464 Can I Win

464 Can I Win

• 題目描述：In the “100 game,” two players take turns adding, to a running total, any integer from 1..10. The player who first causes the running total to reach or exceed 100 wins.

  What if we change the game so that players cannot re-use integers?

  For example, two players might take turns drawing from a common pool of numbers of 1..15 without replacement until they reach a total >= 100.

  Given an integer maxChoosableInteger and another integer desiredTotal, determine if the first player to move can force a win, assuming both players play optimally.

  You can always assume that maxChoosableInteger will not be larger than 20 and desiredTotal will not be larger than 300.

• Example

  Input:
  maxChoosableInteger = 10
  desiredTotal = 11
  
  Output:
  false
  
  Explanation:
  No matter which integer the first player choose, the first player will lose.
  The first player can choose an integer from 1 up to 10.
  If the first player choose 1, the second player can only choose integers from 2 up to 10.
  The second player will win by choosing 10 and get a total = 11, which is >= desiredTotal.
  Same with other integers chosen by the first player, the second player will always win.

• 題目大意：兩個人猜數，給定兩個數，一個代表可以選擇的範圍maxChoosableInteger，一個代表目標數字desiredTotal，每個人可以從maxChoosableInteger選擇數字，但是數字不可重複選擇，給定maxChoosableInteger與desiredTotal判斷第一個人是否能獲勝

• 代碼

   public boolean canIWin(int maxChoosableInteger, int desiredTotal) {
        if (desiredTotal<=0) return true;
        if (maxChoosableInteger*(maxChoosableInteger+1)/2<desiredTotal) return false;
        return canIWin(desiredTotal, new int[maxChoosableInteger], new HashMap<>());
    }
    private boolean canIWin(int total, int[] state, HashMap<String, Boolean> hashMap) {
        String curr=Arrays.toString(state);
        if (hashMap.containsKey(curr)) return hashMap.get(curr);
        for (int i=0;i<state.length;i++) {
            if (state[i]==0) {
                state[i]=1;
  //                另一個人不能贏
                if (total<=i+1 || !canIWin(total-(i+1), state, hashMap)) {
                    hashMap.put(curr, true);
                    state[i]=0;
                    return true;
                }
                state[i]=0;
            }
        }
        hashMap.put(curr, false);
        return false;
    }