DevExCode

920. Number of Music Playlists

MathDynamic ProgrammingCombinatorics

Explanation

To solve this problem, we can use dynamic programming. We can define a dp array where dp[i][j] represents the number of playlists of length i using j different songs. We can then iteratively fill in the dp array by considering the number of ways to choose the next song to add to the playlist.

At each step, we have two choices:

  1. If we have not yet reached the goal number of songs, we can add a new song to the playlist. This can be done in (n - j) ways.
  2. If we have reached the goal number of songs, we can choose from the songs that have already been played, but we need to ensure that no song repeats until k other songs have been played. This can be done in max(0, j - k) ways.

The final answer is stored in dp[goal][n].

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

View Leetcode Problem
class Solution {
    public int numMusicPlaylists(int n, int goal, int k) {
        int mod = 1000000007;
        long[][] dp = new long[goal + 1][n + 1];
        dp[0][0] = 1;

        for (int i = 1; i <= goal; i++) {
            for (int j = 1; j <= n; j++) {
                dp[i][j] += dp[i - 1][j - 1] * (n - j + 1);
                dp[i][j] += dp[i - 1][j] * Math.max(0, j - k);
                dp[i][j] %= mod;
            }
        }

        return (int) dp[goal][n];
    }
}

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