def two_way_trans(forward_state, backward_state, depth):
if depth > 15:
return None, None
if depth % 2 == 0:
for iterator in forward_state.keys():
if backward_state.get(iterator) != None:
return forward_state[iterator], backward_state[iterator]
for action in actions:
new_state = rubik.perm_apply(action, iterator)
if forward_state.get(new_state) is None:
forward_state[new_state] = forward_state[iterator] + [
action
]
return two_way_trans(forward_state, backward_state, depth + 1)
else:
for iterator in backward_state.keys():
if forward_state.get(iterator) != None:
return forward_state[iterator], backward_state[iterator]
for action in actions:
new_state = rubik.perm_apply(action, iterator)
if backward_state.get(new_state) is None:
backward_state[new_state] = backward_state[iterator] + [
action
]
return two_way_trans(forward_state, backward_state, depth + 1)
def shortest_path_optmized(start, end):
"""
For Question 2, using 2-way BFS, finds the shortest path from start_position to
end_position. Returns a list of moves.
You can use the rubik.quarter_twists move set.
Each move can be applied using rubik.perm_apply
"""
movesStart = dict()
movesStart[start] = []
movesEnd = dict()
movesEnd[end] = []
qStart = collections.deque()
qEnd = collections.deque()
qStart.append(start)
qEnd.append(end)
found = False
finalMoves = []
while (len(qStart) != 0 and len(qEnd) != 0 and not found):
s = qStart.popleft()
e = qEnd.popleft()
m = movesStart[s]
n = movesEnd[e]
if len(m) > 8 and len(n) > 8:
break
if s == end:
finalMoves = m
found = True
break
if s in movesEnd:
finalMoves = m + movesEnd[s][::-1]
found = True
break
if e in movesStart:
finalMoves = movesStart[e] + n[::-1]
found = True
break
for i in range(6):
x = rubik.perm_apply(rubik.quarter_twists[i], s)
y = rubik.perm_apply(rubik.quarter_twists[i], e)
if x not in movesStart:
qStart.append(x)
movesStart[x] = m + [
rubik.quarter_twists_names[rubik.quarter_twists[i]]
]
if y not in movesEnd:
qEnd.append(y)
movesEnd[y] = n + [
rubik.quarter_twists_names[rubik.perm_inverse(
rubik.quarter_twists[i])]
]
if found:
sys.stdout.write(str(finalMoves) + "\n")
return finalMoves
else:
sys.stdout.write(str("No solution\n"))
return [None]
def test_shortest_path_2(self):
""" Length 2 path."""
start = rubik.I
middle = rubik.perm_apply(rubik.F, start)
end = rubik.perm_apply(rubik.L, middle)
ans = solver.shortest_path(start, end)
self.assertEqual(len(ans), 2)
self.assertEqual(ans, [rubik.F, rubik.L])
def adj(u, dir):
adj_u = []
for move in rubik.quarter_twists:
if(dir):
adj_u.append(rubik.perm_apply(move, u))
else:
adj_u.append(rubik.perm_apply(rubik.perm_inverse(move), u))
return adj_u
def testShortestPath2(self):
"""Length 2 path."""
start = rubik.I
middle = rubik.perm_apply(rubik.F, start)
end = rubik.perm_apply(rubik.L, middle)
ans = solver.shortest_path(start, end)
self.assertEqual(len(ans), 2)
self.assertEqual(ans, [rubik.F, rubik.L])
def shortest_path(start, end):
"""
Using 2-way BFS, finds the shortest path from start_position to
end_position. Returns a list of moves.
Assumes the rubik.quarter_twists move set.
"""
moves = rubik.quarter_twists
# These dictionaries will have positions as keys, and
# (parent_position, move_used_to_reach_position) as values.
start_parent = {} # For BFS starting at start
end_parent = {} # For BFS starting at end
start_current_level_positions = set()
end_current_level_positions = set()
start_parent[start] = None
start_current_level_positions.add(start)
end_parent[end] = None
end_current_level_positions.add(end)
if end in start_parent: # Check if we're done.
return calculate_path(start_parent, end_parent, end)
for i in range(7):
# Because we know the diameter is 14, we don't need more than
# 7 iterations from each side.
# Expand from start.
start_next_level_positions = set()
for position in start_current_level_positions:
for move in moves:
next_position = rubik.perm_apply(move, position)
if next_position not in start_parent:
start_parent[next_position] = (position, move)
start_next_level_positions.add(next_position)
if next_position in end_parent: # Check if we're done.
return calculate_path(start_parent,
end_parent,
next_position)
start_current_level_positions = start_next_level_positions
# Expand from end.
end_next_level_positions = set()
for position in end_current_level_positions:
for move in moves:
next_position = rubik.perm_apply(move, position)
if next_position not in end_parent:
end_parent[next_position] = (position, move)
end_next_level_positions.add(next_position)
if next_position in start_parent: # Check if we're done.
return calculate_path(start_parent,
end_parent,
next_position)
end_current_level_positions = end_next_level_positions
return None # There is no path from start to end
def find_move(u, v, dir):
for move in rubik.quarter_twists:
if(dir):
if v == rubik.perm_apply(move, u):
return move
else:
if v == rubik.perm_apply(rubik.perm_inverse(move), u):
return move
return -1
def shortest_path(start, end):
"""
Using 2-way BFS, finds the shortest path from start_position to
end_position. Returns a list of moves.
You can use the rubik.quarter_twists move set.
Each move can be applied using rubik.perm_apply
"""
left_checked = {}
right_checked = {}
left_current = {start: []}
right_current = {end: []}
left_new = {}
right_new = {}
left_depth = 0
right_depth = 0
while left_depth < 8:
for x in left_current.keys():
y = right_current.get(x, None)
if y is not None:
ans = left_current[x] + [
rubik.perm_inverse(move) for move in reversed(y)
]
return ans
for x in left_current.keys():
for move in rubik.quarter_twists:
r = rubik.perm_apply(move, x)
if not left_checked.get(r, None) and not left_current.get(
r, None):
left_new[r] = left_current[x] + [move]
left_checked[x] = left_current[x]
left_current = left_new
left_new = {}
left_depth += 1
while right_depth < 8:
for x in right_current.keys():
y = left_current.get(x, None)
if y is not None:
ans = y + [
rubik.perm_inverse(move)
for move in reversed(right_current[x])
]
return ans
for x in right_current.keys():
for move in rubik.quarter_twists:
r = rubik.perm_apply(move, x)
if not right_checked.get(r, None) and not right_current.get(
r, None):
right_new[r] = right_current[x] + [move]
right_checked[x] = right_current[x]
right_current = right_new
right_new = {}
right_depth += 1
return None
def test_shortest_path_3(self):
""" Length 3 path."""
start = rubik.I
middle1 = rubik.perm_apply(rubik.F, start)
middle2 = rubik.perm_apply(rubik.F, middle1)
end = rubik.perm_apply(rubik.Li, middle2)
ans = solver.shortest_path(start, end)
self.assertEqual(len(ans), 3)
self.assert_good_path(start, end, ans)
def shortest_path_optmized(start, end):
"""
For Question 2, using 2-way BFS, finds the shortest path from start_position to
end_position. Returns a list of moves.
You can use the rubik.quarter_twists move set.
