leetcode 292. Nim Game

292. 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.

先想的用递归，结果超时。
class Solution {
public:
bool canWinNim(int n)
{
if (n <= 3) return true;
for (int i = 1; i <= 3; i++)
{
if (!canWinNim(n - i)) //B如果在一种情况下肯定输，那A肯定能赢
return true;
}
return false;
}
};

然后用数组，还是超时。
class Solution {
public:
bool canWinNim(int n)
{
if (n <= 3) return true;
vector<bool> canwin(n + 1, false);
for (int k = 1; k <= 3; k++) canwin[k] = true;
for (int i = 4; i <= n; i++)
{
for (int k = 1; k <= 3; k++)
{
if (!canwin[i - k]) //A取了之后B有一种情况肯定输，那A肯定赢
{
canwin[i] = true;
break;
}
}
}
return canwin
;
}
};

那就只能找规律了 :）



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