375. Guess Number Higher or Lower II

bottom-up dp solution 

class Solution(object):
    def getMoneyAmount(self, n):
        """
        :type n: int
        :rtype: int
        """
        dp=[[0]*(n+1) for _ in xrange(n+1)]
        for lo in xrange(n,0,-1):
            for hi in xrange(lo+1,n+1):
                dp[lo][hi]=min(x+max(dp[lo][x-1],dp[x+1][hi]) for x in xrange(lo,hi))
                
        return dp[1][n]
              

class Solution(object):
    def getMoneyAmount(self, n):
        """
        :type n: int
        :rtype: int
        """
        class helper(dict): 
            def __missing__(self,(lo,hi)):
                if lo>=hi:
                    return 0
                ret=self[lo,hi]=min(x+max(self[lo,x-1],self[x+1,hi]) for x in range(lo,hi))
                return ret
        return helper()[1,n]