LeetCode – Flip Game II (Java)

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.

For example, given s = “++++”, return true. The starting player can guarantee a win by flipping the middle “++” to become “+–+”.

Java Solution

This problem is solved by backtracking.

public boolean canWin(String s) {
    if(s==null||s.length()==0){
        return false;
    }
 
   return canWinHelper(s.toCharArray()); 
}
 
public boolean canWinHelper(char[] arr){
    for(int i=0; i<arr.length-1;i++){
        if(arr[i]=='+'&&arr[i+1]=='+'){
            arr[i]='-';
            arr[i+1]='-';
 
            boolean win = canWinHelper(arr);
 
            arr[i]='+';
            arr[i+1]='+';
 
            //if there is a flip which makes the other player lose, the first play wins
            if(!win){
                return true;
            }
        }
    }
 
    return false;
}

Time Complexity

Roughly, the time is n*n*…n, which is O(n^n). The reason is each recursion takes O(n) and there are totally n recursions.