Description
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.
题目链接：https://leetcode.com/problems/number-of-music-playlists/
Difficulty: hard
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:
- 0 <= K < N <= L <= 100
分析
- updating
参考代码
from functools import lru_cache
class Solution:
def numMusicPlaylists(self, N, L, K):
@lru_cache(None)
def dp(i, j):
if i == 0:
return +(j == 0)
ans = dp(i-1, j-1) * (N-j+1)
ans += dp(i-1, j) * max(j-K, 0)
return ans % (10**9+7)
return dp(L, N)