[LintCode] Coins in a Line 一條線上的硬幣

 

There are n coins in a line. Two players take turns to take one or two coins from right side until there are no more coins left. The player who take the last coin wins.

Could you please decide the first play will win or lose?

Have you met this question in a real interview? 

Yes

Example

n = 1, return true.

n = 2, return true.

n = 3, return false.

n = 4, return true.

n = 5, return true.

Challenge 

O(n) time and O(1) memory

 

跟LeetCode上的那道Nim Game幾乎一模一樣。

 

解法一：

class Solution {
public:
    /**
     * @param n: an integer
     * @return: a boolean which equals to true if the first player will win
     */
     bool firstWillWin(int n) {
        if (n <= 0) return false;
        if (n <= 2) return true;
        vector<bool> dp(n + 1, true);
        dp[3] = false;
        for (int i = 4; i <= n; ++i) {
            dp[i] = dp[i - 3];
        }
        return dp.back();
    }
};

 

解法二：

class Solution {
public:
    /**
     * @param n: an integer
     * @return: a boolean which equals to true if the first player will win
     */
     bool firstWillWin(int n) {
        return n % 3 != 0;
    }
};