Flip Game II

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 "+--+".

Follow up:

Derive your algorithm’s runtime complexity.

Solution:

  1. public class Solution {
  2.   public boolean canWin(String s) {
  3.     if (s == null || s.length() < 2) return false;
  5.     Map<String, Boolean> map = new HashMap<>();
  6.     return canWin(s, map);
  7.   }
  9.   public boolean canWin(String s, Map<String, Boolean> map){
  10.     if (map.containsKey(s)) return map.get(s);
  12.     for (int i = 0; i < s.length() - 1; i++) {
  13.       if (s.charAt(i) == '+' && s.charAt(i + 1) == '+') {
  15.         String sOpponent = s.substring(0, i) + "--" + s.substring(i + 2);
  16.         if (!canWin(sOpponent, map)) {
  17.           map.put(s, true);
  18.           return true;
  19.         }
  20.       }
  21.     }
  23.     map.put(s, false);
  24.     return false;
  25.   }
  26. }