Article From:https://www.cnblogs.com/yaoyudadudu/p/9216138.html

Description of the problem:

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.

Example:

Input: 4
Output: false 
Explanation: 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.

 

The idea of solving the problem:

This is a typical game question: how to win by action.

In this game, you can take away 1, 2, 3 stones, and the last person who takes the stone wins.

Then we can analyze the most basic situation:

  When the remaining 0 stones were taken away by the other party: failure

  When the remaining 1 stones are left, they can be taken away: Victory

  When the remaining 2 stones are left, they can be taken away: Victory

  When the remaining 3 stones are left, they can be taken away: Victory

  When the remaining 4 stones are left, all the rest will be taken away (because you and your opponent are smart enough): failure.

  

  When there are other numbers of stones, you can try to leave 4 stones to your opponent, and your opponent will try to leave 4 stones for you because it is smart enough.

 

Code:

class Solution {
public:
    bool canWinNim(int n) {
        return n%4;
    }
};

 

Link of this Article: 292. Nim Game

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