292.nim-game


描述

You are playing the following Nim Game with your friend:

Initially, there is a heap of stones on the table.

You and your friend will alternate taking turns, and you go first.

On each turn, the person whose turn it is will remove 1 to 3 stones from the heap. The one who removes the last stone is the winner.

Given n, the number of stones in the heap, return true if you can win the game assuming both you and your friend play optimally, otherwise return false.

测试用例

Input: n = 4
Output: false
Explanation: These are the possible outcomes:
1. You remove 1 stone. Your friend removes 3 stones, including the last stone. Your friend wins.
2. You remove 2 stones. Your friend removes 2 stones, including the last stone. Your friend wins.
3. You remove 3 stones. Your friend removes the last stone. Your friend wins.
In all outcomes, your friend wins.

题解

因为我先拿a([1,3])个,所以如果总数是4n(4的倍数),那么对方每次拿4-a个,他就一定可以赢我(对方很聪明)。
所以如果总数是4的倍数,那么我肯定会输。

(这个游戏最重要的就是先拿的吃亏)

var canWinNim = function(n) {
   // 所有的情况内,是否存在赢的可能性
   return n % 4 !== 0
}

结果

Accepted

60/60 cases passed (92 ms)

Your runtime beats 30.82 % of javascript submissions

Your memory usage beats 48.2 % of javascript submissions (38.6 MB)


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