Flip Game II

This can be approached using backtracking. The idea is to simulate all possible game states and determine if there is a guaranteed winning move for the starting player.

The steps for the algorithm are as follows:

1. Loop through the string to find possible moves (i.e., two consecutive “++”).
2. For each possible move, flip the “++” to “–” and let the opponent play on the modified state.
3. If there is a state where the opponent cannot win (i.e., no possible moves), then the current player can guarantee a win by making that move.

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class Solution:
    def canWin(self, currentState: str) -> bool:
        for i in range(len(currentState) - 1):
            # Check if there are two consecutive "++"
            if currentState[i:i+2] == "++":
                # Flip them and let the opponent play
                nextState = currentState[:i] + "--" + currentState[i+2:]
                # If the opponent cannot win in the next state, the current player can guarantee a win
                if not self.canWin(nextState):
                    return True
        # If no guaranteed winning move was found, return False
        return False

This solution, while straightforward, is not optimal. It explores many game states multiple times. To optimize, we can use memoization to store already computed results for particular game states and reuse them. This way, the backtracking solution becomes much faster for larger inputs.