294. Flip Game II

題目：

You are playing the following Flip Game with your friend: Given a string that contains only these two characters: + and -, you and your friend take turns to flip twoconsecutive "++" into "--". The game ends when a person can no longer make a move and therefore the other person will be the winner.

Write a function to determine if the starting player can guarantee a win.

For example, given s = "++++", return true. The starting player can guarantee a win by flipping the middle "++" to become "+--+".

Follow up:
Derive your algorithm's runtime complexity.

鏈接：  http://leetcode.com/problems/flip-game-ii/

題解：

求是否startng player可以有一種策略保證贏取游戲。直覺就是dfs +backtracking。 代碼和Flip Game I基本一樣，不過加入了驗證下一步的一個條件語句。假如下一步next，對手不能贏，則這一步我們可以贏。看了Discuss以后發現還可以有O(n²)的DP做法，有些Game Theory的成分。Stellari大神好厲害。

Time Complexity - O(2ⁿ)， Space Complexity - O(2ⁿ)

public class Solution {
    public boolean canWin(String s) {
        char[] arr = s.toCharArray();
        for(int i = 1; i < s.length(); i++) {
            if(arr[i] == '+' && arr[i - 1] == '+') {
                arr[i] = '-';
                arr[i - 1] = '-';
                String next = String.valueOf(arr);
                if(!canWin(next)) {
                    return true;
                }
                arr[i] = '+';
                arr[i - 1] = '+';
            }
        }
        
        return false;
    }
}

Reference:

https://leetcode.com/discuss/64344/theory-matters-from-backtracking-128ms-to-dp-0ms

https://leetcode.com/discuss/64291/share-my-java-backtracking-solution

https://leetcode.com/discuss/64522/simple-backtracking-inspired-by-flip-game-i

https://leetcode.com/discuss/64357/memoization-3150ms-130ms-44ms-python

https://leetcode.com/discuss/64486/backtracking-solution-time-optimization-through-205ms-19ms

https://leetcode.com/discuss/64350/short-java-%26-ruby

https://leetcode.com/discuss/64293/1-line-python-solution

https://leetcode.com/discuss/64332/java-recursive-backtracking-solution-27ms

https://leetcode.com/discuss/64302/easy-to-understand-java-solution

http://lucida.me/blog/developer-reading-list/