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Flip Game

Solution Explanation for Flip Game

This problem asks to find all possible states of a string after one valid move. A valid move consists of flipping two consecutive '+' characters to '--'.

Approach: Iteration and String Manipulation

The most straightforward approach involves iterating through the input string and checking for consecutive '+' characters. If found, we perform the flip, add the resulting string to the list of possible next states, and then revert the flip to continue the search.

Time and Space Complexity Analysis

  • Time Complexity: O(n), where n is the length of the input string. We iterate through the string once. While we are creating new strings in the process, the string creation is a linear operation relative to the string length. The nested operations within the loop (modifying and adding strings) are constant time relative to n.

  • Space Complexity: O(n * k), where n is the length of the input string and k is the number of possible moves. In the worst case (many consecutive '++' pairs), we might create a number of new strings proportional to the number of occurrences of "++" subsequences. Each new string has a length of 'n'. If we only consider the space used by the resultant array of strings, it could be O(k) or O(n) depending on the worst-case scenario of input.

Code Implementation in Multiple Languages

The code below demonstrates the solution in several languages. The core logic remains consistent across all implementations.

Python:

def generatePossibleNextMoves(currentState: str) -> List[str]:
    result = []
    n = len(currentState)
    for i in range(n - 1):
        if currentState[i:i+2] == "++":
            next_state = list(currentState)  # Convert string to list for mutability
            next_state[i] = '-'
            next_state[i+1] = '-'
            result.append("".join(next_state))
    return result

Java:

import java.util.*;
 
class Solution {
    public List<String> generatePossibleNextMoves(String currentState) {
        List<String> result = new ArrayList<>();
        int n = currentState.length();
        for (int i = 0; i < n - 1; i++) {
            if (currentState.substring(i, i + 2).equals("++")) {
                String nextState = currentState.substring(0, i) + "--" + currentState.substring(i + 2);
                result.add(nextState);
            }
        }
        return result;
    }
}

C++:

#include <string>
#include <vector>
 
class Solution {
public:
    std::vector<std::string> generatePossibleNextMoves(std::string currentState) {
        std::vector<std::string> result;
        int n = currentState.length();
        for (int i = 0; i < n - 1; ++i) {
            if (currentState.substr(i, 2) == "++") {
                std::string nextState = currentState.substr(0, i) + "--" + currentState.substr(i + 2);
                result.push_back(nextState);
            }
        }
        return result;
    }
};

JavaScript:

/**
 * @param {string} currentState
 * @return {string[]}
 */
var generatePossibleNextMoves = function(currentState) {
    let result = [];
    for (let i = 0; i < currentState.length - 1; i++) {
        if (currentState.substring(i, i + 2) === "++") {
            let nextState = currentState.substring(0, i) + "--" + currentState.substring(i + 2);
            result.push(nextState);
        }
    }
    return result;
};

Go:

func generatePossibleNextMoves(currentState string) []string {
    result := []string{}
    for i := 0; i < len(currentState)-1; i++ {
        if currentState[i:i+2] == "++" {
            nextState := currentState[:i] + "--" + currentState[i+2:]
            result = append(result, nextState)
        }
    }
    return result
}

These implementations all follow the same basic algorithm, differing only in syntax and specific library functions used for string manipulation. The overall efficiency remains consistent across languages.