________________________________________________________________________

This file is part of Logtalk <https://logtalk.org/>  
Copyright 1998-2018 Paulo Moura <pmoura@logtalk.org>

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.
________________________________________________________________________


% start by loading the example and the required library files:

| ?- logtalk_load(searching(loader)).
...


% farmer, cabbage, goat and wolf problem

| ?- farmer::initial_state(Initial), depth_first(10)::solve(farmer, Initial, Path), farmer::print_path(Path).

cgwf.<__>..........____
c_w_..........<__>.f_g_
c_wf.<__>..........__g_
__w_..........<__>.fcg_
_gwf.<__>.........._c__
_g__..........<__>.fc_w
_g_f.<__>.........._c_w
____..........<__>.fcgw

Path = [(north,north,north,north),(north,south,north,south),(north,south,north,north),(south,south,north,south),(south,north,north,north),(south,north,south,south),(south,north,south,north),(south,south,south,south)],
Initial = (north,north,north,north) ? 

yes


% missionaries and cannibals problem, solved using a hill-climbing strategy

| ?- miss_cann::initial_state(Initial), hill_climbing(16)::solve(miss_cann, Initial, Path, Cost), miss_cann::print_path(Path).

MMMCCC.<__>..........
MMCC..........<__>.MC
MMMCC.<__>..........C
MMM..........<__>.CCC
MMMC.<__>..........CC
MC..........<__>.MMCC
MMCC.<__>..........MC
CC..........<__>.MMMC
CCC.<__>..........MMM
C..........<__>.MMMCC
CC.<__>..........MMMC
..........<__>.MMMCCC

Cost = 15,
Path = [((3,3),left,0,0),((2,2),right,1,1),((3,2),left,0,1),((3,0),right,0,3),((3,1),left,0,2),((1,1),right,2,2),((2,2),left,1,1),((0,2),right,3,1),((0,3),left,3,0),((0,1),right,3,2),((0,2),left,3,1),((0,0),right,3,3)],
Initial = ((3,3),left,0,0)
yes


% same problem as above with the addition of a monitor to measure hill-climbing performance

| ?- performance::init, miss_cann::initial_state(Initial), hill_climbing(16)::solve(miss_cann, Initial, Path, Cost), miss_cann::print_path(Path), performance::report.

MMMCCC.<__>..........
MMCC..........<__>.MC
MMMCC.<__>..........C
MMM..........<__>.CCC
MMMC.<__>..........CC
MC..........<__>.MMCC
MMCC.<__>..........MC
CC..........<__>.MMMC
CCC.<__>..........MMM
C..........<__>.MMMCC
CC.<__>..........MMMC
..........<__>.MMMCCC
solution length: 12
number of state transitions: 26
ratio solution length / state transitions: 0.461538
minimum branching degree: 1
average branching degree: 2.30769
maximum branching degree: 3
time: 0.02

Cost = 15,
Path = [((3,3),left,0,0),((2,2),right,1,1),((3,2),left,0,1),((3,0),right,0,3),((3,1),left,0,2),((1,1),right,2,2),((2,2),left,1,1),((0,2),right,3,1),((0,3),left,3,0),((0,1),right,3,2),((0,2),left,3,1),((0,0),right,3,3)],
Initial = ((3,3),left,0,0) ? 

yes


% bridge problem, solved using a hill climbing strategy

| ?- performance::init, bridge::initial_state(Initial), hill_climbing(30)::solve(bridge, Initial, Path, Cost), bridge::print_path(Path), performance::report.

 _|____________|_ lamp 1 3 6 8 12 
1 3  lamp _|____________|_ 6 8 12 
3  _|____________|_ lamp 1 6 8 12 
1 3 6  lamp _|____________|_ 8 12 
3 6  _|____________|_ lamp 1 8 12 
3 6 8 12  lamp _|____________|_ 1 
6 8 12  _|____________|_ lamp 1 3 
1 3 6 8 12  lamp _|____________|_ 
solution length: 8
state transitions (including previous solutions): 555
ratio solution length / state transitions: 0.014414414414414415
minimum branching degree: 1
average branching degree: 7.32579185520362
maximum branching degree: 15
time: 0.012381000000000086
Initial = s([], right, [1, 3, 6, 8, 12]),
Path = [s([], right, [1, 3, 6, 8, 12]), s([1, 3], left, [6, 8, 12]), s([3], right, [1, 6, 8, 12]), s([1, 3, 6], left, [8, 12]), s([3, 6], right, [1, 8, 12]), s([3, 6|...], left, [1]), s([6|...], right, [1|...]), s([...|...], left, [])],
Cost = 29

