LeetCode 294: Flip Game II Solution in Python – A Step-by-Step Guide

What Is LeetCode 294: Flip Game II?

In LeetCode 294: Flip Game II, you’re given a string currentState of "+" and "-" characters (e.g., "++++"). Players take turns flipping any two consecutive "++" into "--", and the game ends when no "++" pairs remain—the last player to move wins. You’re the first player, and both you and your opponent play optimally, always picking the best move. Your task is to return True if you can force a win, False if you can’t. For example, with "++++", you can win by flipping strategically. This problem tests your game strategy skills, building on LeetCode 293: Flip Game and echoing game theory challenges like LeetCode 292: Nim Game.

Problem Statement

• Input: A string currentState containing only "+" and "-".
• Output: True if the first player can win, False otherwise.
• Rules: Flip "++" to "--"; you start; last move wins; both play optimally.

Constraints

• currentState length: 0 to 20.
• Contains only "+" and "-".

Examples

• Input: currentState = "++++"
• Output: True
• Input: currentState = "++"
• Output: True
• Input: currentState = "+-+-+"
• Output: False

Understanding the Problem: Can You Win?

To solve LeetCode 294: Flip Game II in Python, we need to figure out if you, as the first player, can always win starting from currentState, assuming both players make the smartest moves. With "++", you flip to "--" and win—no moves left. With "++++", you need to pick a flip that forces your opponent into a losing spot. It’s a game of strategy, and we’ll tackle it with:

• Best Solution (Backtracking with Memoization): O(n * 2^n) time reduced by memo, O(n) space—fast and smart.
• Alternative Solution (Recursive Backtracking): O(2^n) time—simple but slow.

Let’s dive into the memoized backtracking solution with a friendly breakdown that’s easy to follow.

Best Solution: Backtracking with Memoization

Why This Is the Best Solution

Backtracking with memoization is the top choice for LeetCode 294 because it’s efficient—starting at O(n * 2^n) time but sped up by caching repeated states—and uses O(n) space for the memoization table. It explores all possible moves, backtracks when needed, and remembers results to avoid redoing work. It’s like playing the game with a cheat sheet—try moves, learn from them, and win faster!

How It Works

Let’s imagine this like a game where you’re testing moves:

• Step 1: Think Like a Player:
• You win if any move you make leaves your opponent unable to win.
• Your opponent wins if every move you make lets them force a win.
• Step 2: Explore Moves:
• Start with the string (e.g., "++++").
• Find each "++" pair, flip it to "--", and see if your opponent loses with the new string.
• Step 3: Backtrack:
• For each flip, pretend it’s your opponent’s turn and check their moves.
• You win if at least one flip makes your opponent lose.
• Step 4: Memoize:
• Keep a notebook (hash map) of strings you’ve seen and whether you win from them.
• If you see a string again, use the saved answer—no need to replay.
• Step 5: Why It Works:
• Backtracking tries all paths, ensuring you find a winning move if it exists.
• Memoization skips repeated games, making it way faster than trying everything anew.

It’s like exploring a maze with a map—try paths, mark them, and skip revisits!

Step-by-Step Example

Example: currentState = "++++"

• Start: "++++", memo = {}.
• Your Turn:
• Flip 0-1: "--++":
• Opponent’s turn:
• Flip 2-3: "----" → no moves, opponent loses → you win from "--++".
• Memo: {"--++": True}.
• You win from "++++" → stop here, True.
• Check More (if needed):
• Flip 1-2: "+--+":
• Opponent: "+---" (2-3) → loses → you win.
• Flip 2-3: "++--":
• Opponent: "----" → loses → you win.
• Result: True (you win from "++++").

Example: currentState = "+-+-+"

• Your Turn: No "++" → no moves, you lose → False.
• Result: False.

