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%% -*- erlang-indent-level: 2 -*-
%%
%% Licensed under the Apache License, Version 2.0 (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.apache.org/licenses/LICENSE-2.0
%%
%% Unless required by applicable law or agreed to in writing, software
%% distributed under the License is distributed on an "AS IS" BASIS,
%% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
%% See the License for the specific language governing permissions and
%% limitations under the License.
%%
%%-----------------------------------------------------------------------
%% File : hipe_digraph.erl
%% Author : Tobias Lindahl <[email protected]>
%% Purpose : Provides a simple implementation of a directed graph.
%%
%% Created : 9 Feb 2005 by Tobias Lindahl <[email protected]>
%%-----------------------------------------------------------------------
-module(hipe_digraph).
-export([new/0, add_edge/3, add_node/2, add_node_list/2,
from_list/1, to_list/1, get_parents/2, get_children/2]).
-export([reverse_preorder_sccs/1]).
-export_type([hdg/0]).
%%------------------------------------------------------------------------
-type ordset(T) :: [T]. % XXX: temporarily
-record(hipe_digraph, {edges = dict:new() :: dict:dict(),
rev_edges = dict:new() :: dict:dict(),
leaves = ordsets:new() :: ordset(_), % ???
nodes = sets:new() :: sets:set()}).
-opaque hdg() :: #hipe_digraph{}.
%%------------------------------------------------------------------------
-spec new() -> hdg().
new() ->
#hipe_digraph{edges = dict:new(), rev_edges = dict:new(),
leaves = ordsets:new(), nodes = sets:new()}.
-spec from_list([_]) -> hdg().
from_list(List) ->
Edges = lists:foldl(fun({From, To}, Dict) ->
Fun = fun(Set) -> ordsets:add_element(To, Set) end,
dict:update(From, Fun, [To], Dict)
end,
dict:new(), List),
RevEdges = lists:foldl(fun({From, To}, Dict) ->
Fun = fun(Set) ->
ordsets:add_element(From, Set)
end,
dict:update(To, Fun, [From], Dict)
end,
dict:new(), List),
Keys1 = sets:from_list(dict:fetch_keys(Edges)),
Keys2 = sets:from_list(dict:fetch_keys(RevEdges)),
Nodes = sets:union(Keys1, Keys2),
#hipe_digraph{edges = Edges, rev_edges = RevEdges,
leaves = [], nodes = Nodes}.
-spec to_list(hdg()) -> [_].
to_list(#hipe_digraph{edges = Edges}) ->
List1 = dict:to_list(Edges),
List2 = lists:foldl(fun({From, ToList}, Acc) ->
[[{From, To} || To <- ToList]|Acc]
end, [], List1),
lists:flatten(List2).
-spec add_node(_, hdg()) -> hdg().
add_node(NewNode, DG = #hipe_digraph{nodes=Nodes}) ->
DG#hipe_digraph{nodes = sets:add_element(NewNode, Nodes)}.
-spec add_node_list([_], hdg()) -> hdg().
add_node_list(NewNodes, DG = #hipe_digraph{nodes=Nodes}) ->
Set = sets:from_list(NewNodes),
DG#hipe_digraph{nodes = sets:union(Set, Nodes)}.
-spec add_edge(_, _, hdg()) -> hdg().
add_edge(From, To, #hipe_digraph{edges = Edges, rev_edges = RevEdges,
leaves = Leaves, nodes = Nodes}) ->
Fun1 = fun(Set) -> ordsets:add_element(To, Set) end,
NewEdges = dict:update(From, Fun1, [To], Edges),
Fun2 = fun(Set) -> ordsets:add_element(From, Set) end,
NewRevEdges = dict:update(To, Fun2, [From], RevEdges),
NewLeaves = ordsets:del_element(From, Leaves),
#hipe_digraph{edges = NewEdges,
rev_edges = NewRevEdges,
leaves = NewLeaves,
nodes = sets:add_element(From, sets:add_element(To, Nodes))}.
