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15 puzzle solver: Difference between revisions
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{{output}} <pre>
FOUND SOLUTION of length 52 rrrulddluuuldrurdddrullulurrrddldluurddlulurruldrdrd
</pre>
====Alternate====
<lang Lua>
----------
-- SOLVER
----------
local table_concat = table.concat -- local alias
local function Solver(root, h, successors)
local pathlist, pathhash, iters
-- it is required that "h(node)" returns:
-- 0 when "is_goal(node)==true"
-- >0 when "is_goal(node)==false"
-- (because it allows for some simplification herein)
local FOUND = 0 -- ie: "is_goal(node)==true"
local NOT_FOUND = 1e9 -- some number larger than largest possible f
local function hash(node)
return table_concat(node,",")
end
local function search(g, bound)
iters = iters + 1
--if ((iters % 1000000) == 0) then print("iterations:", iters) end
local node = pathlist[#pathlist]
local h = h(node)
local f = g + h
if (f > bound) then return f end
if (h == FOUND) then return FOUND end
local min = NOT_FOUND
for succ, cost in successors(node) do
local succhash = hash(succ)
if (not pathhash[succhash]) then
pathlist[#pathlist+1], pathhash[succhash] = succ, true
local t = search(g+cost, bound)
if (t == FOUND) then return FOUND end
if (t < min) then min = t end
pathlist[#pathlist], pathhash[succhash] = nil, nil
end
end
return min
end
return {
solve = function()
pathlist = { root }
pathhash = { [hash(root)] = true }
iters = 0
local bound = h(root)
while true do
bound = search(0, bound)
if (bound == FOUND) then return bound, iters, pathlist end
if (bound == NOT_FOUND) then return bound, iters, nil end
end
end
}
end
------------------
-- DOMAIN SUPPORT
------------------
local i2c = { [0]=0, 1,2,3,4, 1,2,3,4, 1,2,3,4, 1,2,3,4 } -- convert index to column
local i2r = { [0]=0, 1,1,1,1, 2,2,2,2, 3,3,3,3, 4,4,4,4 } -- convert index to row
local R, U, L, D = 1, -4, -1, 4 -- move indexing values
local movenames = { -- move names
[0]="", [R]="r", [U]="u", [L]="l", [D]="d"
}
local succmoves = { -- successor directions
{R,D}, {R,L,D}, {R,L,D}, {L,D},
{R,U,D}, {R,U,L,D}, {R,U,L,D}, {U,L,D},
{R,U,D}, {R,U,L,D}, {R,U,L,D}, {U,L,D},
{R,U}, {R,U,L}, {R,U,L}, {U,L}
}
local manhdists = { -- manhattan distances
{ [0]=0, 0, 1, 2, 3, 1, 2, 3, 4, 2, 3, 4, 5, 3, 4, 5, 6 },
{ [0]=0, 1, 0, 1, 2, 2, 1, 2, 3, 3, 2, 3, 4, 4, 3, 4, 5 },
{ [0]=0, 2, 1, 0, 1, 3, 2, 1, 2, 4, 3, 2, 3, 5, 4, 3, 4 },
{ [0]=0, 3, 2, 1, 0, 4, 3, 2, 1, 5, 4, 3, 2, 6, 5, 4, 3 },
{ [0]=0, 1, 2, 3, 4, 0, 1, 2, 3, 1, 2, 3, 4, 2, 3, 4, 5 },
{ [0]=0, 2, 1, 2, 3, 1, 0, 1, 2, 2, 1, 2, 3, 3, 2, 3, 4 },
{ [0]=0, 3, 2, 1, 2, 2, 1, 0, 1, 3, 2, 1, 2, 4, 3, 2, 3 },
{ [0]=0, 4, 3, 2, 1, 3, 2, 1, 0, 4, 3, 2, 1, 5, 4, 3, 2 },
{ [0]=0, 2, 3, 4, 5, 1, 2, 3, 4, 0, 1, 2, 3, 1, 2, 3, 4 },
{ [0]=0, 3, 2, 3, 4, 2, 1, 2, 3, 1, 0, 1, 2, 2, 1, 2, 3 },
{ [0]=0, 4, 3, 2, 3, 3, 2, 1, 2, 2, 1, 0, 1, 3, 2, 1, 2 },
{ [0]=0, 5, 4, 3, 2, 4, 3, 2, 1, 3, 2, 1, 0, 4, 3, 2, 1 },
{ [0]=0, 3, 4, 5, 6, 2, 3, 4, 5, 1, 2, 3, 4, 0, 1, 2, 3 },
{ [0]=0, 4, 3, 4, 5, 3, 2, 3, 4, 2, 1, 2, 3, 1, 0, 1, 2 },
{ [0]=0, 5, 4, 3, 4, 4, 3, 2, 3, 3, 2, 1, 2, 2, 1, 0, 1 },
{ [0]=0, 6, 5, 4, 3, 5, 4, 3, 2, 4, 3, 2, 1, 3, 2, 1, 0 },
}
--- create a state from a pattern, optionally applying a move
local function state(patt, move)
local node = {}
for k,v in pairs(patt) do node[k] = v end
if (move) then
local e = node.e
local ep = e + move
node[e], node[ep] = node[ep], 0
node.e, node.m = ep, move
end
return node
end
