LeetCode [920] Number of Music Playlists

 920. Number of Music Playlists

Hard

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.

 

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:

1. 0 <= K < N <= L <= 100

Accepted

13,936

Submissions

29,137

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class Solution { long M = 1000000000+7; public int numMusicPlaylists(int N, int L, int K) { long[][] dp = new long[L][N]; for(int j=0; j<N; ++j){ dp[0][j] = j==0?N:0; } for(int i=1; i<L; ++i){ dp[i][0] = K==0?N:0; } for(int i=1; i<L; ++i){ for(int j=1; j<N; ++j){ dp[i][j] = dp[i-1][j-1]*(N-j)%M; if(j+1-K>0) dp[i][j] = (dp[i][j] + dp[i-1][j]*(j+1-K)%M)%M; } } return (int)dp[L-1][N-1]; } }