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‎Problemset/0464-Can I Win/README.md

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# 464. Can I Win
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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.
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What if we change the game so that players **cannot** re-use integers?
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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.
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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**.
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#### Example 1:
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<pre>
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<strong>Input:</strong> maxChoosableInteger = 10, desiredTotal = 11
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<strong>Output:</strong> false
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<strong>Explanation:</strong>
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No matter which integer the first player choose, the first player will lose.
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The first player can choose an integer from 1 up to 10.
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If the first player choose 1, the second player can only choose integers from 2 up to 10.
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The second player will win by choosing 10 and get a total = 11, which is >= desiredTotal.
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Same with other integers chosen by the first player, the second player will always win.
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</pre>
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#### Example 2:
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<pre>
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<strong>Input:</strong> maxChoosableInteger = 10, desiredTotal = 0
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<strong>Output:</strong> true
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</pre>
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#### Example 3:
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<pre>
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<strong>Input:</strong> maxChoosableInteger = 10, desiredTotal = 1
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<strong>Output:</strong> true
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</pre>
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#### Constraints:
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* `1 <= maxChoosableInteger <= 20`
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* `0 <= desiredTotal <= 300`
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## Solutions (Python)
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### 1. Solution
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```Python
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from functools import cache
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class Solution:
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def canIWin(self, maxChoosableInteger: int, desiredTotal: int) -> bool:
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@cache
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def canIWinWithUsed(usedmask: int) -> bool:
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total = sum(i + 1 for i in range(maxChoosableInteger)
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if (usedmask >> i) & 1 == 1)
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for i in range(maxChoosableInteger):
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if (usedmask >> i) & 1 == 0:
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if total + i + 1 >= desiredTotal or not canIWinWithUsed(usedmask | (1 << i)):
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return True
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return False
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return sum(range(1, maxChoosableInteger + 1)) >= desiredTotal and canIWinWithUsed(0)
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```

‎Problemset/0464-Can I Win/README_CN.md

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# 464. 我能赢吗
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在 "100 game" 这个游戏中，两名玩家轮流选择从 `1` 到 `10` 的任意整数，累计整数和，先使得累计整数和 **达到或超过** 100 的玩家，即为胜者。
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如果我们将游戏规则改为 “玩家 **不能** 重复使用整数” 呢？
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例如，两个玩家可以轮流从公共整数池中抽取从 1 到 15 的整数（不放回），直到累计整数和 >= 100。
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给定两个整数 `maxChoosableInteger` （整数池中可选择的最大数）和 `desiredTotal`（累计和），若先出手的玩家能稳赢则返回 `true` ，否则返回 `false` 。假设两位玩家游戏时都表现 **最佳** 。
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#### 示例 1:
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<pre>
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<strong>输入:</strong> maxChoosableInteger = 10, desiredTotal = 11
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<strong>输出:</strong> false
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<strong>解释:</strong>
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无论第一个玩家选择哪个整数，他都会失败。
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第一个玩家可以选择从 1 到 10 的整数。
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如果第一个玩家选择 1，那么第二个玩家只能选择从 2 到 10 的整数。
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第二个玩家可以通过选择整数 10（那么累积和为 11 >= desiredTotal），从而取得胜利.
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同样地，第一个玩家选择任意其他整数，第二个玩家都会赢。
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</pre>
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#### 示例 2:
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<pre>
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<strong>输入:</strong> maxChoosableInteger = 10, desiredTotal = 0
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<strong>输出:</strong> true
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</pre>
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#### 示例 3:
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<pre>
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<strong>输入:</strong> maxChoosableInteger = 10, desiredTotal = 1
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<strong>输出:</strong> true
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</pre>
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#### 提示:
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* `1 <= maxChoosableInteger <= 20`
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* `0 <= desiredTotal <= 300`
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## 题解 (Python)
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### 1. 题解
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```Python
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from functools import cache
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class Solution:
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def canIWin(self, maxChoosableInteger: int, desiredTotal: int) -> bool:
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@cache
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def canIWinWithUsed(usedmask: int) -> bool:
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total = sum(i + 1 for i in range(maxChoosableInteger)
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if (usedmask >> i) & 1 == 1)
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for i in range(maxChoosableInteger):
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if (usedmask >> i) & 1 == 0:
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if total + i + 1 >= desiredTotal or not canIWinWithUsed(usedmask | (1 << i)):
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return True
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return False
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return sum(range(1, maxChoosableInteger + 1)) >= desiredTotal and canIWinWithUsed(0)
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```

