In this Leetcode Nim Game problem solution You are playing the following Nim Game with your friend:

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

  1. You and your friend will alternate taking turns, and you go first.
  2. On each turn, the person whose turn it is will remove 1 to 3 stones from the heap.
  3. 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.

Leetcode Nim Game problem solution


Problem solution in Python.

class Solution:
    def canWinNim(self, n: int) -> bool:
        if n%4 == 0:
            return False
        else:
            return True



Problem solution in Java.

public boolean canWinNim(int n) {

    if(n>100000000) return !(n%4==0);
    
    boolean[] mem = new boolean[n+1];
    return helper(n, mem);
}


Problem solution in C++.

boolean helper(int n, boolean[] mem) { 
    if(n<=3) return true;
    if(n==4) return false;
            
    if(mem[n]==true) return mem[n];
     
    mem[n] = !helper(n-1, mem) || !helper(n-2, mem) || !helper(n-3, mem);
    return mem[n];
}


Problem solution in C.

bool canWinNim(int n) {
    if(n%4==0)
        return false;
    return true;
}