2020-09-01

486. 预测赢家

博弈型DP：

 dp[i][j] 代表当前玩家在[i,j]以内与另一个玩家的分数之差的最大值.

class Solution:
    def PredictTheWinner(self, nums: List[int]) -> bool:
        n = len(nums)
        dp = [[0 for _ in range(n)] for _ in range(n)] ## dp[i][j] 代表当前玩家在[i,j]以内与另一个玩家的分数之差的最大值
        def dfs(l, r):
            if l==r:
                dp[l][r] = nums[l] 
                return nums[l]
            if dp[l][r]: return dp[l][r]
            ansl = nums[l] - dfs(l+1, r)
            ansr = nums[r] - dfs(l, r-1)
            dp[l][r] = max(ansl, ansr)
            return dp[l][r]
        dfs(0, len(nums)-1)
        return dp[0][len(nums)-1]>=0