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menhir
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POTTIER Francois
menhir
Commits
5eb576e7
Commit
5eb576e7
authored
Jul 06, 2015
by
POTTIER Francois
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Some work to bring [Dijstra] and A* closer to one another.
parent
822ce6f6
Changes
4
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Showing
4 changed files
with
102 additions
and
105 deletions
+102
105
Coverage.ml
src/Coverage.ml
+18
2
astar.ml
src/astar.ml
+76
93
astar.mli
src/astar.mli
+5
7
dijkstra.ml
src/dijkstra.ml
+3
3
No files found.
src/Coverage.ml
View file @
5eb576e7
...
...
@@ 52,7 +52,7 @@ module ForwardAutomaton = struct
(* The sources are the entry states. *)
ProductionMap
.
iter
(
fun
_
s
>
f
s
)
Lr1
.
entry
let
successors
edge
s
=
let
successors
s
edge
=
SymbolMap
.
iter
(
fun
sym
s'
>
(* The weight of the edge from [s] to [s'] is given by the function
[Grammar.Analysis.minimal_symbol]. *)
...
...
@@ 65,6 +65,22 @@ let approximate : Lr1.node > int =
let
module
D
=
Dijkstra
.
Make
(
ForwardAutomaton
)
in
D
.
search
(
fun
(
_
,
_
,
_
)
>
()
)
let
approx
:
Lr1
.
node
>
int
=
let
module
A
=
Astar
.
Make
(
struct
include
ForwardAutomaton
let
estimate
_
=
0
type
node
=
vertex
end
)
in
let
distance
,
_
=
A
.
search
(
fun
(
_
,
_
)
>
()
)
in
distance
(* Debugging. TEMPORARY *)
let
approximate
s
=
let
d1
=
approximate
s
and
d2
=
approx
s
in
assert
(
d1
=
d2
);
d1
(* Test. TEMPORARY *)
let
()
=
...
...
@@ 390,7 +406,7 @@ let backward (s', z) : P.property =
(* Backward search from the single source [s', z]. *)
let
sources
f
=
f
(
s'
,
z
)
let
successors
edge
(
s'
,
z
)
=
let
successors
(
s'
,
z
)
edge
=
match
Lr1
.
incoming_symbol
s'
with

None
>
(* An entry state has no predecessor states. *)
...
...
src/astar.ml
View file @
5eb576e7
...
...
@@ 41,9 +41,6 @@ module Make (G : sig
val
sources
:
(
node
>
unit
)
>
unit
(* Whether a node is a goal node. *)
val
is_goal
:
node
>
bool
(* [successors n f] presents each of [n]'s successors, in
an arbitrary order, to [f], together with the cost of
the edge that was followed. *)
...
...
@@ 59,24 +56,24 @@ end) = struct
type
cost
=
int
type
priority
=
cost
(* Nodes with low priorities are dealt with first. *)
(* Nodes with low priorities are dealt with first. *)
type
priority
=
cost
type
inode
=
{
this
:
G
.
node
;
(* Graph node associated with this internal record. *)
mutable
cost
:
cost
;
(* Cost of the best known path from a source node to this node. (ghat) *)
estimate
:
cost
;
(* Estimated cost of the best path from this node to a goal node. (hhat) *)
mutable
father
:
inode
;
(* Last node on the best known path from a source node to this node. *)
mutable
prev
:
inode
;
(* Previous node on doubly linked priority list *)
mutable
next
:
inode
;
(* Next node on doubly linked priority list *)
mutable
priority
:
priority
;
(* The node's priority, if the node is in the queue; 1 otherwise *)
(* Graph node associated with this internal record. *)
this
:
G
.
node
;
(* Cost of the best known path from a source node to this node. (ghat) *)
mutable
cost
:
cost
;
(* Estimated cost of the best path from this node to a goal node. (hhat) *)
estimate
:
cost
;
(* Best known path from a source node to this node. *)
mutable
path
:
G
.
label
list
;
(* Previous node on doubly linked priority list *)
mutable
prev
:
inode
;
(* Next node on doubly linked priority list *)
mutable
next
:
inode
;
(* The node's priority, if the node is in the queue; 1 otherwise *)
mutable
priority
:
priority
;
}
(* This auxiliary module maintains a mapping of graph nodes
...
...
@@ 120,9 +117,8 @@ end) = struct
can only decrease. *)
val
add_or_decrease
:
inode
>
priority
>
unit
(* Retrieve a node with lowest priority of the queue.
Raises [Not_found] if the queue is empty. *)
val
get
:
unit
>
inode
(* Retrieve a node with lowest priority of the queue. *)
val
get
:
unit
>
inode
option
end
=
struct
...
...
@@ 167,18 +163,18 @@ end) = struct
let
get
()
=
if
!
best
=
max
then
raise
Not_found
(* queue is empty *)
None
else
match
a
.
(
!
best
)
with

