PU Nim Game

You are playing the following Nim Game with your friend: There is a heap of stones on the table, each time one of you take turns to remove 1 to 3 stones. The one who removes the last stone will be the winner. You will take the first turn to remove the stones.

Both of you are very clever and have optimal strategies for the game. Write a function to determine whether you can win the game given the number of stones in the heap.

For example, if there are 4 stones in the heap, then you will never win the game: no matter 1, 2, or 3 stones you remove, the last stone will always be removed by your friend.

C Solution:

bool canWinNim(int n) {
    return n % 4;
}

Summary:

• When 4 stones are left, the opponent wins no matter what I do.
• When 5/6/7 stones left, I can make sure the opponent has 4 stones and then loses.
• When 8 stones left, the opponent can get 5 or 6 or 7, because I can only remove 1 or 2 or 3, then he wins.
• When 9/10/11 stones left, I will make sure the opponent has 8 stones and then loses.
• ...
• I win when 4/8/12/... stones are left.

LeetCode: 292. Nim Game