Code with Detailed Line-by-Line Explanation

Here’s the Python code, broken down so it’s easy to follow:

Copy codeclass Solution:
    def canWin(self, currentState: str) -> bool:
        # Step 1: Notebook to remember who wins
        memo = {}

        # Step 2: Helper to play the game
        def can_win(state):
            # If we’ve seen this state, use the saved answer
            if state in memo:
                return memo[state]

            # Step 3: Try all possible flips
            for i in range(len(state) - 1):
                if state[i:i+2] == "++":  # Find a "++" pair
                    # Flip it to "--"
                    next_state = state[:i] + "--" + state[i+2:]
                    # If opponent loses after this move, you win
                    if not can_win(next_state):
                        memo[state] = True
                        return True

            # Step 4: No winning move found, you lose
            memo[state] = False
            return False

        # Step 5: Start the game
        return can_win(currentState)

• Line 4: Set up an empty hash map to store states and win/lose results.
• Line 7-19: Helper can_win:
• Line 9-10: Check the memo—if we’ve played this state, return the saved result.
• Line 12-17: Loop through the string:
• Find "++" at i and i+1.
• Make a new string with "--" there.
• Recurse: if opponent can’t win from next_state, you win—save and return True.
• Line 19-20: If no flip wins, you lose—save and return False.
• Line 22: Kick off with the input string.

• Time Complexity: O(n * 2^n) without memo, but memoization reduces it to O(n * 2^n) states, often much less in practice.
• Space Complexity: O(n)—memo and recursion stack.

This is like a game plan with notes—try smart, win fast!

Alternative Solution: Recursive Backtracking Without Memoization

Why an Alternative Approach?

Plain recursive backtracking also explores all moves—O(2^n) time, O(n) space—but without memoization, it recalculates every state, making it super slow. It’s simpler to write, like playing the game raw, step-by-step, but not practical for bigger strings.

How It Works

Let’s think of this as a no-notes game:

• Step 1: Start with the string.
• Step 2: Try each "++" flip, recurse to opponent’s turn.
• Step 3: You win if any move leaves opponent losing.
• Step 4: Repeat without saving states.

It’s like playing every round from scratch!

Step-by-Step Example

Example: currentState = "++++"

• Your Turn:
• "--++": Opponent has "----" → loses → you win.
• Stop here (but without memo, it’d check all).

Code for Recursive Backtracking

Copy codeclass Solution:
    def canWin(self, currentState: str) -> bool:
        def can_win(state):
            for i in range(len(state) - 1):
                if state[i:i+2] == "++":
                    next_state = state[:i] + "--" + state[i+2:]
                    if not can_win(next_state):
                        return True
            return False

        return can_win(currentState)

• Time Complexity: O(2^n)—exponential, no caching.
• Space Complexity: O(n)—recursion stack.

It’s a slow grind but works.

Comparing the Two Solutions

• Memoized Backtracking (Best):
• Pros: Faster with memo, O(n) space, smart.
• Cons: Slightly more code.
• Plain Backtracking (Alternative):
• Pros: O(n) space, simpler logic.
• Cons: O(2^n) time, too slow.

Memoized wins hands down.

Additional Examples and Edge Cases

• "+": False (no moves).
• "++": True.
• "": False.

Both handle these, but memoized is faster.

Complexity Breakdown

• Memoized: Time O(n * 2^n) reduced, Space O(n).
• Plain: Time O(2^n), Space O(n).

Memoized rules.

Key Takeaways

• Memoized: Save and win—clever!
• Plain: Try everything—slow!
• Games: Strategy is key.
• Python Tip: Dictionaries rock—see [Python Basics](/python/basics).

Final Thoughts: Flip to Victory

LeetCode 294: Flip Game II in Python is a strategic string game. Memoized backtracking flips fast, while plain recursion shows the basics. Want more? Try LeetCode 293: Flip Game or LeetCode 292: Nim Game. Ready to win? Head to Solve LeetCode 294 on LeetCode and flip your way to the top today!