[Swift]LeetCode920. 播放列表的数量 | Number of Music Playlists

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Your music player contains N different songs and she wants to listen to L (not necessarily different) songs during your trip.  You create a playlist so that:

• Every song is played at least once
• A song can only be played again only if K other songs have been played

Return the number of possible playlists.  As the answer can be very large, return it modulo 10^9 + 7.

 Example 1:

Input: N = 3, L = 3, K = 1
Output: 6
Explanation: There are 6 possible playlists. [1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1].

Example 2:

Input: N = 2, L = 3, K = 0
Output: 6
Explanation: There are 6 possible playlists. [1, 1, 2], [1, 2, 1], [2, 1, 1], [2, 2, 1], [2, 1, 2], [1, 2, 2]

Example 3:

Input: N = 2, L = 3, K = 1
Output: 2
Explanation: There are 2 possible playlists. [1, 2, 1], [2, 1, 2]

 Note:

1. 0 <= K < N <= L <= 100

---

你的音乐播放器里有 N 首不同的歌，在旅途中，你的旅伴想要听 L 首歌（不一定不同，即，允许歌曲重复）。请你为她按如下规则创建一个播放列表：

• 每首歌至少播放一次。
• 一首歌只有在其他 K 首歌播放完之后才能再次播放。

返回可以满足要求的播放列表的数量。由于答案可能非常大，请返回它模 10^9 + 7 的结果。

 示例 1：

输入：N = 3, L = 3, K = 1
输出：6
解释：有 6 种可能的播放列表。[1, 2, 3]，[1, 3, 2]，[2, 1, 3]，[2, 3, 1]，[3, 1, 2]，[3, 2, 1].

示例 2：

输入：N = 2, L = 3, K = 0
输出：6
解释：有 6 种可能的播放列表。[1, 1, 2]，[1, 2, 1]，[2, 1, 1]，[2, 2, 1]，[2, 1, 2]，[1, 2, 2]

示例 3：

输入：N = 2, L = 3, K = 1
输出：2
解释：有 2 种可能的播放列表。[1, 2, 1]，[2, 1, 2]

 提示：

1. 0 <= K < N <= L <= 100

---

56 ms

class Solution {
    func numMusicPlaylists(_ N: Int, _ L: Int, _ K: Int) -> Int {
        var mod:Int = 1000000007
        var dp = Array(repeating:0, count: N+1)
        dp[0] = 1
        for i in 0..<L
        {
            var ndp = Array(repeating:0, count: N+1)
            for j in 0..<N
            {
                ndp[j + 1] += dp[j] * (N-j)
                ndp[j + 1] %= mod
            }
            for j in 0...N
            {
                ndp[j] += dp[j] * max(j - K, 0)
                ndp[j] %= mod
            }
            dp = ndp
        }
        return Int(dp[N])
    }
}