Each move can be applied using rubik.perm_apply
"""
q_front = Queue.Queue()
q_front.put([start, []])
visited_front = {start: []}
q_back = Queue.Queue()
q_back.put([end, []])
visited_back = {end: []}
if start == end:
print([])
return []
while not q_back.empty() or not q_front.empty():
if not q_front.empty():
cur_front = q_front.get()
for twist in rubik.quarter_twists:
x = (rubik.perm_apply(twist, cur_front[0]),
cur_front[1] + [rubik.quarter_twists_names[twist]])
if x[0] in visited_back:
print(x[1] + visited_back[x[0]][::-1])
return x[1] + visited_back[x[0]][::-1]
if x[0] not in visited_front:
visited_front[x[0]] = x[1][:]
if len(x[1]) <= 7:
q_front.put(x)
if not q_back.empty():
cur_back = q_back.get()
for twist in rubik.quarter_twists:
x = (rubik.perm_apply(twist, cur_back[0]), cur_back[1] +
[reversal_name(rubik.quarter_twists_names[twist])])
if x[0] in visited_front:
print(visited_front[x[0]] + x[1][::-1])
return visited_front[x[0]] + x[1][::-1]
if x[0] not in visited_back:
visited_back[x[0]] = x[1][:]
if len(x[1]) <= 7:
q_back.put(x)
print("None")
def testShortestPath3(self):
"""Length 3 path."""
start = rubik.I
middle1 = rubik.perm_apply(rubik.F, start)
middle2 = rubik.perm_apply(rubik.F, middle1)
end = rubik.perm_apply(rubik.Li, middle2)
ans = solver.shortest_path(start, end)
self.assertEqual(len(ans), 3)
self.assertGoodPath(start, end, ans)
def shortest_path(start, end):
"""
Using 2-way BFS, finds the shortest path from start_position to
end_position. Returns a list of moves.
Assumes the rubik.quarter_twists move set.
"""
moves = rubik.quarter_twists
# These dictionaries will have positions as keys, and
# (parent_position, move_used_to_reach_position) as values.
start_parent = {} # For BFS starting at start
end_parent = {} # For BFS starting at end
start_current_level_positions = set()
end_current_level_positions = set()
start_parent[start] = None
start_current_level_positions.add(start)
end_parent[end] = None
end_current_level_positions.add(end)
if end in start_parent: # Check if we're done.
return calculate_path(start_parent, end_parent, end)
for i in range(7):
# Because we know the diameter is 14, we don't need more than
# 7 iterations from each side.
# Expand from start.
start_next_level_positions = set()
for position in start_current_level_positions:
for move in moves:
next_position = rubik.perm_apply(move, position)
if next_position not in start_parent:
start_parent[next_position] = (position, move)
start_next_level_positions.add(next_position)
if next_position in end_parent: # Check if we're done.
return calculate_path(start_parent, end_parent,
next_position)
start_current_level_positions = start_next_level_positions
# Expand from end.
end_next_level_positions = set()
for position in end_current_level_positions:
for move in moves:
next_position = rubik.perm_apply(move, position)
if next_position not in end_parent:
end_parent[next_position] = (position, move)
end_next_level_positions.add(next_position)
if next_position in start_parent: # Check if we're done.
return calculate_path(start_parent, end_parent,
next_position)
end_current_level_positions = end_next_level_positions
return None # There is no path from start to end
def testShortestPath4(self):
"""Length 4 path."""
start = rubik.I
middle1 = rubik.perm_apply(rubik.F, start)
middle2 = rubik.perm_apply(rubik.L, middle1)
middle3 = rubik.perm_apply(rubik.F, middle2)
end = rubik.perm_apply(rubik.L, middle3)
ans = solver.shortest_path(start, end)
self.assertEqual(len(ans), 4)
self.assertGoodPath(start, end, ans)
def testShortestPath3(self):
"""Length 3 path."""
start = rubik.I
middle1 = rubik.perm_apply(rubik.F, start)
middle2 = rubik.perm_apply(rubik.F, middle1)
end = rubik.perm_apply(rubik.Li, middle2)
ans = solver.shortest_path(start, end)
self.assertEqual(len(ans), 3)
self.assertGoodPath(start, end, ans)
print("Test 4 Pass")
def shortest_path(start, end):
"""
Using 2-way BFS, finds the shortest path from start_position to
end_position. Returns a list of moves.
You can use the rubik.quarter_twists move set.
Each move can be applied using rubik.perm_apply
"""
moves = rubik.quarter_twists
parentS = {}
parentE = {}
parentS[start] = None
parentE[end] = None
start_current_positions = set()
end_current_positions = set()
start_current_positions.add(start)
end_current_positions.add(end)
if end in parentS:
return get_moves(parentS, parentE, end)
for i in range(7):
start_next_positions = set()
for position in start_current_positions:
for move in moves:
next_position = rubik.perm_apply(move, position)
if next_position not in parentS:
parentS[next_position] = (position, move)
start_next_positions.add(next_position)
if next_position in parentE:
return get_moves(parentS,
parentE,
next_position)
start_current_positions = start_next_positions
end_next_positions = set()
for position in end_current_positions:
for move in moves:
next_position = rubik.perm_apply(move, position)
if next_position not in parentE:
parentE[next_position] = (position, move)
end_next_positions.add(next_position)
if next_position in parentS:
return get_moves(parentS,
parentE,
next_position)
end_current_positions = end_next_positions
return None
def test(x):
l = [rubik.L, rubik.F, rubik.Fi, rubik.Li, rubik.Ui]
t = {
"L": rubik.L,
"F": rubik.F,
"Fi": rubik.Fi,
"Li": rubik.Li,
"Ui": rubik.Ui,
"U": rubik.U
}
start = (6, 7, 8, 0, 1, 2, 9, 10, 11, 3, 4, 5, 12, 13, 14, 15, 16, 17, 18,
19, 20, 21, 22, 23)
end = (6, 7, 8, 0, 1, 2, 9, 10, 11, 3, 4, 5, 12, 13, 14, 15, 16, 17, 18,
19, 20, 21, 22, 23)
for i in range(x):
end = rubik.perm_apply(l[random.randrange(0, len(l))], end)
print("\nRunning Test Case")
print("start = " + str(start))
print("end = " + str(end))
start_time = time.time()
ans1 = shortest_path_optmized(start, end)
end_time = time.time()
current = start
for move in ans1:
current = rubik.perm_apply(t[move], current)
if (current != end):
print(start, end, "Optimised failed")
exit()
else:
print("Optimised ok | Time Taken:" +
str(round(end_time - start_time, 2)))
#bruteforce will take large time otherwise
# if(len(ans1)>6):
# return
start_time = time.time()
ans2 = shortest_path(start, end)
end_time = time.time()
current = start
for move in ans2:
current = rubik.perm_apply(t[move], current)
if (current != end):
print(start, end, "Bruteforce failed")
exit()
else:
print("Bruteforce ok | Time Taken: " +
str(round(end_time - start_time, 2)))
def shortest_path(start, end):
"""
For Question 1, using BFS, finds the shortest path from start_position to
end_position. Returns a list of moves.
You can use the rubik.quarter_twists move set.
Each move can be applied using rubik.perm_apply
"""
visited_nodes = {}
# initialize
visited_nodes[start] = 0
move_recovery = {}
move_recovery[start] = {None, None}
queue = __import__('collections').deque()
queue.append(start)
u = None
while (len(queue)>0):
u = queue.popleft()
if (u == end):
break
if (visited_nodes[u] > 14):
# no solution
return None
# all neighbours of u
for moves in rubik.quarter_twists:
v = rubik.perm_apply(moves, u)
if not(v in visited_nodes):
visited_nodes[v] = visited_nodes[u] + 1
move_recovery[v] = (u, moves)
queue.append(v)
if u != end:
return None
ans = []
#retrace the moves
ptr = end
while (ptr != start):
ans.append(move_recovery[ptr][1])
ptr = move_recovery[ptr][0]
ans = ans[::-1]
cube = start[:]
for move in ans:
cube = rubik.perm_apply(move, cube)
assert cube == end
return [rubik.quarter_twists_names[x] for x in ans]
def shortest_path_optmized(start, end):
q1 = deque()
q2 = deque()
visited1 = {}
visited2 = {}
path1 = {}
path2 = {}
visited1[start] = 1
visited2[end] = 1
path1[start] = []
path2[end] = []
q1.append(start)
q2.append(end)
while (q1 and q2):
curr1 = q1[0]
curr2 = q2[0]
q1.popleft()
q2.popleft()
for i in rubik.quarter_twists:
p1 = rubik.perm_apply(curr1, i)
if (visited1.has_key(p1) == False):
visited1[p1] = 1
path1[p1] = path1[curr1] + [rubik.quarter_twists_names[i]]
#print(rubik.quarter_twists_names[i])
q1.append(p1)
if (visited2.has_key(p1) == True):
return path1[p1] + path2[p1]
for i in rubik.quarter_twists:
p2 = rubik.perm_apply(curr2, i)
if (visited2.has_key(p2) == False):
visited2[p2] = 1
path2[p2] = [
rubik.quarter_twists_names[rubik.perm_inverse(i)]
] + path2[curr2]
#print(rubik.quarter_twists_names[i])
q2.append(p2)
if (visited1.has_key(p2) == True):
return path1[p2] + path2[p2]
return []
"""
For Question 2, using 2-way BFS, finds the shortest path from start_position to
end_position. Returns a list of moves.
