# 000920-Number-of-Music-Playlists

### Problem

<https://leetcode.com/problems/number-of-music-playlists/description/>

Your music player contains n different songs. You want to listen to goal songs (not necessarily different) during your trip. To avoid boredom, you will 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. Given n, goal, and k, return the number of possible playlists that you can create. Since the answer can be very large, return it modulo 109 + 7.

Example 1:

Input: n = 3, goal = 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], and \[3, 2, 1].

Example 2:

Input: n = 2, goal = 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], and \[1, 2, 2].

Example 3:

Input: n = 2, goal = 3, k = 1 Output: 2 Explanation: There are 2 possible playlists: \[1, 2, 1] and \[2, 1, 2].

Constraints:

0 <= k < n <= goal <= 100

### Solution

```python
class Solution:
    def numMusicPlaylists(self, n: int, goal: int, k: int) -> int:
        MOD = 10**9 + 7
        # dp[i][j] represents the number of possible playlists with i and j distinct songs
        dp = [[0] * (goal+1) for _ in range(n+1)]
        dp[0][0] = 1
        for i in range(1, n+1):
            for j in range(i, goal+1):
                # 1. choose a new song, --> dp[i-1][j-1]*(n-i+1)
                # 2. choose a song already been played --> dp[i][j-1]*max(i-k,0)
                dp[i][j] = (dp[i-1][j-1]*(n-i+1) + dp[i][j-1]*max(i-k,0)) % MOD

        return dp[n][goal] 
```


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://snowan.gitbook.io/study-notes/leetcode/python/000920-number-of-music-playlists.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.