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Question

Formatted question description: https://leetcode.ca/all/292.html

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.

 

Example 1:

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.

Example 2:

Input: n = 1
Output: true

Example 3:

Input: n = 2
Output: true

 

Constraints:

• 1 <= n <= 231 - 1

Algorithm

List 1 to 10 cases as follows:

1 Win

2 Win

3 Win

4 Lost

5 Win

6 Win

7 Win

8 Lost

9 Win

10 Win

From this we can find the law, as long as it is a multiple of 4, we will definitely lose, so take the remainder of 4 to decide.

Code

• Java
• Python
• C++
• Go
• TypeScript
• RenderScript

• 
  public class Nim_Game {
  
      class Solution {
          public boolean canWinNim(int n) {
              return (n % 4 != 0);
          }
      }
  }
  
  ############
  
  class Solution {
      public boolean canWinNim(int n) {
          return n % 4 != 0;
      }
  }
  

• class Solution:
      def canWinNim(self, n: int) -> bool:
          return n % 4 != 0
  
  ############
  
  class Solution(object):
    def canWinNim(self, n):
      """
      :type n: int
      :rtype: bool
      """
      return not n % 4 == 0
  
  

• class Solution {
  public:
      bool canWinNim(int n) {
          return n % 4 != 0;
      }
  };
  

• func canWinNim(n int) bool {
  	return n%4 != 0
  }
  

• function canWinNim(n: number): boolean {
      return n % 4 != 0;
  }
  
  

• impl Solution {
      pub fn can_win_nim(n: i32) -> bool {
          n % 4 != 0
      }
  }
  
  

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