Last updated on March 9th, 2025 at 09:10 pm

Here, we see a Nim Game LeetCode Solution. This Leetcode problem is solved using different approaches in many programming languages, such as C++, Java, JavaScript, Python, etc.

List of all LeetCode Solution

Topics

Brainteaser, Minimax

Companies

Adobe

Level of Question

Easy

Nim Game LeetCode Solution

1. Problem Statement

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.

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.

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

2. Coding Pattern Used in Solution

The coding pattern fall into Mathematical Reasoning or Game Theory. The solution leverages modular arithmetic or bitwise operations to determine the outcome of the game.

3. Code Implementation in Different Languages

3.1 Nim Game C++

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

3.2 Nim Game Java

class Solution {
    public boolean canWinNim(int n) {
        return (n & 0b11) != 0;
    }
}

3.3 Nim Game JavaScript

var canWinNim = function(n) {
    if(n%4==0) return false;
    else return true;
};

3.4 Nim Game Python

class Solution(object):
    def canWinNim(self, n):
        return True if n%100%4 else False

4. Time and Space Complexity

	Time Complexity	Space Complexity
C++	O(1)	O(1)
Java	O(1)	O(1)
JavaScript	O(1)	O(1)
Python	O(1)	O(1)

• The solution is highly efficient because it uses constant-time operations.
• The use of modular arithmetic (n % 4) or bitwise operations (n & 0b11) ensures minimal computational overhead.
• The Python code uses an additional % 100 operation, which is unnecessary and does not affect the result for valid inputs. It can be simplified to n % 4.