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Flip Game

Easy

Google

4 views

Topics:

Strings

You are given a string currentState of length n that contains only '+' and '-'.

You and a friend are playing a game. You are the first player, and you and your friend take turns flipping two consecutive "++" into "--". The game ends when a player can no longer make a move, and the last player to make a move wins.

Return all possible states of the string currentState after one valid move. You may return the answer in any order.

Example 1:

Input: currentState = "++++"
Output: ["--++","+--+","++--"]

Example 2:

Input: currentState = "+"
Output: []

Constraints:

1 <= currentState.length <= 500
currentState[i] is either '+' or '-'.

Try coding it in LeetCode

Flip Game

Easy

Google

4 views

Topics:

Strings

You are given a string currentState of length n that contains only '+' and '-'.

Return all possible states of the string currentState after one valid move. You may return the answer in any order.

Example 1:

Input: currentState = "++++"
Output: ["--++","+--+","++--"]

Example 2:

Input: currentState = "+"
Output: []

Constraints:

1 <= currentState.length <= 500
currentState[i] is either '+' or '-'.

Try coding it in LeetCode

Solution

Clarifying Questions

When you get asked this question in a real-life environment, it will often be ambiguous (especially at FAANG). Make sure to ask these questions in that case:

Can the input string contain characters other than '+' and '-'?
Is the input string guaranteed to be non-null?
What should I return if there are no possible flips?
How large can the input string be?
Should the returned list of strings be in any particular order?

Brute Force Solution

Approach

The game involves flipping adjacent '++' to '--' in a string. A brute force method involves trying every single possible flip and seeing what new strings we can create, one by one.

Here's how the algorithm would work step-by-step:

Look at the string from beginning to end, checking each pair of adjacent characters.
Whenever you find a '++', consider flipping it to '--'.
Make a copy of the string, do the flip, and save this new string as a possible next move.
Continue scanning the string and repeating this flipping process for every '++' pair you find, generating all possible next moves.
Do this until there are no more '++' pairs left in the original string.

Code Implementation

def generate_possible_next_moves(current_state):
    possible_moves = []
    string_length = len(current_state)

    for index in range(string_length - 1):
        # Check if the adjacent characters are '++'
        if current_state[index:index+2] == '++':

            # Create a new state with the flip
            new_state = list(current_state)
            new_state[index] = '-'
            new_state[index+1] = '-'
            possible_moves.append("".join(new_state))

    return possible_moves

Big(O) Analysis

Time Complexity

O(n) – The algorithm iterates through the string of length n to find all occurrences of '++'. In each iteration, it checks two adjacent characters. If '++' is found, a new string is created by flipping those characters. This process involves iterating through the string once. Therefore, the time complexity is directly proportional to the length of the string n, resulting in O(n).

Space Complexity

O(N) – The provided solution generates a list of strings, each representing a possible next move after flipping a '++' to '--'. In the worst-case scenario, where the input string `s` of length N contains approximately N/2 occurrences of '++', the algorithm could create up to N/2 new strings. Each new string is a copy of the original string `s`, thus requiring N space. Therefore, the space complexity is proportional to N, and in the worst case could create N/2 strings of size N. The space needed grows linearly with the input size N, giving a space complexity of O(N).

Optimal Solution

Approach

The Flip Game involves finding valid moves in a string. The best way is to directly identify and record these moves, avoiding unnecessary steps. We efficiently achieve this by searching for the specific pattern that indicates a valid move.

Here's how the algorithm would work step-by-step:

Go through the string from beginning to end.
Look for places where two plus signs are next to each other.
If you find two adjacent plus signs, that's a valid move. Remember this move.
Once you have found all the possible moves, you have your answer. There is no need to explore other possibilities or combinations.

Code Implementation

def generate_possible_moves(current_state):
    possible_moves = []

    # Iterate through the string to find adjacent plus signs
    for index in range(len(current_state) - 1):
        # Check for two adjacent plus signs, indicating a valid move.
        if current_state[index:index+2] == '++':

            # Store the valid move
            possible_moves.append(index)

    return possible_moves

Big(O) Analysis

Time Complexity

O(n) – The algorithm iterates through the input string once, examining each character to identify pairs of adjacent plus signs. The primary cost is determined by the number of characters (n) in the string. Since each character is visited and inspected a constant number of times, the runtime scales linearly with the length of the string, resulting in O(n) time complexity.

