Can I Win — LeetCode 464 Python Solution

The problem

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.

Example

Input

maxChoosableInteger = 10, desiredTotal = 11

Output

false

Explanation

No matter which integer the first player choose, the first player will lose.

Python solution

class Solution:
    def canIWin(self, maxChoosableInteger: int, desiredTotal: int) -> bool:
        @cache
        def dfs(mask: int, s: int) -> bool:
            for i in range(1, maxChoosableInteger + 1):
                if mask >> i & 1 ^ 1:
                    if s + i >= desiredTotal or not dfs(mask | 1 << i, s + i):
                        return True
            return False

        if (1 + maxChoosableInteger) * maxChoosableInteger // 2 < desiredTotal:
            return False
        return dfs(0, 0)

Complexity

Pattern: Bit Manipulation

Use XOR, masks and the low-bit trick to replace whole data structures with an integer. LeetCode 464. Can I Win is filed here because LeetCode tags it Bit Manipulation and Bitmask, which is the vocabulary this hub collects.

The bit manipulation guide has the Python template for the pattern and the 194 LeetCode problems that use it.

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