README.md

464. Can I Win

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 1:

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.

Example 2:

Input: maxChoosableInteger = 10, desiredTotal = 0
Output: true

Example 3:

Input: maxChoosableInteger = 10, desiredTotal = 1
Output: true

Constraints:

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

Solutions (Python)

1. Solution

from functools import cache


class Solution:
    def canIWin(self, maxChoosableInteger: int, desiredTotal: int) -> bool:
        @cache
        def canIWinWithUsed(usedmask: int) -> bool:
            total = sum(i + 1 for i in range(maxChoosableInteger)
                        if (usedmask >> i) & 1 == 1)

            for i in range(maxChoosableInteger):
                if (usedmask >> i) & 1 == 0:
                    if total + i + 1 >= desiredTotal or not canIWinWithUsed(usedmask | (1 << i)):
                        return True

            return False

        return sum(range(1, maxChoosableInteger + 1)) >= desiredTotal and canIWinWithUsed(0)