Space Complexity

O(N) – The algorithm iterates through the string of length N and stores valid moves. The description mentions recording each valid move, which implies storing these moves in an auxiliary data structure such as a list or an array. In the worst-case scenario, every pair of adjacent characters could be '++', leading to a maximum of N/2 possible moves that need to be stored. Therefore, the space complexity is proportional to the size of the input string, N, and simplifies to O(N).

Edge Cases

Case	How to Handle
Null or empty input string	Return an empty list immediately as no flips are possible.
Input string shorter than 2 characters	Return an empty list because there are no possible '++' sequences.
Input string contains characters other than '+' or '-'	Throw an IllegalArgumentException or return an error list, depending on the requirements.
Input string contains only '-' characters	Return an empty list as there are no '++' sequences to flip.
Input string consists entirely of '+' characters	Return a list containing a single string with the first two characters flipped to '--'.
Input string with a single '++' sequence at the beginning	Add the flipped string to the result list.
Input string with multiple overlapping '++' sequences	Ensure that each '++' sequence is flipped independently, generating all possible valid states.
Very long input string (potential performance bottleneck)	Iterating through the string once to identify and flip the '++' sequences should provide linear time complexity, which scales well.

Solution

Clarifying Questions

When you get asked this question in a real-life environment, it will often be ambiguous (especially at FAANG). Make sure to ask these questions in that case:

Can the input string contain characters other than '+' and '-'?
Is the input string guaranteed to be non-null?
What should I return if there are no possible flips?
How large can the input string be?
Should the returned list of strings be in any particular order?

Brute Force Solution

Approach

The game involves flipping adjacent '++' to '--' in a string. A brute force method involves trying every single possible flip and seeing what new strings we can create, one by one.

Here's how the algorithm would work step-by-step:

Look at the string from beginning to end, checking each pair of adjacent characters.
Whenever you find a '++', consider flipping it to '--'.
Make a copy of the string, do the flip, and save this new string as a possible next move.
Continue scanning the string and repeating this flipping process for every '++' pair you find, generating all possible next moves.
Do this until there are no more '++' pairs left in the original string.

Code Implementation

def generate_possible_next_moves(current_state):
    possible_moves = []
    string_length = len(current_state)

    for index in range(string_length - 1):
        # Check if the adjacent characters are '++'
        if current_state[index:index+2] == '++':

            # Create a new state with the flip
            new_state = list(current_state)
            new_state[index] = '-'
            new_state[index+1] = '-'
            possible_moves.append("".join(new_state))

    return possible_moves

Big(O) Analysis

Time Complexity

Space Complexity

Optimal Solution

Approach

Here's how the algorithm would work step-by-step:

Go through the string from beginning to end.
Look for places where two plus signs are next to each other.
If you find two adjacent plus signs, that's a valid move. Remember this move.
Once you have found all the possible moves, you have your answer. There is no need to explore other possibilities or combinations.

Code Implementation

def generate_possible_moves(current_state):
    possible_moves = []

    # Iterate through the string to find adjacent plus signs
    for index in range(len(current_state) - 1):
        # Check for two adjacent plus signs, indicating a valid move.
        if current_state[index:index+2] == '++':

            # Store the valid move
            possible_moves.append(index)

    return possible_moves

Big(O) Analysis

Time Complexity

Space Complexity

Edge Cases

Case	How to Handle
Null or empty input string	Return an empty list immediately as no flips are possible.
Input string shorter than 2 characters	Return an empty list because there are no possible '++' sequences.
Input string contains characters other than '+' or '-'	Throw an IllegalArgumentException or return an error list, depending on the requirements.
Input string contains only '-' characters	Return an empty list as there are no '++' sequences to flip.
Input string consists entirely of '+' characters	Return a list containing a single string with the first two characters flipped to '--'.
Input string with a single '++' sequence at the beginning	Add the flipped string to the result list.
Input string with multiple overlapping '++' sequences	Ensure that each '++' sequence is flipped independently, generating all possible valid states.
Very long input string (potential performance bottleneck)	Iterating through the string once to identify and flip the '++' sequences should provide linear time complexity, which scales well.