You can use the rubik.quarter_twists move set.
Each move can be applied using rubik.perm_apply
"""
raise NotImplementedError
def returnmid(): level=1 while(1): if level>7: return None a=q.dequeue() while(a!=None): for i in range(6): b=r.perm_apply(r.quarter_twists[i],a.tuple) k=0 if hash1.search(b): k=1 if k==0: s=state(b) s.parent=a q.enqueue(s) hash1.insert(s) for i in range(len(hash2.l[hashf(b)])): if b==hash2.l[hashf(b)][i].tuple: hash2.l[hashf(b)][i].parent=a return hash2.l[hashf(b)][i] a=q.dequeue() q.enqueue(None) c=p.dequeue() while(c!=None): for i in range(6): d=r.perm_apply(r.quarter_twists[i],c.tuple) k=0 if hash2.search(d): k=1 if k==0: s=state(d) s.child=c p.enqueue(s) hash2.insert(s) for i in range(len(hash1.l[hashf(d)])): if d==hash1.l[hashf(d)][i].tuple: hash1.l[hashf(d)][i].child=c return hash1.l[hashf(d)][i] c=p.dequeue() p.enqueue(None) level+=1
def shortest_path(start, end):
"""
Using 2-way BFS, finds the shortest path from start_position to
end_position. Returns a list of moves.
You can use the rubik.quarter_twists move set.
Each move can be applied using rubik.perm_apply
"""
level = {start:0}
backLevel = {end:0}
parent = {start:None}
backParent = {end:None}
i = 1
frontier = [start]
solution = []
backFrontier = [end]
connected = False
connections = []
while (not connected) and (i <= 7): # explore graph
next = []
for u in frontier: # move forwards
for move in rubik.quarter_twists:
v = rubik.perm_apply(move,u)
if v not in level:
level[v] = i
parent[v] = (u,move)
next.append(v)
frontier = next
backNext = []
for u in backFrontier: # move backwards
for move in rubik.quarter_twists:
v = rubik.perm_apply(move,u)
if v not in backLevel:
backLevel[v] = i
backParent[v] = (u,rubik.perm_inverse(move))
backNext.append(v)
backFrontier = backNext
for config in level.keys(): # check for a solution
if config in backLevel:
connected = True
connections.append(config)
i += 1
if not connected: # we have explored all options and found no solution
return None
minConn = findShortestPath(connections,level,backLevel)
buildSolution(level,parent,minConn,solution,'forwards')
buildSolution(backLevel,backParent,minConn,solution,'backwards')
return solution
def shortest_path(start, end):
"""
For Question 1, using BFS, finds the shortest path from start_position to
end_position. Returns a list of moves.
You can use the rubik.quarter_twists move set.
Each move can be applied using rubik.perm_apply
"""
q = deque()
visited = {}
path = {}
visited[start] = 1
path[start] = []
q.append(start)
while(q):
curr = q[0]
q.popleft()
for i in rubik.quarter_twists:
p = rubik.perm_apply(curr,i)
if(visited.has_key(p)==False):
visited[p]=1
path[p] = path[curr]+[rubik.quarter_twists_names[i]]
#print(rubik.quarter_twists_names[i])
q.append(p)
if(p==end):
return path[p]
return []
def next_frontier(frontier, p_nodes):
starting_order = frontier[0].order
"""
Invariant: At each iteration, we are looking at the nodes in the frontier of the same order as starting_order
Initialization: The order of the frontier node is the same as starting_order
Maintenance: Given that the starting_order and frontier node order is the same, the loop will continue
Termination: The order of the frontier no longer equals the order we want to look at
"""
while starting_order == frontier[0].order:
elm = frontier.popleft()
"""
Invariant: At each iteration, the position of move in quarter_twists is less than the len(quarter_twists)
Initialization: There are moves in quarter_twists
Maintenance: Given that there are still moves in quarter_twists to go through, the loop will continue
and apply the permutation to the node and add the permutation to the frontier if it
doesn't already exist
Termination: We have gone through the entire tuple of twists
"""
# Changes the rubik state
for move in rubik.quarter_twists:
move_st = rubik.perm_apply(move, elm.st)
# Checks to see if the new move_st is not in the nodes list
if move_st not in p_nodes:
# new node_info with the new move_st, the move command it took
# frontier that was popped, and the new depth of node
new_st = node_info(move_st, (move, elm), elm.order + 1)
frontier.append(new_st)
p_nodes.append(move_st)
def process(u, parent, next_):
for move in rubik.quarter_twists:
v = rubik.perm_apply(move, u)
if v not in parent:
## parent[v]=(rubik.perm_inverse(move),move,u) #u
parent[v] = (move, u) #u
next_.append(v)
def testShortestPath1(self):
"""Length 1 path."""
start = rubik.I
end = rubik.perm_apply(rubik.F, start)
ans = solver.shortest_path(start, end)
self.assertEqual(len(ans), 1)
self.assertEqual(ans, [rubik.F])
def test_shortest_path_1(self):
""" Length 1 path."""
start = rubik.I
end = rubik.perm_apply(rubik.F, start)
ans = solver.shortest_path(start, end)
self.assertEqual(len(ans), 1)
self.assertEqual(ans, [rubik.F])
def shortest_path(start, end):
"""
For Question 1, using BFS, finds the shortest path from start_position to
end_position. Returns a list of moves.
You can use the rubik.quarter_twists move set.
Each move can be applied using rubik.perm_apply
"""
L = Queue.Queue()
L.put([start, []])
visited = {start}
mov = None
while not L.empty():
cur = L.get()
if cur[0] == end:
mov = cur[1]
break
for twist in rubik.quarter_twists:
x = (rubik.perm_apply(twist, cur[0]),
cur[1] + [rubik.quarter_twists_names[twist]])
if x[0] not in visited:
visited.add(x[0])
L.put(x)
print(mov)
return mov
def rubik_list_states(start):
""" Gives all the states of the rubiks during solution rather than what twists to make."""
path_twists = bidirectional_bfs_search(start)
rubik_configs = [start]
for twist in path_twists:
rubik_configs.append(perm_apply(twist, rubik_configs[-1]))
return rubik_configs
def shortest_path(start, end):
if start == end: return []
fparents = {start: None}
bparents = {end: None}
fmoves = {}
bmoves = {}
for move in rubik.quarter_twists:
fmoves[move] = move
bmoves[rubik.perm_inverse(move)] = move
forward = (fmoves, fparents, bparents)
backward = (bmoves, bparents, fparents)
queue = deque([(start, forward), (end, backward), None])
for i in xrange(7):
while True:
vertex = queue.popleft()
if vertex is None:
queue.append(None)
break
position = vertex[0]
moves, parents, other_parents = vertex[1]
for move in moves:
nextp = rubik.perm_apply(move, position)
if nextp not in parents:
parents[nextp] = (moves[move], position)
queue.append((nextp, vertex[1]))
if nextp in other_parents:
forwardp = path(nextp, fparents)
backwardp = path(nextp, bparents)
forwardp.reverse()
return forwardp + backwardp
return None
def shortest_path(start, end):
"""
For Question 1, using BFS, finds the shortest path from start_position to
end_position. Returns a list of moves.
