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zuma-game.py
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zuma-game.py
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# Time: O((b+h)^2 * h!*(b+h-1)!/(b-1)!)
# Space: O((b+h) * h!*(b+h-1)!/(b-1)!)
import collections
# brute force solution with worse complexity but pass
class Solution(object):
def findMinStep(self, board, hand):
"""
:type board: str
:type hand: str
:rtype: int
"""
def shrink(s): # Time: O(n^2), Space: O(1)
while True:
i = 0
for start in xrange(len(s)):
while i < len(s) and s[start] == s[i]:
i += 1
if i-start >= 3:
s = s[0:start]+s[i:]
break
else:
break
return s
def findMinStepHelper(board, hand, lookup):
if not board: return 0
if not hand: return float("inf")
if tuple(hand) in lookup[tuple(board)]: return lookup[tuple(board)][tuple(hand)]
result = float("inf")
for i in xrange(len(hand)):
for j in xrange(len(board)+1):
next_board = shrink(board[0:j] + hand[i:i+1] + board[j:])
next_hand = hand[0:i] + hand[i+1:]
result = min(result, findMinStepHelper(next_board, next_hand, lookup) + 1)
lookup[tuple(board)][tuple(hand)] = result
return result
lookup = collections.defaultdict(dict)
board, hand = list(board), list(hand)
result = findMinStepHelper(board, hand, lookup)
return -1 if result == float("inf") else result
# Time: O((b+h) * h!*(b+h-1)!/(b-1)!)
# Space: O((b+h) * h!*(b+h-1)!/(b-1)!)
import collections
# brute force solution
class Solution_TLE(object):
def findMinStep(self, board, hand):
"""
:type board: str
:type hand: str
:rtype: int
"""
def shrink(s): # Time: O(n), Space: O(n)
stack = []
start = 0
for i in xrange(len(s)+1):
if i == len(s) or s[i] != s[start]:
if stack and stack[-1][0] == s[start]:
stack[-1][1] += i - start
if stack[-1][1] >= 3:
stack.pop()
elif s and i - start < 3:
stack += [s[start], i - start],
start = i
result = []
for p in stack:
result += [p[0]] * p[1]
return result
def findMinStepHelper(board, hand, lookup):
if not board: return 0
if not hand: return float("inf")
if tuple(hand) in lookup[tuple(board)]: return lookup[tuple(board)][tuple(hand)]
result = float("inf")
for i in xrange(len(hand)):
for j in xrange(len(board)+1):
next_board = shrink(board[0:j] + hand[i:i+1] + board[j:])
next_hand = hand[0:i] + hand[i+1:]
result = min(result, findMinStepHelper(next_board, next_hand, lookup) + 1)
lookup[tuple(board)][tuple(hand)] = result
return result
lookup = collections.defaultdict(dict)
board, hand = list(board), list(hand)
result = findMinStepHelper(board, hand, lookup)
return -1 if result == float("inf") else result
# Time: O((b * h) * b * b! * h!)
# Space: O(b * b! * h!)
import collections
# greedy solution without proof (possibly incorrect)
class Solution_GREEDY_ACCEPT_BUT_NOT_PROVED(object):
def findMinStep(self, board, hand):
"""
:type board: str
:type hand: str
:rtype: int
"""
def shrink(s): # Time: O(n), Space: O(n)
stack = []
start = 0
for i in xrange(len(s)+1):
if i == len(s) or s[i] != s[start]:
if stack and stack[-1][0] == s[start]:
stack[-1][1] += i - start
if stack[-1][1] >= 3:
stack.pop()
elif s and i - start < 3:
stack += [s[start], i - start],
start = i
result = []
for p in stack:
result += [p[0]] * p[1]
return result
def findMinStepHelper2(board, hand, lookup):
result = float("inf")
for i in xrange(len(hand)):
for j in xrange(len(board)+1):
next_board = shrink(board[0:j] + hand[i:i+1] + board[j:])
next_hand = hand[0:i] + hand[i+1:]
result = min(result, findMinStepHelper(next_board, next_hand, lookup) + 1)
return result
def find(board, c, j):
for i in xrange(j, len(board)):
if board[i] == c:
return i
return -1
def findMinStepHelper(board, hand, lookup):
if not board: return 0
if not hand: return float("inf")
if tuple(hand) in lookup[tuple(board)]: return lookup[tuple(board)][tuple(hand)]
result = float("inf")
for i in xrange(len(hand)):
j = 0
while j < len(board):
k = find(board, hand[i], j)
if k == -1:
break
if k < len(board) - 1 and board[k] == board[k+1]:
next_board = shrink(board[0:k] + board[k+2:])
next_hand = hand[0:i] + hand[i+1:]
result = min(result, findMinStepHelper(next_board, next_hand, lookup) + 1)
k += 1
elif i > 0 and hand[i] == hand[i-1]:
next_board = shrink(board[0:k] + board[k+1:])
next_hand = hand[0:i-1] + hand[i+1:]
result = min(result, findMinStepHelper(next_board, next_hand, lookup) + 2)
j = k+1
lookup[tuple(board)][tuple(hand)] = result
return result
board, hand = list(board), list(hand)
hand.sort()
result = findMinStepHelper(board, hand, collections.defaultdict(dict))
if result == float("inf"):
result = findMinStepHelper2(board, hand, collections.defaultdict(dict))
return -1 if result == float("inf") else result
# Time: O(b * b! * h!)
# Space: O(b * b! * h!)
# if a ball can be only inserted beside a ball with same color,
# we can do by this solution
class Solution_WRONG_GREEDY_AND_NOT_ACCEPT_NOW(object):
def findMinStep(self, board, hand):
"""
:type board: str
:type hand: str
:rtype: int
"""
def shrink(s): # Time: O(n), Space: O(n)
stack = []
start = 0
for i in xrange(len(s)+1):
if i == len(s) or s[i] != s[start]:
if stack and stack[-1][0] == s[start]:
stack[-1][1] += i - start
if stack[-1][1] >= 3:
stack.pop()
elif s and i - start < 3:
stack += [s[start], i - start],
start = i
result = []
for p in stack:
result += [p[0]] * p[1]
return result
def find(board, c, j):
for i in xrange(j, len(board)):
if board[i] == c:
return i
return -1
def findMinStepHelper(board, hand, lookup):
if not board: return 0
if not hand: return float("inf")
if tuple(hand) in lookup[tuple(board)]: return lookup[tuple(board)][tuple(hand)]
result = float("inf")
for i in xrange(len(hand)):
j = 0
while j < len(board):
k = find(board, hand[i], j)
if k == -1:
break
if k < len(board) - 1 and board[k] == board[k+1]:
next_board = shrink(board[0:k] + board[k+2:])
next_hand = hand[0:i] + hand[i+1:]
result = min(result, findMinStepHelper(next_board, next_hand, lookup) + 1)
k += 1
elif i > 0 and hand[i] == hand[i-1]:
next_board = shrink(board[0:k] + board[k+1:])
next_hand = hand[0:i-1] + hand[i+1:]
result = min(result, findMinStepHelper(next_board, next_hand, lookup) + 2)
j = k+1
lookup[tuple(board)][tuple(hand)] = result
return result
lookup = collections.defaultdict(dict)
board, hand = list(board), list(hand)
hand.sort()
result = findMinStepHelper(board, hand, lookup)
return -1 if result == float("inf") else result