Number of Music Playlists — LeetCode 920 Python Solution

The problem

Your music player contains n different songs. You want to listen to goal songs (not necessarily different) during your trip.

Example

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].

Python solution

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]

Complexity

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 920. Number of Music Playlists is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.

The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.

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