[題目]?

? ? ? ? You are playing the following Nim Game with your friend: There is a heap of stones on the table, each time one of you take turns to remove 1 to 3 stones. The one who removes the last stone will be the winner. You will take the first turn to remove the stones.

? ? ? ? Both of you are very clever and have optimal strategies for the game. Write a function to determine whether you can win the game given the number of stones in the heap.

? ? ? ? For example, if there are 4 stones in the heap, then you will never win the game: no matter 1, 2, or 3 stones you remove, the last stone will always be removed by your friend.

[題目解析]： 根據(jù)題目進(jìn)行分析，當(dāng)有4個(gè)石頭的時(shí)候，無(wú)論你拿1，2還是3個(gè)，對(duì)手都可以最后一個(gè)拿完，你永遠(yuǎn)不會(huì)贏。

? ? ? ? 依次類(lèi)推，當(dāng)有5個(gè)石頭的時(shí)候，你拿1個(gè)，留給對(duì)方4個(gè)，對(duì)方必輸；當(dāng)有6個(gè)石頭的時(shí)候，你拿2個(gè)，對(duì)方必輸；當(dāng)有7個(gè)石頭的時(shí)候，你拿3個(gè)，對(duì)方必輸。而當(dāng)有8個(gè)石頭的時(shí)候，你無(wú)論拿1，2，還是3個(gè)，都留給對(duì)方7，6，5三種，對(duì)方都必贏。繼續(xù)類(lèi)推呢，發(fā)現(xiàn)規(guī)律了嗎？n%4等于0的時(shí)候，你必輸，其他情況你都可以贏。

? ? ? ??

public boolean canWinNim(int n) {if(n <= 0) return false;return !(n%4 == 0);}

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轉(zhuǎn)載于:https://www.cnblogs.com/zzchit/p/5767704.html

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