None
>
assert
false

Some
inode
>

Some
inode
as
result
>
remove
inode
;
(* look for next nonempty bucket *)
while
(
!
best
<
max
)
&&
(
a
.
(
!
best
)
=
None
)
do
incr
best
done
;
inode
result
let
add_or_decrease
inode
priority
=
if
inode
.
priority
>=
0
then
...
...
@@ 195,7 +191,7 @@ end) = struct
this
=
node
;
cost
=
0
;
estimate
=
G
.
estimate
node
;
father
=
inode
;
path
=
[]
;
prev
=
inode
;
next
=
inode
;
priority
=

1
...
...
@@ 207,91 +203,78 @@ end) = struct
let
expanded
=
ref
0
(* Search. *)
let
rec
search
()
=
(* Pick the open node that currently has lowest fhat, (* TEMPORARY resolve ties in favor of goal nodes *)
that is, lowest estimated distance to a goal node. *)
(* Access to the search results (after the search is over). *)
let
inode
=
P
.
get
()
in
(* may raise Not_found; then, no goal node is reachable *)
let
node
=
inode
.
this
in
let
distance
node
=
try
(
M
.
get
node
)
.
cost
with
Not_found
>
max_int
(* If it is a goal node, we are done. *)
if
G
.
is_goal
node
then
inode
else
begin
let
path
node
=
(
M
.
get
node
)
.
path
(* let [Not_found] escape if no path was found *)
(* Monitoring. *)
incr
expanded
;
(* Otherwise, examine its successors. *)
G
.
successors
node
(
fun
_
edge_cost
son
>
(* Determine the cost of the best known path from the
start node, through this node, to this son. *)
let
new_cost
=
inode
.
cost
+
edge_cost
in
(* Search. *)
try
let
ison
=
M
.
get
son
in
if
new_cost
<
ison
.
cost
then
begin
let
rec
search
f
=
(* This son has been visited before, but this new
path to it is shorter. If it was already open
and waiting in the priority queue, increase its
priority; otherwise, mark it as open and insert
it into the queue. *)
(* Pick the open node that currently has lowest fhat,
that is, lowest estimated distance to a goal node. *)
let
new_fhat
=
new_cost
+
ison
.
estimate
in
P
.
add_or_decrease
ison
new_fhat
;
ison
.
cost
<
new_cost
;
ison
.
father
<
inode
match
P
.
get
()
with

None
>
(* Finished. *)
distance
,
path
end
with
Not_found
>

Some
inode
>
let
node
=
inode
.
this
in
(* This son was never visited before. Allocate a new
status record for it and mark it as open. *)
(* Let the user know about this newly discovered node. *)
f
(
node
,
inode
.
path
);
let
e
=
G
.
estimate
son
in
let
rec
ison
=
{
this
=
son
;
cost
=
new_cost
;
estimate
=
e
;
father
=
inode
;
prev
=
ison
;
next
=
ison
;
priority
=

