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solitaire.py
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solitaire.py
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# DIRECTIONS :: {String : (int, int)}
# Maps the string names of directions to their vector representations
DIRECTIONS = {"N":(-1,0),"NE":(-1,1),"E":(0,1),"SE":(1,1),
"S":(1,0),"SW":(1,-1),"W":(0,-1),"NW":(-1,-1)}
##################################################
### THIS CODE IS FOR TESTING, YOU MAY IGNORE ###
##################################################
class Board:
def __init__(self, B, D):
self.B = B
self.D = D
def __hash__(self):
return hash(self.B)
def __eq__(self, other):
return self.B == other.B
def is_solved(self):
nonempty = False
for p in self:
if nonempty:
return False
nonempty=True
return nonempty
def is_legal_move(self, m, orientation = "forward"):
r, c, d = m
dr, dc = DIRECTIONS[d]
before = (1, 1, 0)
if orientation == "reverse":
before = (0, 0, 1)
for i in range(3):
if self[r + i*dr, c + i*dc] != before[i]:
return False
return True
def all_legal_moves(self, orientation = "forward"):
for r,c in self:
for d in self.D:
if self.is_legal_move((r,c,d), orientation):
yield((r,c,d))
class NormalBoard(Board):
def __init__(self, B, D):
super().__init__(tuple(tuple(p for p in row) for row in B), D)
def __iter__(self):
for r in range(len(self.B)):
for c in range(len(self.B[r])):
if self.B[r][c] == 1:
yield (r, c)
def __str__(self):
return "\n".join([str(row) for row in self.B])
def __getitem__(self, i):
r,c = i
if (0 <= r < len(self.B)) and (0 <= c < len(self.B[r])):
return self.B[r][c]
return 2
def make_move(self, m, orientation = "forward"):
r, c, d = m
dr, dc = DIRECTIONS[d]
after = (0, 0, 1)
if orientation == "reverse":
after = (1, 1, 0)
B = [[p for p in row]for row in self.B]
for i in range(3):
B[r + i*dr][c + i*dc] = after[i]
return NormalBoard(B, self.D)
def sparsify(self):
blocked = []
for r in range(len(self.B)):
for c in range(len(self.B[0])):
if self[r,c] == 2:
blocked.append((r,c))
return SparseBoard(len(self.B), len(self.B[0]), frozenset(self), self.D, frozenset(blocked))
def desparsify(self):
return self
class SparseBoard(Board):
def __init__(self, R, C, B, D, blocked = frozenset()):
super().__init__(B, D)
self.R = R
self.C = C
self.blocked = blocked
def __iter__(self):
for p in self.B:
yield p
def __str__(self):
return "{} x {}\n{}".format(self.R, self.C, str(self.B))
def __getitem__(self, i):
if (i[0] < 0) or (i[0] >= self.R) or (i[1] < 0) or (i[1] >= self.C):
return 2
if i in self.blocked:
return 2
if i in self.B:
return 1
return 0
def make_move(self, m, orientation = "forward"):
r, c, d = m
dr, dc = DIRECTIONS[d]
B = {p for p in self}
if orientation == "reverse":
B.add((r, c))
B.add((r+dr, c+dc))
B.remove((r+dr*2, c+dc*2))
else:
B.remove((r, c))
B.remove((r+dr, c+dc))
B.add((r+dr*2, c+dc*2))
return SparseBoard(self.R, self.C, frozenset(B), self.D, self.blocked)
def sparsify(self):
return self
def desparsify(self):
return NormalBoard([[self[r,c] for c in range(self.C)] for r in range(self.R)], self.D)
##########################
### STOP IGNORING HERE ###
##########################
# get_path :: int, {int : (Board, (int, int, String))} -> [(int, int, String)]
# Computes a list of moves that will transform the starting configuration into
# a target configuration
# h is the hash value of the target configuration
# bfs_tree maps a hash value H(B) to (B, m), where m is the last move on the
# path to B found during the BFS search
def get_path(h, bfs_tree):
path = []
while True:
m = bfs_tree[h][1]
if m is None:
path.reverse()
return path
path.append(m)
h = hash_homomorphism(h, m)
# homomorphic_hash :: Board -> int
# Hashes a board in O(k) time
def homomorphic_hash(B): # takes in input as board, outputs hashed value
h = 0
for p in B:
h ^= hash(p)
return h
###################################################
### PLEASE DO NOT MODIFY ANY OF THE ABOVE CODE! ###
### This code is included for your convenience, ###
### but modifications may cause you a headache! ###
###################################################
# hash_homomorphism :: int, (int, int, String) -> int
def hash_homomorphism(h, m): # h: hash value of board. m: move. generates new hash of new board config
#########################
### Implement me pls! ###
#########################
return h^hash((m[0], m[1]))^hash((m[0]+DIRECTIONS[m[2]][0], m[1]+DIRECTIONS[m[2]][1]))^hash(((m[0]+2*DIRECTIONS[m[2]][0], m[1]+2*DIRECTIONS[m[2]][1])))
# solve :: Board -> [(int, int, String)]
def solve(B):
#########################
### Implement me pls! ###
#########################
if B.is_solved(): return []
queue = [B]
bfs_tree = {homomorphic_hash(B): (None, None)}
while queue:
# node we're looking at rn
current = queue[0]
for move in current.all_legal_moves(): # all possible moves from B
possible_config = hash_homomorphism(homomorphic_hash(current), move)
if possible_config not in bfs_tree: # to see if we've seen tree b4
bfs_tree[possible_config] = (current, move)
new_B = current.make_move(move)
queue.append(new_B) # this is where we change where B is
if new_B.is_solved():
return get_path(possible_config, bfs_tree)
queue.remove(current)
# done w/ while loop
return None