You can use the rubik.quarter_twists move set.
Each move can be applied using rubik.perm_apply
"""
moves = dict()
moves[start] = []
finalm = []
q = collections.deque([start])
found = False
while (len(q) != 0 and not found):
s = q.popleft()
m = moves[s]
if s == end:
found = True
finalm = m
break
for i in range(6):
x = rubik.perm_apply(rubik.quarter_twists[i], s)
if x not in moves:
q.append(x)
moves[x] = m + [
rubik.quarter_twists_names[rubik.quarter_twists[i]]
]
if found:
sys.stdout.write(str(finalm) + "\n")
return finalm
else:
sys.stdout.write(str("No solution\n"))
return [None]
def BFS(frontier, dic, lis):
for pos in frontier:
for turn in rubik.quarter_twists:
new_config=rubik.perm_apply(turn,pos)
if dic.get(new_config, False):
continue
dic[new_config]={'parent':pos,'move':turn}
lis.append(new_config)
def testShortestPath1(self):
"""Length 1 path."""
start = rubik.I
end = rubik.perm_apply(rubik.F, start)
ans = solver.shortest_path(start, end)
# print 'ans ',ans, 'has length',len(ans)
self.assertEqual(len(ans), 1)
self.assertEqual(ans, [rubik.F])
def _path(start, end, moves, rev_edge_func):
p = []
cur = end
while moves[cur]:
move_before = moves[cur]
p.append(move_before)
# Apply the inverse of the move before to get to the previous state.
cur = perm_apply(rev_edge_func(move_before), cur)
return p[::-1]
def neighborsMovePairs(position):
nbMovePairs=[]
for twist in rubik.quarter_twists:
# print "apply twist " + rubik.quarter_twists_names[twist]
# + "i.e. " + rubik.perm_to_string + "to "+ "position u"
neighbor=rubik.perm_apply(twist, position)
move=twist
nbMovePairs.append((neighbor,move))
return nbMovePairs
def check(start, end, sol):
for i in sol:
x = rubik.quarter_twists_names.keys()[
rubik.quarter_twists_names.values().index(i)]
start = rubik.perm_apply(x, start)
if start == end:
sys.stdout.write("Correct\n")
else:
sys.stdout.write("Wrong\n")
def verify(start, end, solution):
if solution is None:
return
for i in solution:
start = rubik.perm_apply(X[i], start)
if start == end:
print("Verification: Correct Solution")
else:
print("Verification: Incorrect Solution")
def shortest_path(start, end):
M = [] # Moves
P = {start: "START"} # Parent
Q = deque() # Queue
F = False # Flag
if start == end:
return M
Q.append(start)
while len(Q) > 0 and F == False: # BFS
x = Q.popleft()
for i in range(6):
p = rubik.quarter_twists[i]
y = rubik.perm_apply(p, x)
if y not in P:
Q.append(y)
P[y] = i
if y == end:
F = True
break
if F == False: # Back-Tracking to generate solution
M = None
else:
z = end
while P[z] != "START":
c = rubik.quarter_twists[P[z]]
if P[z] % 2 == 0: # F, L, U
n = rubik.quarter_twists[P[z] + 1]
else: # Fi, Li, Ui
n = rubik.quarter_twists[P[z] - 1]
M.append(rubik.quarter_twists_names[c])
z = rubik.perm_apply(n, z)
if (M != None):
M = M[::-1]
return M
def shortest_path(start, end):
"""
Using 2-way BFS, finds the shortest path from start_position to
end_position. Returns a list of moves.
You can use the rubik.quarter_twists move set.
Each move can be applied using rubik.perm_apply
"""
if start == end:
return []
forward = ([start], {start : []})
backward = ([end], {end : []})
for iter in range(7):
(forward_states, forward_moves) = forward
(backward_states, backward_moves) = backward
next_forward_states = []
for state in forward_states:
moves = forward_moves[state]
for twist in rubik.quarter_twists:
next_state = rubik.perm_apply(twist, state)
if next_state in backward_moves:
return moves + [twist] + backward_moves[next_state]
if not next_state in forward_moves:
next_forward_states.append(next_state)
forward_moves[next_state] = moves + [twist]
next_backward_states = []
for state in backward_states:
moves = backward_moves[state]
for twist in rubik.quarter_twists:
next_state = rubik.perm_apply(rubik.perm_inverse(twist), state)
if next_state in forward_moves:
return forward_moves[next_state] + [twist] + moves
if not next_state in backward_moves:
next_backward_states.append(next_state)
backward_moves[next_state] = [twist] + moves
forward = (next_forward_states, forward_moves)
backward = (next_backward_states, backward_moves)
return None
def count_repetitive_twists(moves):
"""
When you apply the same twists to a cube over and over again, the
cube will eventually return to its original position. This applies
each move in moves repeatedly, until the cube returns to its
original position, and counts the length of the cycle.
"""
current_position = rubik.I
for count in xrange(1, 100000):
for move in moves:
current_position = rubik.perm_apply(move, current_position)
if(current_position == rubik.I):
return count
def shortest_path(start, end):
"""
Using 2-way BFS, finds the shortest path from start_position to
end_position. Returns a list of moves.
You can use the rubik.quarter_twists move set.
Each move can be applied using rubik.perm_apply
"""
frontier = deque()
frontier.append(start)
parent = {start: None}
ans_found = False
while frontier:
u = frontier.popleft()
if u == end:
ans_found = True
break
for x in xrange(6):
temp = rubik.perm_apply(rubik.quarter_twists[x], u)
if temp not in parent:
parent[temp] = x + 1 if x%2 == 0 else x - 1
frontier.append(temp)
ans = deque()
if ans_found:
m = end
j = parent[m]
while parent[m] != None:
ans.appendleft(rubik.quarter_twists[j + 1 if j%2 == 0 else j - 1])
print(rubik.quarter_twists_names[ans[0]])
m = rubik.perm_apply(rubik.quarter_twists[j], m)
j = parent[m]
return list(ans)
else:
return None
def shortest_path(start, end):
"""
Using 2-way BFS, finds the shortest path from start_position to
end_position. Returns a list of moves.
You can use the rubik.quarter_twists move set.
Each move can be applied using rubik.perm_apply
"""
if start == end: return []
forward_parents = {start: None}
backward_parents = {end: None}
forward_moves = {}
backward_moves = {}
for move in rubik.quarter_twists:
forward_moves[move] = move
backward_moves[rubik.perm_inverse(move)] = move
forward = (forward_moves, forward_parents, backward_parents)
backward = (backward_moves, backward_parents, forward_parents)
queue = deque([(start, forward), (end, backward), None])
for i in range(7):
while True:
vertex = queue.popleft()
if vertex is None:
queue.append(None)
break
position = vertex[0]
moves, parents, other_parents = vertex[1]
for move in moves:
next_position = rubik.perm_apply(move, position)
if next_position in parents: continue
parents[next_position] = (moves[move], position)
queue.append((next_position, vertex[1]))
if next_position in other_parents:
forward_path = path(next_position, forward_parents)
backward_path = path(next_position, backward_parents)
backward_path.reverse()
return forward_path + backward_path
return None
def shortest_path(start, end):
"""
Using 2-way BFS, finds the shortest path from start to end position.
Returns a list of moves and assumes the rubik.quarter_twists move set.
