AC代碼:
class Solution(object): def PRedictTheWinner(self, nums): """ :type nums: List[int] :rtype: bool """ total = sum(nums) sum1 = [[0 for i in range(len(nums))]for i in range(len(nums))] dp = [[0 for i in range(len(nums)+1)] for i in range(len(nums)+1)] for i in range(len(nums)): dp[i][i] = nums[i] for i in range(len(nums)): for j in range(i,len(nums)): sum1[i][j] = sum(nums[:j+1]) - sum(nums[:i]) print sum1 for k in range(1,len(nums)): for i in range(len(nums)-k): j = i + k dp[i][j] = max(nums[i]+sum1[i+1][j] - dp[i+1][j],nums[j]+sum1[i][j-1]-dp[i][j-1]) #print dp tmp = dp[0][len(nums)-1] if tmp*2 >= total: return True else: return False思路:定義兩個二維數組,sum1和dp,sum1[i][j]表示的是i-j的總和,dp[i][j]則表示i-j中,先選擇的人能獲得的最大加和,因為兩人需要輪流選擇,每人每次都會選擇最有利于自己的結果,因此下次選擇時,需從前面的總和減去前一組選擇可獲得的最大值,然后再比較先選左邊還是先選右邊能獲得更大的結果,
于是可以得到動態轉換方程:
dp[i][j] = max(nums[i]+sum1[i+1][j] - dp[i+1][j],nums[j]+sum1[i][j-1]-dp[i][j-1])
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