%%-------------------------------------------------------------------------
-spec take_indep_scc(hdg()) -> 'none' | {'ok', [_], hdg()}.
take_indep_scc(DG = #hipe_digraph{edges = Edges, rev_edges = RevEdges,
leaves = Leaves, nodes = Nodes}) ->
case sets:size(Nodes) =:= 0 of
true -> none;
false ->
{SCC, NewLeaves} =
case Leaves of
[H|T] ->
{[H], T};
[] ->
case find_all_leaves(Edges) of
[] ->
{[Node|_], _} = dfs(Nodes, RevEdges),
{SCC1, _} = dfs(Node, Edges),
{SCC1, []};
[H|T] ->
{[H], T}
end
end,
NewEdges = remove_edges(SCC, Edges, RevEdges),
NewRevEdges = remove_edges(SCC, RevEdges, Edges),
NewNodes = sets:subtract(Nodes, sets:from_list(SCC)),
{ok, reverse_preorder(SCC, Edges),
DG#hipe_digraph{edges = NewEdges, rev_edges = NewRevEdges,
leaves = NewLeaves, nodes = NewNodes}}
end.
find_all_leaves(Edges) ->
List = dict:fold(fun(Key, [Key], Acc) -> [Key|Acc];
(_, _, Acc) -> Acc
end, [], Edges),
ordsets:from_list(List).
remove_edges(Nodes0, Edges, RevEdges) ->
Nodes = ordsets:from_list(Nodes0),
Fun = fun(N, Dict) -> dict:erase(N, Dict) end,
Edges1 = lists:foldl(Fun, Edges, Nodes),
remove_edges_in(Nodes, Edges1, RevEdges).
remove_edges_in([Node|Nodes], Edges, RevEdges) ->
NewEdges =
case dict:find(Node, RevEdges) of
error ->
Edges;
{ok, Set} ->
Fun = fun(Key, Dict) ->
case dict:find(Key, Dict) of
error ->
Dict;
{ok, OldTo} ->
case ordsets:del_element(Node, OldTo) of
[] -> dict:store(Key, [Key], Dict);
NewSet -> dict:store(Key, NewSet, Dict)
end
end
end,
lists:foldl(Fun, Edges, Set)
end,
remove_edges_in(Nodes, NewEdges, RevEdges);
remove_edges_in([], Edges, _RevEdges) ->
Edges.
reverse_preorder([_] = Nodes, _Edges) ->
Nodes;
reverse_preorder([N|_] = Nodes, Edges) ->
NodeSet = sets:from_list(Nodes),
{PreOrder, _} = dfs(N, Edges),
DFS = [X || X <- PreOrder, sets:is_element(X, NodeSet)],
lists:reverse(DFS).
%%---------------------------------------------------------------------
-spec reverse_preorder_sccs(hdg()) -> [[_]].
reverse_preorder_sccs(DG) ->
reverse_preorder_sccs(DG, []).
reverse_preorder_sccs(DG, Acc) ->
case take_indep_scc(DG) of
none -> lists:reverse(Acc);
{ok, SCC, DG1} -> reverse_preorder_sccs(DG1, [SCC|Acc])
end.
%%---------------------------------------------------------------------
-spec get_parents(_, hdg()) -> [_].
get_parents(Node, #hipe_digraph{rev_edges = RevEdges}) ->
case dict:is_key(Node, RevEdges) of
true -> dict:fetch(Node, RevEdges);
false -> []
end.
-spec get_children(_, hdg()) -> [_].
get_children(Node, #hipe_digraph{edges = Edges}) ->
case dict:is_key(Node, Edges) of
true -> dict:fetch(Node, Edges);
false -> []
end.
%%---------------------------------------------------------------------
%% dfs/2 returns a preordered depth first search and the nodes visited.
dfs(Node, Edges) ->
case sets:is_set(Node) of
true ->
dfs(sets:to_list(Node), Edges, sets:new(), []);
false ->
dfs([Node], Edges, sets:new(), [])
end.
dfs([Node|Left], Edges, Visited, Order) ->
case sets:is_element(Node, Visited) of
true ->
dfs(Left, Edges, Visited, Order);
false ->
NewVisited = sets:add_element(Node, Visited),
case dict:find(Node, Edges) of
error ->
dfs(Left, Edges, NewVisited, [Node|Order]);
{ok, Succ} ->
{NewOrder, NewVisited1} = dfs(Succ, Edges, NewVisited, Order),
dfs(Left, Edges, NewVisited1, [Node|NewOrder])
end
end;
dfs([], _Edges, Visited, Order) ->
{Order, Visited}.
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