"""
if start == end: return [] #if no shortest path exists (start==end), return empty list
fparents = {start: None} #first half parents
sparents = {end: None} #second half parents
fmoves = {} #first half moves
smoves = {} #second half moves
for turn in rubik.quarter_twists:
fmoves[turn] = turn #insert forward moves from quarter_twists
smoves[rubik.perm_inverse(turn)] = turn #insert reverse moves (starting from second half)
forward = (fmoves, fparents, sparents) #set of moves and first/second half parents
backward = (smoves, sparents, fparents) #set of inverse moves with first/second half parents
Q = deque([(start, forward), (end, backward), None]) #create new deque(quicklist) Q = (first half, second half, None)
for x in range(7): #for each move in quarter_twist
while True: #loop
v = Q.popleft() #return leftmost element from Q
if v is None: #if at the end of Q (None)
Q.append(None) #add None to Q
break #break from loop
position = v[0] #set vertex to start or end
moves, parents, otherparents = v[1] #set moves, parents, other parents to forward or backward
for i in moves: #start two way BFS
nextpos = rubik.perm_apply(i, position) #set node to search
if nextpos in parents: continue #if node in parents, continue
parents[nextpos] = (moves[i], position) #set parent pointer to node, vertex
Q.append((nextpos, v[1])) #add expanded search to Q
if nextpos in otherparents: #if node discovered in both searches
fpath = path(nextpos, fparents) #forward path set with node + parent pointers
spath = path(nextpos, sparents) #backward path set with node + parent pointers
spath.reverse() #must reverse the inverse path before joining it with forward path
return fpath + spath #return list of moves for the shortest path (forward + backward moves)
return None #else return None
def shortest_path(start, end):
"""
Using 2-way BFS, finds the shortest path from start_position to
end_position. Returns a list of moves.
You can use the rubik.quarter_twists move set.
Each move can be applied using rubik.perm_apply
"""
if start == end:
return []
startroot = node(start)
endroot = node(end)
startq = queue([startroot, None])
endq = queue([endroot, None])
starth = []
endh = []
for i in range(0, 335923):
starth.append([])
endh.append([])
startd = {}
starth[hash(start)] = (start, None, None)
endd = {}
endh[hash(end)] = (end, None, None)
startd[startroot.list] = (startroot.list, startroot.parent, startroot.orientation)
endd[endroot.list] = (endroot.list, endroot.parent, endroot.orientation)
i = 0
while i < 7:
while True:
g = startq.dequeue()
if g == None:
startq.enqueue(None)
break
if rubik.perm_apply(rubik.F, g.list) is not starth[hash(rubik.perm_apply(rubik.F, g.list))]:
g.child[0] = node(rubik.perm_apply(rubik.F, g.list), g.list, rubik.F)
starth[hash(rubik.perm_apply(rubik.F, g.list))].append(
(rubik.perm_apply(rubik.F, g.list), g.list, rubik.F)
)
startq.enqueue(g.child[0])
if rubik.perm_apply(rubik.F, g.list) is endh[hash(rubik.perm_apply(rubik.F, g.list))]:
fr = moves(rubik.perm_apply(rubik.F, g.list), starth)
br = moves(rubik.perm_apply(rubik.F, g.list), endh)
fr.reverse()
z = fr + br
return z
if rubik.perm_apply(rubik.Fi, g.list) is not starth[hash(rubik.perm_apply(rubik.Fi, g.list))]:
g.child[1] = node(rubik.perm_apply(rubik.Fi, g.list), g.list, rubik.Fi)
starth[hash(rubik.perm_apply(rubik.Fi, g.list))].append(
(rubik.perm_apply(rubik.Fi, g.list), g.list, rubik.Fi)
)
startq.enqueue(g.child[1])
if rubik.perm_apply(rubik.Fi, g.list) is endh[hash(rubik.perm_apply(rubik.Fi, g.list))]:
fr = moves(rubik.perm_apply(rubik.Fi, g.list), starth)
br = moves(rubik.perm_apply(rubik.Fi, g.list), endh)
fr.reverse()
z = fr + br
return z
if rubik.perm_apply(rubik.L, g.list) is not starth[hash(rubik.perm_apply(rubik.L, g.list))]:
g.child[2] = node(rubik.perm_apply(rubik.L, g.list), g.list, rubik.L)
starth[hash(rubik.perm_apply(rubik.L, g.list))].append(
(rubik.perm_apply(rubik.L, g.list), g.list, rubik.L)
)
startq.enqueue(g.child[2])
if rubik.perm_apply(rubik.L, g.list) is endh[hash(rubik.perm_apply(rubik.L, g.list))]:
fr = moves(rubik.perm_apply(rubik.L, g.list), starth)
br = moves(rubik.perm_apply(rubik.L, g.list), endh)
fr.reverse()
z = fr + br
return z
if rubik.perm_apply(rubik.Li, g.list) is not starth[hash(rubik.perm_apply(rubik.Li, g.list))]:
g.child[3] = node(rubik.perm_apply(rubik.Li, g.list), g.list, rubik.Li)
starth[hash(rubik.perm_apply(rubik.Li, g.list))].append(
(rubik.perm_apply(rubik.Li, g.list), g.list, rubik.Li)
)
startq.enqueue(g.child[3])
if rubik.perm_apply(rubik.Li, g.list) is endh[hash(rubik.perm_apply(rubik.Li, g.list))]:
fr = moves(rubik.perm_apply(rubik.Li, g.list), starth)
br = moves(rubik.perm_apply(rubik.Li, g.list), endh)
fr.reverse()
z = fr + br
return z
if rubik.perm_apply(rubik.U, g.list) is not starth[hash(rubik.perm_apply(rubik.U, g.list))]:
g.child[4] = node(rubik.perm_apply(rubik.U, g.list), g.list, rubik.U)
starth[hash(rubik.perm_apply(rubik.U, g.list))].append(
(rubik.perm_apply(rubik.U, g.list), g.list, rubik.U)
)
startq.enqueue(g.child[4])
if rubik.perm_apply(rubik.U, g.list) is endh[hash(rubik.perm_apply(rubik.U, g.list))]:
fr = moves(rubik.perm_apply(rubik.U, g.list), starth)
br = moves(rubik.perm_apply(rubik.U, g.list), endh)
fr.reverse()
z = fr + br
return z
if rubik.perm_apply(rubik.Ui, g.list) is not starth[hash(rubik.perm_apply(rubik.Ui, g.list))]:
g.child[5] = node(rubik.perm_apply(rubik.Ui, g.list), g.list, rubik.Ui)
starth[hash(rubik.perm_apply(rubik.Ui, g.list))].append(
(rubik.perm_apply(rubik.Ui, g.list), g.list, rubik.Ui)
)
startq.enqueue(g.child[5])
if rubik.perm_apply(rubik.Li, g.list) is endh[hash(rubik.perm_apply(rubik.Ui, g.list))]:
fr = moves(rubik.perm_apply(rubik.Ui, g.list), starth)
br = moves(rubik.perm_apply(rubik.Ui, g.list), endh)
fr.reverse()
z = fr + br
return z
while True:
k = endq.dequeue()
if k == None:
endq.enqueue(None)
break
if (
