Description

In the "100 game" two players take turns adding, to a running total, any integer from 1 to 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 from 1 to 15 without replacement until they reach a total >= 100.

Given two integers maxChoosableInteger and desiredTotal, return true if the first player to move can force a win, otherwise, return false. Assume both players play optimally.

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.

Tips

1 <= maxChoosableInteger <= 20
0 <= desiredTotal <= 300

分析

      一个 target 数用可以有多种组合方式。使用最少个数字的组成是我们需要求的，如果是奇数，则是 alice win 否则就是 bob 赢。
比如 n == 20 时，目标数在 1-20 内肯定是 alice win。 目标在 21-39 内肯定是 bob win。依次类推（需要注意的是 ）。
虽然 1-20 内中数字 10 也可以用两个数字 （ 2 +8， 1+9， 来实现，但是组合它的最少数字个数是 1， 所以是 alice win


待实现

总结