15 puzzle solver
Your task is to write a program that solves the Fifteen Puzzle Game in the fewest number of moves.
For this task you will be using the following puzzle:
15 14 1 6 9 11 4 12 0 10 7 3 13 8 5 2
Solution:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0
The output must show the moves' directions, like so: left, left, left, down, right... and so on.
Phix
Brute force width-first search, probably not quite optimal, since the scoring algorithm may trim some better paths from the search space.
Shows first solution found. No multi-tile moves.
<lang Phix>constant udlr = {"up", "down", "left", "right"}
sequence board = tagset(15)&0
integer pos = 16
procedure print_board()
for i=1 to length(board) do
puts(1,iff(i=pos?" ":sprintf("%3d",{board[i]})))
if mod(i,4)=0 then puts(1,"\n") end if
end for
puts(1,"\n")
end procedure
function move(integer d) integer valid = 0 integer stick = 0
for k=1 to 8 by 2 do
if board[k]!=k then exit end if
if board[k+1]!=k+1 then exit end if
stick = k+1
end for
integer new_pos = pos+{+4,-4,+1,-1}[d]
if new_pos>=1 and new_pos<=16
and (mod(pos,4)=mod(new_pos,4) -- same col, or row:
or floor((pos-1)/4)=floor((new_pos-1)/4)) then
{board[pos],board[new_pos]} = {board[new_pos],0}
valid = pos>stick and new_pos>stick
pos = new_pos
end if
return {valid,stick}
end function
constant posns = {1,2,3,4,5,6,7,8,9,13,10,14,11,12,15}
function score(sequence board) integer res = 0, pos, act_pos
for i=1 to 15 do
pos = posns[i]
act_pos = find(pos,board)
res += (abs(mod(pos,4)-mod(act_pos,4))+
abs(floor((pos-1)/4)-floor((act_pos-1)/4)))*10*pos
end for
return res
end function
if 0 then
for i=1 to 5555555 do {}=move(rand(4)) end for -- (25% are likely invalid)
else
board = {15,14, 1, 6,
9,11, 4,12,
0,10, 7, 3,
13, 8, 5, 2}
pos = find(0,board)
end if atom t0 = time() integer pos0 = pos, s, valid, stick sequence board0 = board, boards = {{0,score(board),{},board,pos}}, new_boards, moves integer visited = new_dict() while 1 do
new_boards = {}
for i=1 to length(boards) do
for c=1 to 4 do
{?,?,moves,board,pos} = boards[i]
{valid,stick} = move(c)
if valid and getd_index(board,visited)=0 then
moves &= c
s = score(board)
if s=0 then exit end if
new_boards = append(new_boards,{8-stick,s,moves,board,pos})
setd(board,0,visited)
end if
end for
if s=0 then exit end if
end for
if s=0 then exit end if
if length(new_boards)>16384 then
boards = sort(new_boards)[1..16384]
integer dsv = dict_size(visited)
{?,s,{},board,pos} = boards[1]
printf(1,"thinking... %d boards visited, best score: %d (0=solved):\n",{dsv,s})
print_board()
else
boards = new_boards
end if
end while
pos = pos0 board = board0 printf(1,"\n\nsolved!!:\n=========\n") print_board() for i=1 to length(moves) do
integer mi = moves[i]
string m = udlr[mi]
printf(1,"move %d, %s:\n",{i,m})
moves[i] = upper(m[1])
{} = move(mi)
print_board()
end for printf(1,"solved in %d moves (%d boards visited, %s)\n",{length(moves),dict_size(visited),elapsed(time()-t0)}) printf(1,"moves: %s\n",{moves}) {} = wait_key()</lang>
- Output:
thinking... 39204 boards visited, best score: 1910 (0=solved):
15 1 6
8 14 11 4
9 10 3 12
13 5 7 2
thinking... 71666 boards visited, best score: 1760 (0=solved):
15 1 6
8 14 11 4
9 10 3 12
13 5 7 2
thinking... 103082 boards visited, best score: 1840 (0=solved):
15 1 6
8 14 11 4
9 10 3 12
13 5 7 2
<snip>
1 2 3 4
9 7 5 6
10 15 8
13 14 12 11
move 44, down:
1 2 3 4
9 5 6
10 7 15 8
13 14 12 11
move 45, left:
1 2 3 4
9 5 6
10 7 15 8
13 14 12 11
move 46, left:
1 2 3 4
9 5 6
10 7 15 8
13 14 12 11
move 47, up:
1 2 3 4
9 5 6 8
10 7 15
13 14 12 11
move 48, up:
1 2 3 4
9 5 6 8
10 7 15 11
13 14 12
move 49, right:
1 2 3 4
9 5 6 8
10 7 15 11
13 14 12
move 50, down:
1 2 3 4
9 5 6 8
10 7 11
13 14 15 12
move 51, right:
1 2 3 4
9 5 6 8
10 7 11
13 14 15 12
move 52, right:
1 2 3 4
9 5 6 8
10 7 11
13 14 15 12
move 53, down:
1 2 3 4
5 6 8
9 10 7 11
13 14 15 12
move 54, left:
1 2 3 4
5 6 8
9 10 7 11
13 14 15 12
move 55, left:
1 2 3 4
5 6 8
9 10 7 11
13 14 15 12
move 56, up:
1 2 3 4
5 6 7 8
9 10 11
13 14 15 12
move 57, left:
1 2 3 4
5 6 7 8
9 10 11
13 14 15 12
move 58, up:
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15
solved in 58 moves (1330046 boards visited, 49.11s)
moves: LDDLUULURRDDLULURRDLLDDRURURDDLURULDLULURDRDLLUURDRRDLLULU