rubik.perm_apply(rubik.perm_inverse(rubik.F), k.list)
is not endh[hash(rubik.perm_apply(rubik.perm_inverse(rubik.F), k.list))]
):
k.child[0] = node(rubik.perm_apply(rubik.perm_inverse(rubik.F), k.list), k.list, rubik.F)
endh[hash(rubik.perm_apply(rubik.perm_inverse(rubik.F), k.list))].append(
(rubik.perm_apply(rubik.perm_inverse(rubik.F), k.list), k.list, rubik.F)
)
endq.enqueue(k.child[0])
if (
rubik.perm_apply(rubik.perm_inverse(rubik.F), k.list)
is starth[hash(rubik.perm_apply(rubik.perm_inverse(rubik.F), k.list))]
):
fr = moves(rubik.perm_apply(rubik.perm_inverse(rubik.F), k.list), starth)
br = moves(rubik.perm_apply(rubik.perm_inverse(rubik.F), k.list), endh)
fr.reverse()
z = fr + br
return z
if (
rubik.perm_apply(rubik.perm_inverse(rubik.Fi), k.list)
is not endh[hash(rubik.perm_apply(rubik.perm_inverse(rubik.Fi), k.list))]
):
k.child[1] = node(rubik.perm_apply(rubik.perm_inverse(rubik.Fi), k.list), k.list, rubik.Fi)
endh[hash(rubik.perm_apply(rubik.perm_inverse(rubik.Fi), k.list))] = (
rubik.perm_apply(rubik.perm_inverse(rubik.Fi), k.list),
k.list,
rubik.Fi,
)
endq.enqueue(k.child[1])
if rubik.perm_apply(rubik.perm_inverse(rubik.Fi), k.list) is startd:
fr = moves(rubik.perm_apply(rubik.perm_inverse(rubik.Fi), k.list), starth)
br = moves(rubik.perm_apply(rubik.perm_inverse(rubik.Fi), k.list), endh)
fr.reverse()
z = fr + br
return z
if (
rubik.perm_apply(rubik.perm_inverse(rubik.L), k.list)
is not endh[hash(rubik.perm_apply(rubik.perm_inverse(rubik.L), k.list))]
):
k.child[2] = node(rubik.perm_apply(rubik.perm_inverse(rubik.L), k.list), k.list, rubik.L)
endh[hash(rubik.perm_apply(rubik.perm_inverse(rubik.L), k.list))] = (
rubik.perm_apply(rubik.perm_inverse(rubik.L), k.list),
k.list,
rubik.L,
)
endq.enqueue(k.child[2])
if (
rubik.perm_apply(rubik.perm_inverse(rubik.L), k.list)
is starth[hash(rubik.perm_apply(rubik.perm_inverse(rubik.L), k.list))]
):
fr = moves(rubik.perm_apply(rubik.perm_inverse(rubik.L), k.list), starth)
br = moves(rubik.perm_apply(rubik.perm_inverse(rubik.L), k.list), endh)
fr.reverse()
z = fr + br
return z
if (
rubik.perm_apply(rubik.perm_inverse(rubik.Li), k.list)
is not endh[hash(rubik.perm_apply(rubik.perm_inverse(rubik.Li), k.list))]
):
k.child[3] = node(rubik.perm_apply(rubik.perm_inverse(rubik.Li), k.list), k.list, rubik.Li)
endh[hash(rubik.perm_apply(rubik.perm_inverse(rubik.Li), k.list))] = (
rubik.perm_apply(rubik.perm_inverse(rubik.Li), k.list),
k.list,
rubik.Li,
)
endq.enqueue(k.child[3])
if (
rubik.perm_apply(rubik.perm_inverse(rubik.Li), k.list)
is starth[hash(rubik.perm_apply(rubik.perm_inverse(rubik.Li), k.list))]
):
fr = moves(rubik.perm_apply(rubik.perm_inverse(rubik.Li), k.list), starth)
br = moves(rubik.perm_apply(rubik.perm_inverse(rubik.Li), k.list), endh)
fr.reverse()
z = fr + br
return z
if (
rubik.perm_apply(rubik.perm_inverse(rubik.U), k.list)
is not endh[hash(rubik.perm_apply(rubik.perm_inverse(rubik.U), k.list))]
):
k.child[4] = node(rubik.perm_apply(rubik.perm_inverse(rubik.U), k.list), k.list, rubik.U)
endh[hash(rubik.perm_apply(rubik.perm_inverse(rubik.U), k.list))] = (
rubik.perm_apply(rubik.perm_inverse(rubik.U), k.list),
k.list,
rubik.U,
)
endq.enqueue(k.child[4])
if (
rubik.perm_apply(rubik.perm_inverse(rubik.U), k.list)
is starth[hash(rubik.perm_apply(rubik.perm_inverse(rubik.U), k.list))]
):
fr = moves(rubik.perm_apply(rubik.perm_inverse(rubik.U), k.list), starth)
br = moves(rubik.perm_apply(rubik.perm_inverse(rubik.U), k.list), endh)
fr.reverse()
z = fr + br
return z
if (
rubik.perm_apply(rubik.perm_inverse(rubik.Ui), k.list)
is not endh[hash(rubik.perm_apply(rubik.perm_inverse(rubik.Ui), k.list))]
):
k.child[5] = node(rubik.perm_apply(rubik.perm_inverse(rubik.Ui), k.list), k.list, rubik.Ui)
endh[hash(rubik.perm_apply(rubik.perm_inverse(rubik.Ui), k.list))] = (
rubik.perm_apply(rubik.perm_inverse(rubik.Ui), k.list),
k.list,
rubik.Ui,
)
endq.enqueue(k.child[5])
if (
rubik.perm_apply(rubik.perm_inverse(rubik.Ui), k.list)
is starth[hash(rubik.perm_apply(rubik.perm_inverse(rubik.Ui), k.list))]
):
fr = moves(rubik.perm_apply(rubik.perm_inverse(rubik.Ui), k.list), starth)
br = moves(rubik.perm_apply(rubik.perm_inverse(rubik.Ui), k.list), endh)
fr.reverse()
z = fr + br
return z
i += 1
return None
def insert_e(x,h,arr,ser): if h<8: flag=0 z=rubik.perm_apply(rubik.F,x) x.c1=node(z) y=(hash(z))%100000 for i in range(0,len(ser[y])): if z is ser[y][i]: flag=1 break else: flag=0 if flag==0: ser[y].append(z) arr[h].append(x.c1) x.c1.parent=x x.c1.ht=h z2=rubik.perm_apply(rubik.Fi,x) x.c2=node(z2) flag=0 y=(hash(z2))%100000 for i in range(0,len(ser[y])): if z2 is ser[y][i]: flag=1 break else: flag=0 if flag==0: ser[y].append(z2) arr[h].append(x.c2) x.c2.parent=x x.c2.ht=h z3=rubik.perm_apply(rubik.L,x) x.c3=node(z3) flag=0 y=(hash(z3))%100000 for i in range(0,len(ser[y])): if z3 is ser[y][i]: flag=1 break else: flag=0 if flag==0: ser[y].append(z3) arr[h].append(x.c3) x.c3.parent=x x.c3.ht=h z4=rubik.perm_apply(rubik.Li,x) x.c4=node(z4) flag=0 y=(hash(z4))%100000 for i in range(0,len(ser[y])): if z4 is ser[y][i]: flag=1 break else: flag=0 if flag==0: ser[y].append(z4) arr[h].append(x.c4) x.c4.parent=x x.c4.ht=h z5=rubik.perm_apply(rubik.U,x) x.c5=node(z5) flag=0 y=(hash(z5))%100000 for i in range(0,len(ser[y])): if z5 is ser[y][i]: flag=1 break else: flag=0 if flag==0: ser[y].append(z5) arr[h].append(x.c5) x.c5.parent=x x.c5.ht=h z6=rubik.perm_apply(rubik.Ui,x) x.c6=node(z6) flag=0 y=(hash(z6))%100000 for i in range(0,len(ser[y])): if z6 is ser[y][i]: flag=1 break else: flag=0 if flag==0: ser[y].append(z6) arr[h].append(x.c6) x.c6.parent=x x.c6.ht=h return [arr,ser]
def adjacency(pos):
adj_list = []
for t in twists:
p = rubik.perm_apply(t, pos)
adj_list.append(p)
return adj_list
def shortest_path(start, end):
"""
Using 2-way BFS, finds the shortest path from start_position to
end_position. Returns a list of moves.
