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Diffstat (limited to 'lib/hipe/misc/hipe_segment_trees.erl')
-rw-r--r-- | lib/hipe/misc/hipe_segment_trees.erl | 150 |
1 files changed, 150 insertions, 0 deletions
diff --git a/lib/hipe/misc/hipe_segment_trees.erl b/lib/hipe/misc/hipe_segment_trees.erl new file mode 100644 index 0000000000..cbee328125 --- /dev/null +++ b/lib/hipe/misc/hipe_segment_trees.erl @@ -0,0 +1,150 @@ +%%% +%%% %CopyrightBegin% +%%% +%%% Copyright Ericsson AB 2016. All Rights Reserved. +%%% +%%% 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. +%%% +%%% %CopyrightEnd% +%%% +%%% Segment trees. +%%% +%%% Keys are the (0-based) indices into the list passed to build/1. +%%% +%%% Range bounds are inclusive. +%%% +%%% TODO: Change the shape of the tree to a perfect binary tree, and pack it as +%%% an implicit data structure into tuples (like a binary heap would be) for +%%% improved efficiency. + +-module(hipe_segment_trees). + +-export([build/1, intersect/2]). + +-record(segment_tree, { + lo :: integer(), + hi :: integer(), + root :: tnode() + }). + +%% X =< Mid belongs in Left +-define(NODE(Left, Right, Mid, Segments), {Left, Right, Mid, Segments}). + +-define(POINT_LEAF(Val), Val). +-define(RANGE_LEAF(Lo, Hi), {Lo, Hi}). + +-type segments() :: [non_neg_integer()]. +-type leaf() :: segments(). +-type tnode() :: ?NODE(tnode(), tnode(), integer(), segments()) | leaf(). + +-opaque tree() :: #segment_tree{} | nil. +-export_type([tree/0]). + +%% @doc Builds a segment tree of the given intervals. +-spec build([{integer(), integer()}]) -> tree(). +build(ListOfIntervals) -> + case + lists:usort( + lists:append( + [[Lo, Hi] || {Lo, Hi} <- ListOfIntervals, Lo =< Hi])) + of + [] -> nil; + Endpoints -> + Tree0 = empty_tree_from_endpoints(Endpoints), + [Lo|_] = Endpoints, + Hi = lists:last(Endpoints), + Tree1 = insert_intervals(0, ListOfIntervals, Lo, Hi, Tree0), + Tree = squash_empty_subtrees(Tree1), + #segment_tree{lo=Lo, hi=Hi, root=Tree} + end. + +empty_tree_from_endpoints(Endpoints) -> + Leaves = leaves(Endpoints), + {T, [], _, _} = balanced_bst(Leaves, length(Leaves)), + T. + +leaves([Endpoint]) -> [?POINT_LEAF(Endpoint)]; +leaves([A | [B|_] = Tail]) -> + %% We could omit the range leaf if it's empty, but we want to pack this data + %% structure into an array (tuple) eventually, and then we *really* want + %% every other leaf to be a range + case A<B-1 of + true -> [?POINT_LEAF(A),?RANGE_LEAF(A+1,B-1) | leaves(Tail)]; + false -> [?POINT_LEAF(A) | leaves(Tail)] + end. + +balanced_bst(L, S) when S > 1 -> + Sm = S, %% - 1 + S2 = Sm div 2, + S1 = Sm - S2, + {Left, L1, LeftLo, LeftHi} = balanced_bst(L, S1), + {Right, L2, _, RightHi} = balanced_bst(L1, S2), + T = ?NODE(Left, Right, LeftHi, []), + {T, L2, LeftLo, RightHi}; +balanced_bst([?RANGE_LEAF(Lo, Hi) | L], 1) -> + {[], L, Lo, Hi}; +balanced_bst([?POINT_LEAF(Val) | L], 1) -> + {[], L, Val, Val}. + +insert_intervals(_Ix, [], _Lo, _Hi, Tree) -> Tree; +insert_intervals(Ix, [Int|Ints], Lo, Hi, Tree) -> + insert_intervals(Ix + 1, Ints, Lo, Hi, + insert_interval(Ix, Int, Lo, Hi, Tree)). + +insert_interval(_, {Lo, Hi}, _, _, Node) when Lo > Hi -> Node; +insert_interval(I, Int={Lo,Hi}, NLo, NHi, + ?NODE(Left0, Right0, Mid, Segments)) -> + if Lo =< NLo, NHi =< Hi -> + ?NODE(Left0, Right0, Mid, [I|Segments]); + true -> + Left = case intervals_intersect(Lo, Hi, NLo, Mid) of + true -> insert_interval(I, Int, NLo, Mid, Left0); + false -> Left0 + end, + Right = case intervals_intersect(Lo, Hi, Mid+1, NHi) of + true -> insert_interval(I, Int, Mid+1, NHi, Right0); + false -> Right0 + end, + ?NODE(Left, Right, Mid, Segments) + end; +insert_interval(I, {_Lo,_Hi}, _NLo, _NHi, Leaf) -> [I|Leaf]. + +intervals_intersect(ALo, AHi, BLo, BHi) -> + (ALo =< AHi) andalso (BLo =< BHi) %% both nonempty + andalso (BLo =< AHi) andalso (ALo =< BHi). + +%% Purely optional optimisation +squash_empty_subtrees(?NODE(Left0, Right0, Mid, Segs)) -> + build_squash_node(squash_empty_subtrees(Left0), + squash_empty_subtrees(Right0), + Mid, Segs); +squash_empty_subtrees(Leaf) -> Leaf. + +build_squash_node([], [], _, Segs) -> Segs; +build_squash_node(Left, Right, Mid, Segs) -> + ?NODE(Left, Right, Mid, Segs). + +%% @doc Returns the indices of the intervals in the tree that contains Point. +-spec intersect(integer(), tree()) -> [non_neg_integer()]. +intersect(Point, nil) when is_integer(Point) -> []; +intersect(Point, #segment_tree{lo=Lo, hi=Hi, root=Root}) + when is_integer(Point) -> + case Lo =< Point andalso Point =< Hi of + false -> []; + true -> intersect_1(Point, Root, []) + end. + +intersect_1(Point, ?NODE(Left, Right, Mid, Segs), Acc0) -> + Child = if Point =< Mid -> Left; true -> Right end, + intersect_1(Point, Child, Segs ++ Acc0); +intersect_1(_, LeafSegs, Acc) -> LeafSegs ++ Acc. |