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37 lines
1.5 KiB
Python
37 lines
1.5 KiB
Python
#coding: utf-8
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''' mbinary
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#######################################################################
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# File : stoneGame.py
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# Author: mbinary
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# Mail: zhuheqin1@gmail.com
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# Blog: https://mbinary.xyz
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# Github: https://github.com/mbinary
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# Created Time: 2018-12-14 14:32
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# Description:
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亚历克斯和李用几堆石子在做游戏。偶数堆石子排成一行，每堆都有正整数颗石子 piles[i] 。游戏以谁手中的石子最多来决出胜负。石子的总数是奇数，所以没有平局。
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亚历克斯和李轮流进行. 每回合，玩家从行的开始或结束处取走整堆石头。 这种情况一直持续到没有更多的石子堆为止，此时手中石子最多的玩家获胜。
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那么先手一定会赢吗? 是的, 求出先手比后手多的石子数.
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leetcode-cn 877: https://leetcode-cn.com/problems/stone-game/
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#######################################################################
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'''
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def stoneGame(li):
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'''li: list, len(li)%2==0, sum(li)%2==1'''
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def f(p,q):
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ret = dp[p][q]
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if ret is None:
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if p+1==q:
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ret = abs(li[p]-li[q])
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else:
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# max min
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# take the first one
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n1 = li[p] + min(-li[p+1]+f(p+2,q),-li[q]+f(p+1,q-1))
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# take the last one
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n2 = li[q] + min(-li[p]+f(p+1,q-1),-li[q-1]+f(p,q-2))
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ret = max(n1,n2)
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dp[p][q] = ret
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#print(li[p:q+1],ret)
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return ret
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n = len(li)
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dp = [[None for i in range(n)] for i in range(n)]
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return f(0,n-1)
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