Coins in a Line

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

Tags Expand

Greedy Dynamic Programming Array Game Theory

思路

• 特殊规律

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

动态规划

• 参考九章算法
• coins类题目

public class Solution {

    public boolean firstWillWin(int n) {
        // write your code here
        if (n <= 0 || n == 3) {
            return false;
        }
        if (n <= 2) {
           return true;
        }


       boolean[] dp = new boolean[n + 1];
       //dp[0] = true;
       dp[1] = true;
       dp[2] = true;
       dp[3] = false;
       dp[4] = true;
       for (int i = 5; i <= n; i++) {
           dp[i] = (dp[i - 3] && dp[i - 4]) || (dp[i - 3] && dp[i - 2]);
       }
       return dp[n];
    }
}