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920. Number of Music Playlists

中文文档

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

Python3

class Solution:
    def numMusicPlaylists(self, n: int, goal: int, k: int) -> int:
        mod = 10**9 + 7
        f = [[0] * (n + 1) for _ in range(goal + 1)]
        f[0][0] = 1
        for i in range(1, goal + 1):
            for j in range(1, n + 1):
                f[i][j] += f[i - 1][j - 1] * (n - j + 1)
                if j >= k:
                    f[i][j] += f[i - 1][j] * (j - k)
                f[i][j] %= mod
        return f[goal][n]

Java

class Solution {
    public int numMusicPlaylists(int n, int goal, int k) {
        final int mod = (int) 1e9 + 7;
        long[][] f = new long[goal + 1][n + 1];
        f[0][0] = 1;
        for (int i = 1; i <= goal; ++i) {
            for (int j = 1; j <= n; ++j) {
                f[i][j] += f[i - 1][j - 1] * (n - j + 1);
                if (j >= k) {
                    f[i][j] += f[i - 1][j] * (j - k);
                }
                f[i][j] %= mod;
            }
        }
        return (int) f[goal][n];
    }
}

C++

class Solution {
public:
    int numMusicPlaylists(int n, int goal, int k) {
        const int mod = 1e9 + 7;
        long long f[goal + 1][n + 1];
        memset(f, 0, sizeof(f));
        f[0][0] = 1;
        for (int i = 1; i <= goal; ++i) {
            for (int j = 1; j <= n; ++j) {
                f[i][j] += f[i - 1][j - 1] * (n - j + 1);
                if (j >= k) {
                    f[i][j] += f[i - 1][j] * (j - k);
                }
                f[i][j] %= mod;
            }
        }
        return f[goal][n];
    }
};

Go

func numMusicPlaylists(n int, goal int, k int) int {
	const mod = 1e9 + 7
	f := make([][]int, goal+1)
	for i := range f {
		f[i] = make([]int, n+1)
	}
	f[0][0] = 1
	for i := 1; i <= goal; i++ {
		for j := 1; j <= n; j++ {
			f[i][j] += f[i-1][j-1] * (n - j + 1)
			if j >= k {
				f[i][j] += f[i-1][j] * (j - k)
			}
			f[i][j] %= mod
		}
	}
	return f[goal][n]
}

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