294. Flip Game II

• Difficulty: Medium

• Topics: Backtracking, Minimax

• Similar Questions:

  • Nim Game

  • Flip Game

  • Guess Number Higher or Lower II

  • Can I Win

Problem:

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.

Example:

Input: s = "++++"
Output: true 
Explanation: The starting player can guarantee a win by flipping the middle "++" to become "+--+".

Follow up:
Derive your algorithm's runtime complexity.

Solutions:

class Solution {
public:
    bool canWin(string s) {
        unordered_map<string, bool> cache;
        return helper(s, cache);
    }

private:
    bool helper(string& s, unordered_map<string, bool>& cache) {
        if (cache.count(s) > 0) return cache[s];
        for (int i = 0; i < (int)s.length() - 1; ++i) {
            if (s[i] == '+' && s[i+1] == '+') {
                s[i] = '-';
                s[i+1] = '-';
                auto ret =  (!helper(s, cache));
                s[i + 1] = '+';
                s[i] = '+';
                if (ret == true) { // it is wrong to return result intermediately without set s back!
                    cache[s] = ret;
                    return true;
                }
            }
        }
        cache[s] = false;
        return false;
    }
};