Number of music playlists

Math Dynamic Programming Combinatorics

60.0% acceptance

Feb 25, 2026

2462

206

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.

Solution

Rust

Time O(n * m)

Space O(n * m)

LeetCode

solution.rs

impl Solution {
  pub fn num_music_playlists(n: i32, goal: i32, k: i32) -> i32 {
    let md = 1_000_000_007i64;
    let (n, goal, k) = (n as usize, goal as usize, k as usize);
    let mut dp = vec![vec![0i64; n + 1]; goal + 1];
    dp[0][0] = 1;
    for i in 1..=goal {
      for j in 1..=n {
        dp[i][j] = (dp[i][j] + dp[i-1][j-1] * (n - (j - 1)) as i64) % md;
        if j > k { dp[i][j] = (dp[i][j] + dp[i-1][j] * (j - k) as i64) % md; }
      }
    }
    dp[goal][n] as i32
  }
}