1
}
in
M
.
add
son
ison
;
P
.
add
ison
(
new_cost
+
e
)
(* Monitoring. *)
incr
expanded
;
);
(* Otherwise, examine its successors. *)
G
.
successors
node
(
fun
label
edge_cost
son
>
search
()
(* Determine the cost of the best known path from the
start node, through this node, to this son. *)
let
new_cost
=
inode
.
cost
+
edge_cost
in
end
try
let
ison
=
M
.
get
son
in
if
new_cost
<
ison
.
cost
then
begin
(* Main function. *)
(* This son has been visited before, but this new
path to it is shorter. If it was already open
and waiting in the priority queue, increase its
priority; otherwise, mark it as open and insert
it into the queue. *)
let
path
()
=
let
new_fhat
=
new_cost
+
ison
.
estimate
in
P
.
add_or_decrease
ison
new_fhat
;
ison
.
cost
<
new_cost
;
ison
.
path
<
label
::
inode
.
path
(* Find the nearest goal node. *)
end
with
Not_found
>
let
goal
=
search
()
in
(* This son was never visited before. Allocate a new
status record for it and mark it as open. *)
(* Build the shortest path back to the start node. *)
let
e
=
G
.
estimate
son
in
let
rec
ison
=
{
this
=
son
;
cost
=
new_cost
;
estimate
=
e
;
path
=
label
::
inode
.
path
;
prev
=
ison
;
next
=
ison
;
priority
=

1
}
in
M
.
add
son
ison
;
P
.
add
ison
(
new_cost
+
e
)
let
rec
build
path
inode
=
let
path
=
inode
.
this
::
path
in
let
father
=
inode
.
father
in
if
father
==
inode
then
path
else
build
path
father
);
in
let
path
=
build
[]
goal
in
path
search
f
end
src/astar.mli
View file @
5eb576e7
...
...
@@ 23,9 +23,6 @@ module Make (G : sig
the edge that was followed. *)
val
successors
:
node
>
(
label
>
int
>
node
>
unit
)
>
unit
(* Whether a node is a goal node. *)
val
is_goal
:
node
>
bool
(* An estimate of the cost of the shortest path from the
supplied node to some goal node. This estimate must
be a correct underapproximation of the actual cost. *)
...
...
@@ 33,9 +30,10 @@ module Make (G : sig
end
)
:
sig
(* This function produces a shortest path from the start
node to some goal node. It raises [Not_found] if no
such path exists. *)
val
path
:
unit
>
G
.
node
list
(* Search. Newly discovered nodes are presented to the user, in order of
increasing distance from the source nodes, by invoking the usersupplied
function [f]. At the end, a mapping of nodes to distances to the source
nodes and a mapping of nodes to shortest paths are returned. *)
val
search
:
(
G
.
node
*
G
.
label
list
>
unit
)
>
(
G
.
node
>
int
)
*
(
G
.
node
>
G
.
label
list
)
end
src/dijkstra.ml
View file @
5eb576e7
...
...
@@ 18,7 +18,7 @@ module Make (G : sig
(* The weighted outgoing edges of a vertex. *)
val
successors
:
(
label
>
int
>
vertex
>
unit
)
>
vertex
>
unit
val
successors
:
vertex
>
(
label
>
int
>
vertex
>
unit
)
>
unit
end
)
=
struct
open
G
...
...
@@ 67,14 +67,14 @@ end) = struct
(* Let the client know about it. *)
f
(
w
,
v
,
p
);
(* Examine its outgoing edges. *)
successors
(
fun
label
weight
v'
>
successors
v
(
fun
label
weight
v'
>
let
w'
=
weight
+
w
in
if
w'
<
distance
v'
then
begin
assert
(
not
(
H
.
mem
fixed
v'
));
H
.
replace
dist
v'
w'
;
PQ
.
add
queue
(
w'
,
v'
,
label
::
p
)
end
)
v
)
end
done
;
distance
...
...
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