Coins in a Line

Easy Greedy Dynamic Programming Array Game Theory

LintCode: http://www.lintcode.com/en/problem/coins-in-a-line/

Question

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?

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

Thinking

• DP: Check previous 2 values, if both are true, return false. If has false, return true.
• O(1) time and O(1) memory: If n is 3 times, first will lose.

Solution

Java (DP)

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
        if (n < 1) {
            return false;
        }
        if (n > 0 && n < 3) {
            return true;
        }
        boolean win1 = true;
        boolean win2 = true;
        for (int i = 3; i <= n; i ++) {
            boolean tmp = win2;
            win2 = !(win1 && win2);
            win1 = tmp;
        }
        return win2;
    }
}

Java (O(1) time and space)

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
        if (n < 1) {
            return false;
        }
        if (n % 3 != 0) {
            return true;
        }
        return false;
    }
}