class Solution(object):
def canIWin(self, maxChoosableInteger, desiredTotal):
"""
:type maxChoosableInteger: int
:type desiredTotal: int
:rtype: bool
"""
if sum(range(1,maxChoosableInteger+1))<desiredTotal:
return False
self.memo=dict()
return self.helper(range(1,maxChoosableInteger+1),desiredTotal)
def helper(self,array,desiredTotal):
array_hash=str(array)
#this is memoization, if this subproblem has already been calculated then return directly
if array_hash in self.memo:
return self.memo[array_hash]
#this is the base case of the problem. if it is my turn and the max number in the array is enough to reach the desiredTotal , then i can force a win by simply picking this max number
if array[-1]>=desiredTotal:
self.memo[array_hash]=True
return True
#pick a number, if the opponent can't force a win with the rest, that means i can force a win with picking this number
for i in xrange(len(array)):
if not self.helper(array[:i]+array[i+1:],desiredTotal-array[i]):
self.memo[array_hash]=True
return True
#if there is no number that i can pick to force a win, then this array, total combination is false.
self.memo[array_hash]=False
return False
464. Can I Win
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