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// 920. Number of Music Playlists
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
/*
* 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, k', return the number of possible playlists that you can
* create. since the answer can be very large, return it modulo 10^9+7
*/
int numMusicPlaylists(int n, int goal, int k) {
const int mod = 1e9 + 7;
long **dp = (long **)calloc(goal + 1, sizeof(long *));
for (int i = 0; i < goal + 1; i++)
dp[i] = (long *)calloc(n + 1, sizeof(long));
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))) % mod;
dp[i][j] += (dp[i - 1][j] * (long)fmax(0, j - k)) % mod;
dp[i][j] %= mod;
}
int ans = dp[goal][n];
for (int i = 0; i < goal + 1; i++)
free(dp[i]);
free(dp);
return ans;
}
int main() {
printf("%d\n", numMusicPlaylists(3, 3, 1)); // expect: 6
printf("%d\n", numMusicPlaylists(2, 3, 0)); // expect: 6
printf("%d\n", numMusicPlaylists(2, 3, 1)); // expect: 2
}
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