MusicSystem.java

import java.util.ArrayList;
import java.util.LinkedList;
import java.util.Random; 
import java.util.Queue; 

enum Genre
{
	POP,
	HIPHOP,
	JAZZ,
	FOLK,
	ROCK
}

class Song
{
	int songID;
	String singer;
	String song_name;
	Genre type;
	
	Song(int ID,String singer,String songname,Genre type)
	{
		this.songID=ID;
		this.singer=singer;
		this.song_name=songname;
		this.type=type;
	}
}

class MusicPlayer {
	
	ArrayList<Song> musiclist;
	Queue<Song> musicQ;
	int total_Song_Count;
	Random rand;
	
	MusicPlayer()
	{
		System.out.println("<<<<<< Initialize Music Player >>>>>>");
		musiclist=new ArrayList<Song>();
		rand = new Random();
		musicQ=new LinkedList<Song>();
		total_Song_Count=0;
	}
	
	void addSong(int ID,String singer,String songname,Genre type)
	{
		musiclist.add(total_Song_Count,new Song(ID,singer,songname,type));
		total_Song_Count++;
	}
	
	void playRandomSong()
	{
		int rand_int = rand.nextInt(total_Song_Count); 
		Song playingSong=musiclist.remove(rand_int);
		total_Song_Count--;
		musicQ.add(playingSong);
		System.out.println("The song : "+playingSong.song_name+" is been added to playing queue.");
		musiclist.add(playingSong);
	}
	
	void playSong(int ID,Boolean addtoQ)
	{
		for(int i=0;i<total_Song_Count;i++)
		{
			Song x=(Song)musiclist.get(i);
			if(x.songID==ID)
			{
				musiclist.remove(i);
				total_Song_Count--;
				if(addtoQ)
				{
					System.out.println("The song : "+x.song_name+" is been added to playing queue.");
					musicQ.add(x);
				}
				else
				{
					System.out.println("The song : "+x.song_name+" is currently played.");
				}
				musiclist.add(x);
				return;
			}
		}
		
		for(int i=total_Song_Count;i<musiclist.size();i++)
		{
			Song x=(Song)musiclist.get(i);
			if(x.songID==ID)
			{
				if(addtoQ)
				{
					System.out.println("The song : "+x.song_name+" is been added to playing queue.");
					musicQ.add(x);
				}
				else
				{
					System.out.println("The song : "+x.song_name+" is currently played.");
				}
				return;
			}
		}
		return;
	}
	
	void closeMusicPlayer()
	{
		System.out.println("<<<<<< Closing Music Player >>>>>>");
		musicQ.clear();
		total_Song_Count=musiclist.size();
	}
	
	void playMusicFromQueue()
	{
		//Play the song in the front of queue and remove it from the queue,
		//if queue is empty wait till songs come in the queue
		System.out.print("The current queue contains : [ ");
		for(Song s:musicQ)
		{
			System.out.println(s.song_name+" ");
		}
		System.out.println("]");
	}
	
}
public class MusicSystem {
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		MusicPlayer mp=new MusicPlayer();
		
		mp.addSong(1,"Maroon5","Memories",Genre.POP);
		mp.addSong(2,"Queen","Bohemian Rhapsody",Genre.ROCK);
		mp.addSong(3,"Led Zeppelin","Stairway to Heaven",Genre.ROCK);
		mp.addSong(4, "Lee Morgan", "Coera", Genre.JAZZ);
		mp.addSong(5,"BennyGoodman","Sing Sing Sing",Genre.JAZZ);
		mp.playMusicFromQueue();
		
		mp.playRandomSong();
		mp.playRandomSong();
		mp.playRandomSong();
		mp.playSong(3,true);
		mp.playSong(5,false);
		mp.playMusicFromQueue();
		
		mp.closeMusicPlayer();
		
		mp.playRandomSong();
		mp.playRandomSong();
		mp.playRandomSong();
		mp.playRandomSong();
		mp.playRandomSong();
		mp.playMusicFromQueue();	
	}

}

Good Approach !!!

Few things to note:

To play every song ( Particular song ) , It will take O( PlayListSize).
To Play Every Random Song , It will take again O(PlaylistSize) , Because while removing , you are shifting the entire Array Elements.
when you say “Don’t Repeat” , You don’t have to repeat a song untill all the songs in the play list are played . Once you have played all the songs randomly from the playlist , You can start fresh. But In your Implementation , there is no support to Choose a random song again once all the songs in the list is played.

How can we Improve the Time Complexity?

To overcome this problem ( Choosing Particular Song ) you can have additional Storage HashMap ( key — Song Id , Value -> Song location ), But I understand it will introduce Memory Complexity , But Always Time Complexity should be given Importance.
To overcome this ( Choosing Random Song) . Instead of removing that song and insert it from the last ( Which requires shift the entire list), You can swap the last element[Total_Song_Count] with the current random element and update the same in the HashMap . 
For Ex: List → [1,2,3,4] , Map — [ 1,0] , [2,1],[3,2],[4,3]
- Now Random song is 2
- Swap the last element with 2 -> [1,4,3,2] , Decrease the total count -> 3
- Update the HashMap -> [1,0][2,3][3,2][4,1]
The above set of Operation will take O(1) Complexity for sure.
Note: You don’t need to do this operation when Total_Song_Count is one.
To Overcome this one , You can provide support by Re-updating Total_Song_Count in PlayRandom function to PlayList Size when it becomes zero.

Any thoughts on this???