You can use the rubik.quarter_twists move set.
Each move can be applied using rubik.perm_apply
"""
if start==end:
return []
startroot=node(start)
endroot=node(end)
startq=queue([startroot,None])
endq=queue([endroot,None])
startd={}
startd[start]=(start,None,None)
endd={}
endd[end]=(end,None,None)
i=0
while i<7:
while True:
g=startq.dequeue()
if g==None:
startq.enqueue(None)
break
if rubik.perm_apply(rubik.F,g.list) not in startd:
g.child[0]=node(rubik.perm_apply(rubik.F,g.list),g.list,rubik.F)
startd[rubik.perm_apply(rubik.F,g.list)]=(rubik.perm_apply(rubik.F,g.list),g.list,rubik.F)
startq.enqueue(g.child[0])
if rubik.perm_apply(rubik.F,g.list) in endd:
fr=moves(rubik.perm_apply(rubik.F,g.list),startd)
br=moves(rubik.perm_apply(rubik.F,g.list),endd)
fr.reverse()
z=fr+br
return z
if rubik.perm_apply(rubik.Fi,g.list) not in startd:
g.child[1]=node(rubik.perm_apply(rubik.Fi,g.list),g.list,rubik.Fi)
startd[rubik.perm_apply(rubik.Fi,g.list)]=(rubik.perm_apply(rubik.Fi,g.list),g.list,rubik.Fi)
startq.enqueue(g.child[1])
if rubik.perm_apply(rubik.Fi,g.list) in endd:
fr=moves(rubik.perm_apply(rubik.Fi,g.list),startd)
br=moves(rubik.perm_apply(rubik.Fi,g.list),endd)
fr.reverse()
z=fr+br
return z
if rubik.perm_apply(rubik.L,g.list) not in startd:
g.child[2]=node(rubik.perm_apply(rubik.L,g.list),g.list,rubik.L)
startd[rubik.perm_apply(rubik.L,g.list)]=(rubik.perm_apply(rubik.L,g.list),g.list,rubik.L)
startq.enqueue(g.child[2])
if rubik.perm_apply(rubik.L,g.list) in endd:
fr=moves(rubik.perm_apply(rubik.L,g.list),startd)
br=moves(rubik.perm_apply(rubik.L,g.list),endd)
fr.reverse()
z=fr+br
return z
if rubik.perm_apply(rubik.Li,g.list) not in startd:
g.child[3]=node(rubik.perm_apply(rubik.Li,g.list),g.list,rubik.Li)
startd[rubik.perm_apply(rubik.Li,g.list)]=(rubik.perm_apply(rubik.Li,g.list),g.list,rubik.Li)
startq.enqueue(g.child[3])
if rubik.perm_apply(rubik.Li,g.list) in endd:
fr=moves(rubik.perm_apply(rubik.Li,g.list),startd)
br=moves(rubik.perm_apply(rubik.Li,g.list),endd)
fr.reverse()
z=fr+br
return z
if rubik.perm_apply(rubik.U,g.list) not in startd:
g.child[4]=node(rubik.perm_apply(rubik.U,g.list),g.list,rubik.U)
startd[rubik.perm_apply(rubik.U,g.list)]=(rubik.perm_apply(rubik.U,g.list),g.list,rubik.U)
startq.enqueue(g.child[4])
if rubik.perm_apply(rubik.U,g.list) in endd:
fr=moves(rubik.perm_apply(rubik.U,g.list),startd)
br=moves(rubik.perm_apply(rubik.U,g.list),endd)
fr.reverse()
z=fr+br
return z
if rubik.perm_apply(rubik.Ui,g.list) not in startd:
g.child[5]=node(rubik.perm_apply(rubik.Ui,g.list),g.list,rubik.Ui)
startd[rubik.perm_apply(rubik.Ui,g.list)]=(rubik.perm_apply(rubik.Ui,g.list),g.list,rubik.Ui)
startq.enqueue(g.child[5])
if rubik.perm_apply(rubik.Li,g.list) in endd:
fr=moves(rubik.perm_apply(rubik.Ui,g.list),startd)
br=moves(rubik.perm_apply(rubik.Ui,g.list),endd)
fr.reverse()
z=fr+br
return z
while True:
k=endq.dequeue()
if k==None:
endq.enqueue(None)
break
if rubik.perm_apply(rubik.perm_inverse(rubik.F),k.list) not in endd:
k.child[0]=node(rubik.perm_apply(rubik.perm_inverse(rubik.F),k.list),k.list,rubik.F)
endd[rubik.perm_apply(rubik.perm_inverse(rubik.F),k.list)]=(rubik.perm_apply(rubik.perm_inverse(rubik.F),k.list),k.list,rubik.F)
endq.enqueue(k.child[0])
if rubik.perm_apply(rubik.perm_inverse(rubik.F),k.list) in startd:
fr=moves(rubik.perm_apply(rubik.perm_inverse(rubik.F),k.list),startd)
br=moves(rubik.perm_apply(rubik.perm_inverse(rubik.F),k.list),endd)
fr.reverse()
z=fr+br
return z
if rubik.perm_apply(rubik.perm_inverse(rubik.Fi),k.list) not in endd:
k.child[1]=node(rubik.perm_apply(rubik.perm_inverse(rubik.Fi),k.list),k.list,rubik.Fi)
endd[rubik.perm_apply(rubik.perm_inverse(rubik.Fi),k.list)]=(rubik.perm_apply(rubik.perm_inverse(rubik.Fi),k.list),k.list,rubik.Fi)
endq.enqueue(k.child[1])
if rubik.perm_apply(rubik.perm_inverse(rubik.Fi),k.list) in startd:
fr=moves(rubik.perm_apply(rubik.perm_inverse(rubik.Fi),k.list),startd)
br=moves(rubik.perm_apply(rubik.perm_inverse(rubik.Fi),k.list),endd)
fr.reverse()
z=fr+br
return z
if rubik.perm_apply(rubik.perm_inverse(rubik.L),k.list) not in endd:
k.child[2]=node(rubik.perm_apply(rubik.perm_inverse(rubik.L),k.list),k.list,rubik.L)
endd[rubik.perm_apply(rubik.perm_inverse(rubik.L),k.list)]=(rubik.perm_apply(rubik.perm_inverse(rubik.L),k.list),k.list,rubik.L)
endq.enqueue(k.child[2])
if rubik.perm_apply(rubik.perm_inverse(rubik.L),k.list) in startd:
fr=moves(rubik.perm_apply(rubik.perm_inverse(rubik.L),k.list),startd)
br=moves(rubik.perm_apply(rubik.perm_inverse(rubik.L),k.list),endd)
fr.reverse()
z=fr+br
return z
if rubik.perm_apply(rubik.perm_inverse(rubik.Li),k.list) not in endd:
k.child[3]=node(rubik.perm_apply(rubik.perm_inverse(rubik.Li),k.list),k.list,rubik.Li)
endd[rubik.perm_apply(rubik.perm_inverse(rubik.Li),k.list)]=(rubik.perm_apply(rubik.perm_inverse(rubik.Li),k.list),k.list,rubik.Li)
endq.enqueue(k.child[3])
if rubik.perm_apply(rubik.perm_inverse(rubik.Li),k.list) in startd:
fr=moves(rubik.perm_apply(rubik.perm_inverse(rubik.Li),k.list),startd)
br=moves(rubik.perm_apply(rubik.perm_inverse(rubik.Li),k.list),endd)
fr.reverse()
z=fr+br
return z
if rubik.perm_apply(rubik.perm_inverse(rubik.U),k.list) not in endd:
k.child[4]=node(rubik.perm_apply(rubik.perm_inverse(rubik.U),k.list),k.list,rubik.U)
endd[rubik.perm_apply(rubik.perm_inverse(rubik.U),k.list)]=(rubik.perm_apply(rubik.perm_inverse(rubik.U),k.list),k.list,rubik.U)
endq.enqueue(k.child[4])
if rubik.perm_apply(rubik.perm_inverse(rubik.U),k.list) in startd:
fr=moves(rubik.perm_apply(rubik.perm_inverse(rubik.U),k.list),startd)
br=moves(rubik.perm_apply(rubik.perm_inverse(rubik.U),k.list),endd)
fr.reverse()
z=fr+br
return z
if rubik.perm_apply(rubik.perm_inverse(rubik.Ui),k.list) not in endd:
k.child[5]=node(rubik.perm_apply(rubik.perm_inverse(rubik.Ui),k.list),k.list,rubik.Ui)
endd[rubik.perm_apply(rubik.perm_inverse(rubik.Ui),k.list)]=(rubik.perm_apply(rubik.perm_inverse(rubik.Ui),k.list),k.list,rubik.Ui)
endq.enqueue(k.child[5])
if rubik.perm_apply(rubik.perm_inverse(rubik.Ui),k.list) in startd:
fr=moves(rubik.perm_apply(rubik.perm_inverse(rubik.Ui),k.list),startd)
br=moves(rubik.perm_apply(rubik.perm_inverse(rubik.Ui),k.list),endd)
fr.reverse()
z=fr+br
return z
i+=1
return None
def assertGoodPath(self, start, end, path):
current = start
for move in path:
current = rubik.perm_apply(move, current)
self.assertEqual(current, end)
def shortest_path(start, end):
"""
Using 2-way BFS, finds the shortest path from start_position to
end_position. Returns a list of moves.
