Harsh Rajpal

Posted on

# 292. Nim Game

Problem Statement:
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

Solution:

Algorithm:

1. If the number of stones is divisible by 4, then the player will lose.
2. If the number of stones is not divisible by 4, then the player will win.
3. Return the result.

Code:

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

Time Complexity:
O(1)

Space Complexity:
O(1)