English
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
Click to open Hints
- If there are 5 stones in the heap, could you figure out a way to remove the stones such that you will always be the winner?
Solution:
rs
impl Solution {
pub fn can_win_nim(n: i32) -> bool {
// if n is divisible by 4, then the first player will always lose
if n % 4 == 0 {
return false;
}
true
}
}
...