You can use the rubik.quarter_twists move set.
Each move can be applied using rubik.perm_apply
"""
if start==end:
return []
startroot=node(start)
endroot=node(end)
startq=queue([startroot,None])
endq=queue([endroot,None])
starth=[]
endh=[]
for i in range(0,335923):
starth.append([])
endh.append([])
starth[hash(start)].append((start,None,None))
endh[hash(end)].append((end,None,None))
#startd[startroot.list]=(startroot.list,startroot.parent,startroot.orientation)
#endd[endroot.list]=(endroot.list,endroot.parent,endroot.orientation)
move=[rubik.F,rubik.Fi,rubik.L,rubik.Li,rubik.U,rubik.Ui]
i=0
while i<7:
while True:
g=startq.dequeue()
if g is None:
startq.enqueue(None)
break
j=0
for k in move:
m=rubik.perm_apply(k,g.list)
if search(m,starth[hash(m)]) is None:
g.child[j]=node(m,g,k)
starth[hash(m)].append((m,g,k))
startq.enqueue(g.child[j])
if search(m,endh[hash(m)]) is not None:
fr=path(m,starth[hash(m)])
br=path(m,endh[hash(m)])
fr.reverse()
return fr + br
j+=1
while True:
g=endq.dequeue()
if g is None:
endq.enqueue(None)
break
j=0
for k in move:
m=rubik.perm_apply(rubik.perm_inverse(k),g.list)
if search(m,endh[hash(m)]) is None:
g.child[j]=node(m,g,k)
endh[hash(m)].append((m,g,k))
endq.enqueue(g.child[j])
if search(m,starth[hash(m)]) is not None:
fr=path(m,starth[hash(m)])
br=path(m,endh[hash(m)])
fr.reverse()
return fr + br
j+=1
i+=1
#print i
return None
def shortest_path(start, end):
"""
Using 2-way BFS, finds the shortest path from start_position to
end_position. Returns a list of moves.
"""
if start==end:
return []
p=queue()
q=queue()
hash1=hashtable()
hash2=hashtable()
s=state(start)
hash2.insert(s)
p.enqueue(s)
p.enqueue(None)
s=state(end)
hash1.insert(s)
q.enqueue(s)
q.enqueue(None)
def returnmid():
level=1
while(1):
if level>7:
return None
a=q.dequeue()
while(a!=None):
for i in range(6):
b=r.perm_apply(r.quarter_twists[i],a.tuple)
k=0
if hash1.search(b):
k=1
if k==0:
s=state(b)
s.parent=a
q.enqueue(s)
hash1.insert(s)
for i in range(len(hash2.l[hashf(b)])):
if b==hash2.l[hashf(b)][i].tuple:
hash2.l[hashf(b)][i].parent=a
return hash2.l[hashf(b)][i]
a=q.dequeue()
q.enqueue(None)
c=p.dequeue()
while(c!=None):
for i in range(6):
d=r.perm_apply(r.quarter_twists[i],c.tuple)
k=0
if hash2.search(d):
k=1
if k==0:
s=state(d)
s.child=c
p.enqueue(s)
hash2.insert(s)
for i in range(len(hash1.l[hashf(d)])):
if d==hash1.l[hashf(d)][i].tuple:
hash1.l[hashf(d)][i].child=c
return hash1.l[hashf(d)][i]
c=p.dequeue()
p.enqueue(None)
level+=1
mid=returnmid()
x=mid
y=mid
if mid==None:
return None
u=[]
while x.tuple!=start:
for i in range(6):
b=r.perm_apply(r.quarter_twists[i],x.tuple)
if b==x.child.tuple:
if i%2==0:
u.append(r.quarter_twists[i+1])
else:
u.append(r.quarter_twists[i-1])
break
x=x.child
path1=u[::-1]
v=[]
while y.tuple!=end:
for i in range(6):
b=r.perm_apply(r.quarter_twists[i],y.tuple)
if b==y.parent.tuple:
v.append(r.quarter_twists[i])
break
y=y.parent
path2=v
path=path1+path2
return path
d=c.orientation
c=c.parent
return path
start=rubik.F
'''end=rubik.I
start = rubik.I
middle = rubik.perm_apply(rubik.F, start)
end = rubik.perm_apply(rubik.L, middle)
start = rubik.I
middle1 = rubik.perm_apply(rubik.F, start)
middle2 = rubik.perm_apply(rubik.F, middle1)
end = rubik.perm_apply(rubik.Li, middle2)
start = rubik.I
middle1 = rubik.perm_apply(rubik.F, start)
middle2 = rubik.perm_apply(rubik.L, middle1)
middle3 = rubik.perm_apply(rubik.F, middle2)
end = rubik.perm_apply(rubik.L, middle3)
#start = (6, 7, 8, 20, 18, 19, 3, 4, 5, 16, 17, 15, 0, 1, 2, 14, 12, 13, 10, 11, 9, 21, 22, 23)
#end = rubik.I
#start = (7, 8, 6, 20, 18, 19, 3, 4, 5, 16, 17, 15, 0, 1, 2, 14, 12, 13, 10, 11, 9, 21, 22, 23)
#end = rubik.I
#start = rubik.I'''
middle1 = rubik.perm_apply(rubik.F, start)
middle2 = rubik.perm_apply(rubik.L, middle1)
middle3 = rubik.perm_apply(rubik.F, middle2)
end = rubik.perm_apply(rubik.L, middle3)
print shortest_path(start,end)
import rubik
twists = ( rubik.F, rubik.L, rubik.Fi, rubik.Li, rubik.U, rubik.Ui, rubik.perm_apply(rubik.F, rubik.F),
rubik.perm_apply(rubik.L, rubik.L), rubik.perm_apply(rubik.U, rubik.U) )
def adjacency(pos):
adj_list = []
for t in twists:
p = rubik.perm_apply(t, pos)
adj_list.append(p)
return adj_list
def positions_at_level(level):
"""
Using BFS, returns the number of cube configurations that are
exactly a given number of levels away from the starting position
(rubik.I), using the rubik.quarter_twists move set.
"""
if level == 0:
return i
blevel = {rubik.I:0}
parent = {rubik.I: None}
i = 1
frontier = [rubik.I]
