leetcode 375. Guess Number Higher or Lower II

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We are playing the Guess Game. The game is as follows:

I pick a number from 1 to n. You have to guess which number I picked.

Every time you guess wrong, I’ll tell you whether the number I picked is higher or lower.

However, when you guess a particular number x, and you guess wrong, you pay $x. You win the game when you guess the number I picked.

Example:


n = 10, I pick 8.

First round: You guess 5, I tell you that it’s higher. You pay $5.
Second round: You guess 7, I tell you that it’s higher. You pay $7.
Third round: You guess 9, I tell you that it’s lower. You pay $9.

Game over. 8 is the number I picked.

You end up paying $5 + $7 + $9 = $21.

Given a particular n ≥ 1, find out how much money you need to have to guarantee a win.

  • dfs
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class Solution(object):
    def getMoneyAmount(self, n):
        """
        :type n: int
        :rtype: int
        :dfs
        """
        #dp[i][j] = x + max(dp[i][x-1],dp[x+1][j])
        def dfs(dp,left,right):
            if left >= right:return 0
            if dp[left][right]: return dp[left][right]
            ans = float("inf")
            for i in range(left,right+1):
                ans = min(ans,i+max(dfs(dp,left,i-1),dfs(dp,i+1,right)))
            dp[left][right] = ans
            return ans
        
        dp = [[0 for i in range(n+1)] for j in range(n+1) ]
        dfs(dp,1,n)
        return dp[1][n]
  • dp
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def getMoneyAmountDP(self, n):
        dp = [[0] * (n+1) for _ in xrange(n+1)]
        for l in xrange(2, n+1):
            for i in xrange(1, n-l+2):
                min_cost = float('inf')
                j = i + l - 1
                for p in xrange(i, j):
                    res = p + max(dp[i][p-1], dp[p+1][j])
                    min_cost = min(min_cost, res)
                dp[i][j] = min_cost