464 Can I Win

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464. Can I Win

题目描述

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

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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.

题目大意

提供两个整数 maxChoosableInteger 和 desiredTotal 两个玩家轮流从 1~maxChoosableInteger,直到 总和 >= desiredTotal，确定第一个玩家是否能获胜。 1~maxChoosableInteger 不能重复选择。

解题思路

通过 visited 数组记录是否数字是否已经被访问过。
map 记录当前组合是否被访问过。
简单粗暴的 DFS。

代码

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class Solution {
    func canIWin(_ maxChoosableInteger: Int, _ desiredTotal: Int) -> Bool {
        if desiredTotal <= maxChoosableInteger { return true }
        if (1+maxChoosableInteger)*maxChoosableInteger/2 < desiredTotal { return false }
        var visited = Array(repeating: false, count: maxChoosableInteger)
        var map = [Int: Bool]()
        func dfs(target: Int) -> Bool {
            let key = (visited.reduce(0) { (res, v) -> Int in
                var next = res << 1
                if v { next |= 1 }
                return next
            })
            if let v = map[key] { return v }
            for (i, v) in visited.enumerated() {
                if !v {
                    visited[i] = true
                    if target <= i + 1 || !dfs(target: target - i - 1) {
                        map[key] = true
                        visited[i] = false
                        return true
                    }
                    visited[i] = false
                }
            }
            map[key] = false
            return false
        }
        return dfs(target: desiredTotal)
    }
}
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