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 two consecutive "++" 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 "+--+".

一刷
方法1: backtracking
因为是in turn的游戏，一方胜出，下一方失败。
Time complexity: O(n!), 31ms

public class Solution {
    int len;
    char[] ss;
    public boolean canWin(String s) {
        len = s.length();
        ss = s.toCharArray();
        return canWin();
    }
    
    boolean canWin(){
        for(int is = 0; is<=len-2; is++){
            if(ss[is] == '+' && ss[is+1] == '+'){
                ss[is] = '-';
                ss[is+1] = '-';
                boolean wins = !canWin();
                ss[is] = '+';
                ss[is+1] = '+';
                if(wins) return true;
            }
        }
        return false;
    }
}

方法2: 用DP提高速度。19ms

public class Solution {
    public boolean canWin(String s) {
        if(s == null || s.length()<2) return false;
        Map<String, Boolean> winMap = new HashMap<String, Boolean>();
        return helper(s, winMap);
    }
    
    boolean helper(String s, Map<String, Boolean> winMap){
        if(winMap.containsKey(s)) return winMap.get(s);
        
        for(int i = 0; i<s.length(); i++){
            if(s.startsWith("++", i)){
                String t = s.substring(0, i) + "--" + s.substring(i+2);
                if(!helper(t, winMap)){
                    winMap.put(s, true);
                    return true;
                }
            }
        }
        winMap.put(s, false);
        return false;
    }
}

三刷
同上

class Solution {
    public boolean canWin(String s) {
        if(s == null || s.length()<2) return false;
        Map<String, Boolean> winMap = new HashMap<>();
        return helper(winMap, s);
    }
    
    public boolean helper(Map<String, Boolean> winMap, String s){
        if(winMap.containsKey(s)) return winMap.get(s);
        for(int i=0; i<s.length()-1; i++){
            boolean result = true;
            if(s.charAt(i) == '+' && s.charAt(i+1) == '+'){
                String cur = s.substring(0, i) + "--" + s.substring(i+2);
                if(!helper(winMap, cur)){
                    winMap.put(s, true);
                    return true;
                }
            }
        }
        winMap.put(s, false);
        return false;
    }
}