yes


% water jugs problem solved using a breadth and a depth first strategy, with performance monitors
% it's interesting to compare the results

| ?- performance::init, water_jug::initial_state(Initial), breadth_first(6)::solve(water_jug, Initial, Path), water_jug::print_path(Path), performance::report.

4-gallon jug: 0
3-gallon jug: 0

4-gallon jug: 0
3-gallon jug: 3

4-gallon jug: 3
3-gallon jug: 0

4-gallon jug: 3
3-gallon jug: 3

4-gallon jug: 4
3-gallon jug: 2

4-gallon jug: 0
3-gallon jug: 2

solution length: 6
number of state transitions: 109
ratio solution length / state transitions: 0.0550459
minimum branching degree: 2
average branching degree: 3.63158
maximum branching degree: 4
time: 0.02

Path = [(0,0),(0,3),(3,0),(3,3),(4,2),(0,2)],
Initial = (0,0) ? 

yes


| ?- performance::init, water_jug::initial_state(Initial), depth_first(10)::solve(water_jug, Initial, Path), water_jug::print_path(Path), performance::report.

4-gallon jug: 0
3-gallon jug: 0

4-gallon jug: 4
3-gallon jug: 0

4-gallon jug: 4
3-gallon jug: 3

4-gallon jug: 0
3-gallon jug: 3

4-gallon jug: 3
3-gallon jug: 0

4-gallon jug: 3
3-gallon jug: 3

4-gallon jug: 4
3-gallon jug: 2

4-gallon jug: 0
3-gallon jug: 2

solution length: 8
number of state transitions: 12
ratio solution length / state transitions: 0.666667
minimum branching degree: 1
average branching degree: 2
maximum branching degree: 3
time: 0.00

Path = [(0,0),(4,0),(4,3),(0,3),(3,0),(3,3),(4,2),(0,2)],
Initial = (0,0) ? 

yes


% salt puzzle using breadth first search

| ?- performance::init, salt(100, 500, 200)::initial_state(Initial), breadth_first(6)::solve(salt(100, 500, 200), Initial, Path), salt(100, 500, 200)::print_path(Path), performance::report.

(0, 0, 0)	all_empty
(0, 500, 0)	fill(m1)
(0, 300, 200)	transfer(m1, m2)
(0, 300, 0)	empty(m2)
(0, 100, 200)	transfer(m1, m2)
(100, 0, 200)	transfer(m1, acc)
solution length: 6
state transitions (including previous solutions): 405
ratio solution length / state transitions: 0.0148148
minimum branching degree: 1
average branching degree: 4.06863
maximum branching degree: 6
time: 0.03
Initial = (0, 0, 0, all_empty),
Path = [ (0, 0, 0, all_empty), (0, 500, 0, fill(m1)), (0, 300, 200, transfer(m1, m2)), (0, 300, 0, empty(m2)), (0, 100, 200, transfer(m1, m2)), (100, 0, 200, transfer(..., ...))] .

yes


| ?- performance::init, salt(200, 250, 550)::initial_state(Initial), breadth_first(7)::solve(salt(200, 250, 550), Initial, Path), salt(200, 250, 550)::print_path(Path), performance::report.

(0, 0, 0)	all_empty
(0, 250, 0)	fill(m1)
(0, 0, 250)	transfer(m1, m2)
(0, 250, 250)	fill(m1)
(0, 0, 500)	transfer(m1, m2)
(0, 250, 500)	fill(m1)
(0, 200, 550)	transfer(m1, m2)
(200, 0, 550)	transfer(m1, acc)
solution length: 8
state transitions (including previous solutions): 2475
ratio solution length / state transitions: 0.00323232
minimum branching degree: 1
average branching degree: 4.21042
maximum branching degree: 6
time: 0.29
Initial = (0, 0, 0, all_empty),
Path = [ (0, 0, 0, all_empty), (0, 250, 0, fill(m1)), (0, 0, 250, transfer(m1, m2)), (0, 250, 250, fill(m1)), (0, 0, 500, transfer(m1, m2)), (0, 250, 500, fill(...)), (0, 200, ..., ...), (200, ..., ...)] .

yes


| ?- performance::init, salt(100, 250, 550)::initial_state(Initial), breadth_first(11)::solve(salt(100, 250, 550), Initial, Path), salt(100, 250, 550)::print_path(Path), performance::report.