‎Problemset/0464-Can I Win/Solution.py

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from functools import cache
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class Solution:
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def canIWin(self, maxChoosableInteger: int, desiredTotal: int) -> bool:
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@cache
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def canIWinWithUsed(usedmask: int) -> bool:
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total = sum(i + 1 for i in range(maxChoosableInteger)
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if (usedmask >> i) & 1 == 1)
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for i in range(maxChoosableInteger):
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if (usedmask >> i) & 1 == 0:
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if total + i + 1 >= desiredTotal or not canIWinWithUsed(usedmask | (1 << i)):
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return True
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return False
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return sum(range(1, maxChoosableInteger + 1)) >= desiredTotal and canIWinWithUsed(0)

‎README.md

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[461][461l] |[Hamming Distance][461] |![rs]
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[462][462l] |[Minimum Moves to Equal Array Elements II][462] |![rs]
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[463][463l] |[Island Perimeter][463] |![rs]
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[464][464l] |[Can I Win][464] |![py]
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[467][467l] |[Unique Substrings in Wraparound String][467] |![rb]&nbsp;&nbsp;![rs]
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[468][468l] |[Validate IP Address][468] |![rs]
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[470][470l] |[Implement Rand10() Using Rand7()][470] |![rs]
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[461]:Problemset/0461-Hamming%20Distance/README.md#461-hamming-distance
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[462]:Problemset/0462-Minimum%20Moves%20to%20Equal%20Array%20Elements%20II/README.md#462-minimum-moves-to-equal-array-elements-ii
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[463]:Problemset/0463-Island%20Perimeter/README.md#463-island-perimeter
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[464]:Problemset/0464-Can%20I%20Win/README.md#464-can-i-win
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[467]:Problemset/0467-Unique%20Substrings%20in%20Wraparound%20String/README.md#467-unique-substrings-in-wraparound-string
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[468]:Problemset/0468-Validate%20IP%20Address/README.md#468-validate-ip-address
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[470]:Problemset/0470-Implement%20Rand10\(\)%20Using%20Rand7\(\)/README.md#470-implement-rand10-using-rand7
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[461l]:https://leetcode.com/problems/hamming-distance/
37513753
[462l]:https://leetcode.com/problems/minimum-moves-to-equal-array-elements-ii/
37523754
[463l]:https://leetcode.com/problems/island-perimeter/
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[464l]:https://leetcode.com/problems/can-i-win/
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[467l]:https://leetcode.com/problems/unique-substrings-in-wraparound-string/
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[468l]:https://leetcode.com/problems/validate-ip-address/
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[470l]:https://leetcode.com/problems/implement-rand10-using-rand7/

‎README_CN.md

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[461][461l] |[汉明距离][461] |![rs]
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[462][462l] |[最少移动次数使数组元素相等 II][462] |![rs]
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[463][463l] |[岛屿的周长][463] |![rs]
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[464][464l] |[我能赢吗][464] |![py]
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[467][467l] |[环绕字符串中唯一的子字符串][467] |![rb]&nbsp;&nbsp;![rs]
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[468][468l] |[验证IP地址][468] |![rs]
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[470][470l] |[用 Rand7() 实现 Rand10()][470] |![rs]
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[461]:Problemset/0461-Hamming%20Distance/README_CN.md#461-汉明距离
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[462]:Problemset/0462-Minimum%20Moves%20to%20Equal%20Array%20Elements%20II/README_CN.md#462-最少移动次数使数组元素相等-ii
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[463]:Problemset/0463-Island%20Perimeter/README_CN.md#463-岛屿的周长
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[464]:Problemset/0464-Can%20I%20Win/README_CN.md#464-我能赢吗
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[467]:Problemset/0467-Unique%20Substrings%20in%20Wraparound%20String/README_CN.md#467-环绕字符串中唯一的子字符串
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[468]:Problemset/0468-Validate%20IP%20Address/README_CN.md#468-验证ip地址
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[470]:Problemset/0470-Implement%20Rand10\(\)%20Using%20Rand7\(\)/README_CN.md#470-用-Rand7-实现-Rand10
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[461l]:https://leetcode.cn/problems/hamming-distance/
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[462l]:https://leetcode.cn/problems/minimum-moves-to-equal-array-elements-ii/
37523754
[463l]:https://leetcode.cn/problems/island-perimeter/
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[464l]:https://leetcode.cn/problems/can-i-win/
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[467l]:https://leetcode.cn/problems/unique-substrings-in-wraparound-string/
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[468l]:https://leetcode.cn/problems/validate-ip-address/
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[470l]:https://leetcode.cn/problems/implement-rand10-using-rand7/

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