920. 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

 

Solutions

Solution: Dynamic Programming

• Time complexity: O(goal * n)
• Space complexity: O(n)

 

JavaScript

/**
 * @param {number} n
 * @param {number} goal
 * @param {number} k
 * @return {number}
 */
const numMusicPlaylists = function (n, goal, k) {
  const MODULO = 10 ** 9 + 7;
  let dp = new Array(n + 1).fill(0);

  dp[0] = 1;

  for (let index = 1; index <= goal; index++) {
    const nextDp = new Array(n + 1).fill(0);

    for (let song = 1; song <= n; song++) {
      const newSongs = (dp[song - 1] * (n - (song - 1))) % MODULO;
      const oldSongs = (dp[song] * Math.max(0, song - k)) % MODULO;

      nextDp[song] = (newSongs + oldSongs) % MODULO;
    }
    dp = nextDp;
  }
  return dp[n];
};