(0, 0, 0)	all_empty
(0, 0, 550)	fill(m2)
(0, 250, 300)	transfer(m2, m1)
(0, 0, 300)	empty(m1)
(0, 250, 50)	transfer(m2, m1)
(50, 250, 0)	transfer(m2, acc)
(50, 0, 0)	empty(m1)
(50, 0, 550)	fill(m2)
(50, 250, 300)	transfer(m2, m1)
(50, 0, 300)	empty(m1)
(50, 250, 50)	transfer(m2, m1)
(100, 250, 0)	transfer(m2, acc)
solution length: 12
state transitions (including previous solutions): 189914
ratio solution length / state transitions: 6.31865e-05
minimum branching degree: 1
average branching degree: 4.47592
maximum branching degree: 6
time: 94.44
Initial = (0, 0, 0, all_empty),
Path = [ (0, 0, 0, all_empty), (0, 0, 550, fill(m2)), (0, 250, 300, transfer(m2, m1)), (0, 0, 300, empty(m1)), (0, 250, 50, transfer(m2, m1)), (50, 250, 0, transfer(..., ...)), (50, 0, ..., ...), (50, ..., ...), (..., ...)|...] .

yes


% eight puzzle solved using a hill-climbing strategy

| ?- performance::init, eight_puzzle::initial_state(five_steps, Initial), hill_climbing(25)::solve(eight_puzzle, Initial, Path, Cost), eight_puzzle::print_path(Path), performance::report.

283
164
7 5

283
1 4
765

2 3
184
765

 23
184
765

123
 84
765

123
8 4
765
solution length: 6
number of state transitions: 15
ratio solution length / state transitions: 0.4
minimum branching degree: 2
average branching degree: 3.13333
maximum branching degree: 4
time: 0.01

Cost = 5,
Path = [[2/1,1/2,1/3,3/3,3/2,3/1,2/2,1/1,2/3],[2/2,1/2,1/3,3/3,3/2,3/1,2/1,1/1,2/3],[2/3,1/2,1/3,3/3,3/2,3/1,2/1,1/1,2/2],[1/3,1/2,2/3,3/3,3/2,3/1,2/1,1/1,2/2],[1/2,1/3,2/3,3/3,3/2,3/1,2/1,1/1,2/2],[2/2,1/3,2/3,3/3,3/2,3/1,2/1,1/1,1/2]],
Initial = [2/1,1/2,1/3,3/3,3/2,3/1,2/2,1/1,2/3] ? 

yes


% eight puzzle solved using a best-first strategy

| ?- performance::init, eight_puzzle::initial_state(five_steps, Initial), best_first(25)::solve(eight_puzzle, Initial, Path, Cost), eight_puzzle::print_path(Path), performance::report.

283
164
7 5

283
1 4
765

2 3
184
765

 23
184
765

123
 84
765

123
8 4
765
solution length: 6
number of state transitions: 15
ratio solution length / state transitions: 0.4
minimum branching degree: 2
average branching degree: 3.13333
maximum branching degree: 4
time: 0.02

Cost = 5,
Path = [[2/1,1/2,1/3,3/3,3/2,3/1,2/2,1/1,2/3],[2/2,1/2,1/3,3/3,3/2,3/1,2/1,1/1,2/3],[2/3,1/2,1/3,3/3,3/2,3/1,2/1,1/1,2/2],[1/3,1/2,2/3,3/3,3/2,3/1,2/1,1/1,2/2],[1/2,1/3,2/3,3/3,3/2,3/1,2/1,1/1,2/2],[2/2,1/3,2/3,3/3,3/2,3/1,2/1,1/1,1/2]],
Initial = [2/1,1/2,1/3,3/3,3/2,3/1,2/2,1/1,2/3] ? 

yes


% turn off performance monitor

| ?- performance::stop.
