnectedDAG)),
dependency_digraph:is_vertex_splitter(ConnectedDAG, Vertices)],
Candidates2 =
begin
MinimumVertexSplittersForEveryExitVertex =
lists:foldl(fun(VertexSplitter, Acc) ->
lists:foldl(fun(ExitVertex, Acc2) ->
maps:update_with(ExitVertex,
fun(VertexSplitters) ->
case
compare(length(VertexSplitter),
length(hd(VertexSplitters)))
of
less -> [VertexSplitter];
greater -> VertexSplitters;
equal ->
[VertexSplitter
| VertexSplitters]
end
end,
Acc2)
end,
Acc,
[V
|| V <- VertexSplitter,
is_exit_vertex(ConnectedDAG, V)])
end,
maps:from_keys(exit_vertices(ConnectedDAG),
[digraph:vertices(ConnectedDAG)]),
Candidates),
lists:usort(
lists:map(fun lists:sort/1,
my_lists:flatten(
maps:values(MinimumVertexSplittersForEveryExitVertex))))
end,
[S1
|| S1 <- Candidates2,
not
lists:any(fun(S2) ->
sets:is_subset(
sets:from_list(S2), sets:from_list(S1))
end,
lists:delete(S1, Candidates2))].
lists:filter(fun(Candidate) ->
not
lists:any(fun(Vertices) ->
dependency_digraph:is_vertex_splitter(ConnectedDAG,
Candidate -- Vertices)
end,
lists:delete([], my_lists:power(Candidate)))
end,
Candidates).

%% ===================================================================
%% Private API
%% ===================================================================
-spec compare(term(), term()) -> less | greater | equal.
compare(X, Y) when X < Y -> less;
compare(X, Y) when X > Y -> greater;
compare(_, _) -> equal.

-spec exit_vertices(digraph:graph()) -> [digraph:vertex()].
exit_vertices(Digraph) ->
[V || V <- digraph:vertices(Digraph), is_exit_vertex(Digraph, V)].

-spec is_exit_vertex(digraph:graph(), digraph:vertex()) -> boolean().
is_exit_vertex(Digraph, Vertex) -> digraph:out_degree(Digraph, Vertex) =:= 0.
6 changes: 1 addition & 5 deletions src/core/my_lists.erl
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Original file line number Diff line number Diff line change
@@ -1,6 +1,6 @@
-module(my_lists).

-export([shuffle/1, sublist_randomly/1, power/1, flatten/1]).
-export([shuffle/1, sublist_randomly/1, power/1]).

-spec shuffle(list()) -> list().
shuffle(List) -> [X || {_, X} <- lists:sort([{rand:uniform(), Y} || Y <- List])].
Expand All @@ -16,7 +16,3 @@ power(List) -> power_([], List, []).
power_(Subset, [], Family) -> [Subset | Family];
power_(Subset, [Head | Rest], Family) ->
power_(Subset, Rest, power_([Head | Subset], Rest, Family)).

% NOTE: Unlike `lists:flatten/1`, this function removes only one level of the nested list.
-spec flatten([list()]) -> list().
flatten(ListList) -> [X || List <- ListList, X <- List].
33 changes: 32 additions & 1 deletion test/all_local_minimum_vertex_splitters_solver_tests.erl
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Original file line number Diff line number Diff line change
Expand Up @@ -114,5 +114,36 @@ solve_in_exp_time_with_correctness_test_() ->
lists:map(fun lists:sort/1, [[2, 3], [5], [8]])),
lists:sort(
lists:map(fun lists:sort/1,
all_local_minimum_vertex_splitters_solver:solve_in_exp_time_with_correctness(G5))))
all_local_minimum_vertex_splitters_solver:solve_in_exp_time_with_correctness(G5)))),
G6 = my_digraph:create(
lists:seq(1, 16),
[{1, 2},
{2, 3},
{3, 4},
{3, 5},
{6, 5},
{7, 4},
{7, 8},
{9, 10},
{10, 8},
{10, 11},
{11, 12},
{11, 13},
{14, 2},
{14, 15},
{15, 12},
{16, 13},
{16, 15}]),
?assertEqual(lists:sort(
lists:map(fun lists:sort/1,
[[4, 8],
[4, 12, 13],
[4, 12, 15],
[5],
[8, 12, 13],
[8, 12, 15],
[12, 13, 15]])),
lists:sort(
lists:map(fun lists:sort/1,
all_local_minimum_vertex_splitters_solver:solve_in_exp_time_with_correctness(G6))))
end}]}.
14 changes: 0 additions & 14 deletions test/prop_my_lists.erl
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Original file line number Diff line number Diff line change
Expand Up @@ -60,17 +60,3 @@ prop_power2() ->
?SUCHTHAT(L, list(random_type()), length(L) =< 15),
lists:all(fun(List2) -> lists:sort(List2 ++ List -- List2) =:= lists:sort(List) end,
my_lists:power(List))).

%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% my_lists:flatten/1 %%%
%%%%%%%%%%%%%%%%%%%%%%%%%%
% NOTE:
% It is easy to give a different implementation,
% so I test by "Wording the specification differently".
prop_flatten1(doc) -> "Wording the specification differently".

prop_flatten1() ->
?FORALL(ListList,
list(list(random_type())),
lists:foldl(fun(List, Acc) -> List ++ Acc end, [], lists:reverse(ListList))
=:= my_lists:flatten(ListList)).
16 changes: 14 additions & 2 deletions test/prop_optimum_supervision_tree_solver.erl
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Original file line number Diff line number Diff line change
Expand Up @@ -9,10 +9,10 @@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% optimum_supervision_tree_solver:solve/1 %%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
prop_solve(doc) ->
prop_solve1(doc) ->
"When a process is restarted, the processes that depend on it are also restarted".

prop_solve() ->
prop_solve1() ->
?FORALL(Graph,
dependency_graph_generator:dependency_graph(),
begin
Expand Down Expand Up @@ -48,3 +48,15 @@ take_restart_processes({_, Children}) ->
lists:flatten(
lists:map(fun take_restart_processes/1, Children));
take_restart_processes(Child) -> Child.

prop_solve2(doc) -> "About cost, exp time & correct ≤ polynomial time & incorrect".

prop_solve2() ->
?FORALL(Graph,
dependency_graph_generator:dependency_graph(),
supervision_tree:calc_cost(
optimum_supervision_tree_solver:solve(Graph,
fun all_local_minimum_vertex_splitters_solver:solve_in_exp_time_with_correctness/1))
=< supervision_tree:calc_cost(
optimum_supervision_tree_solver:solve(Graph,
fun all_local_minimum_vertex_splitters_solver:solve_in_polynomial_time_without_correctness/1))).

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