--- iterator for successors of node
local function successors(node)
local moves = succmoves[node.e]
local i, n = 0, #moves
return function()
i = i + 1
if (i <= n) then
return state(node, moves[i]), 1
end
end
end
--- hueristic estimate of travel cost from node to goal
local function h(node)
local sum, ijx, jix, t = 0, 1, 1
for i = 1, 4 do
local colmax, rowmax = 0, 0
for j = 1, 4 do
t = node[ijx]
sum = sum + manhdists[ijx][t] -- manhattan
if (i2r[t] == i) then -- row conflicts
if (t > rowmax) then rowmax=t else sum=sum+2 end
end
t = node[jix]
if (i2c[t] == i) then -- col conflicts
if (t > colmax) then colmax=t else sum=sum+2 end
end
ijx, jix = ijx+1, jix+4
end
jix = jix - 15
end
return sum
end
------------------
-- PRINT SUPPORT:
------------------
local function printnode(node)
print("+--+--+--+--+")
for i = 0, 12, 4 do
print( string.format("|%2d|%2d|%2d|%2d|", node[i+1], node[i+2], node[i+3], node[i+4]) )
print("+--+--+--+--+")
end
end
local function printpath(path)
-- note that #path is 1 longer than solution due to root node at path[1]
-- concatenated result will be correct length since movenames[root.m]==""
local t = {}
for i, node in ipairs(path) do
t[i] = movenames[node.m]
end
local pathstr = table_concat(t)
print("SOLUTION: " .. pathstr .. " (length: " .. #pathstr .. ")")
end
---------
-- TASKS:
---------
-- goal is implied by h(), never actually used (see solver's notes)
-- local goal = state({ 1,2,3,4, 5,6,7,8, 9,10,11,12, 13,14,15,0, e=16, m=0 })
do
print("PRIMARY TASK (OPTIMALLY)")
local sclock = os.clock()
local root = state({ 15,14,1,6, 9,11,4,12, 0,10,7,3, 13,8,5,2, e=9, m=0 })
printnode(root)
local solver = Solver(root, h, successors)
local bound, iters, path = solver:solve()
printpath(path)
printnode(path[#path])
print("ITERATIONS: " .. iters)
print("ELAPSED: " .. (os.clock()-sclock) .. "s")
end
print()
do
print("EXTRA CREDIT TASK (APPROXIMATELY, NON-OPTIMALLY)")
-- only primary task specifies "fewest possible moves"
-- extra credit task only specifies "solve", so..
local sclock = os.clock()
local root = state({ 0,12,9,13, 15,11,10,14, 3,7,2,5, 4,8,6,1, e=1, m=0 })
printnode(root)
local function hec(node)
-- overweighting h makes it not admissible,
-- causing solver to favor g when minimizing,
-- leading to non-optimal (but much easier to find!) solutions
return h(node)*1.5
end
local solver = Solver(root, hec, successors)
local bound, iters, path = solver:solve()
printpath(path) --> 86, optimal solution is known to be 80
printnode(path[#path])
print("ITERATIONS: " .. iters)
print("ELAPSED: " .. (os.clock()-sclock) .. "s")
end
</lang>
{{out}}
<pre>
PRIMARY TASK (OPTIMALLY)
+--+--+--+--+
|15|14| 1| 6|
+--+--+--+--+
| 9|11| 4|12|
+--+--+--+--+
| 0|10| 7| 3|
+--+--+--+--+
|13| 8| 5| 2|
+--+--+--+--+
SOLUTION: rrruldluuldrurdddluulurrrdlddruldluurddlulurruldrrdd (length: 52)
+--+--+--+--+
| 1| 2| 3| 4|
+--+--+--+--+
| 5| 6| 7| 8|
+--+--+--+--+
| 9|10|11|12|
+--+--+--+--+
|13|14|15| 0|
+--+--+--+--+
ITERATIONS: 4963696
ELAPSED: 34.279s
EXTRA CREDIT TASK (APPROXIMATELY, NON-OPTIMALLY)
+--+--+--+--+
| 0|12| 9|13|
+--+--+--+--+
|15|11|10|14|
+--+--+--+--+
| 3| 7| 2| 5|
+--+--+--+--+
| 4| 8| 6| 1|
+--+--+--+--+
SOLUTION: rrdldruldluruldrdrrululdrddlluurrddlluurrdrdllurrdlluruurddluurddluulddrdluluruldddrrr (length: 86)
+--+--+--+--+
| 1| 2| 3| 4|
+--+--+--+--+
| 5| 6| 7| 8|
+--+--+--+--+
| 9|10|11|12|
+--+--+--+--+
|13|14|15| 0|
+--+--+--+--+
ITERATIONS: 1325248
ELAPSED: 9.101s
</pre>
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