Algorithm
Problem Name: 292. Nim Game
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
Code Examples
#1 Code Example with C Programming
Code -
C Programming
bool canWinNim(int n) {
#if 0
int i, hewins;
if (n < = 3) return true;
for (i = 1; i < = 3; i ++) {
hewins = canWinNim(n - i);
if (!hewins) return true;
}
return false;
#else
return (n % 4) ? true : false;
#endif
}
Input
n = 4
Output
false
#2 Code Example with Java Programming
Code -
Java Programming
class Solution {
public boolean canWinNim(int n) {
return n % 4 != 0;
}
}
Input
n = 4
Output
false
#3 Code Example with Javascript Programming
Code -
Javascript Programming
const canWinNim = function(n) {
return n % 4 !== 0 ;
};
Input
n = 1
Output
true
#4 Code Example with Python Programming
Code -
Python Programming
class Solution:
def canWinNim(self, n):
"""
:type n: int
:rtype: bool
"""
return False if n%4==0 else True
Input
n = 1
Output
true
#5 Code Example with C# Programming
Code -
C# Programming
namespace LeetCode
{
public class _0292_NimGame
{
public bool CanWinNim(int n)
{
return n % 4 != 0;
}
}
}
Input
n = 2
Output
true