Let Tickets be a random access list
Let Rating(i) be the user rating of the ith song

Initialization:
	Tickets[0] = 0
	For (i=1 to SongNumber-1)
		Tickets[i] = (L[i-1] + Rating(i-1))

	RatingSum = Tickets[SongNumber-1] + Rating(SongNumber-1)
	TicketSum = RatingSum



Select Next Song:
	rnd = Random from 0 to TicketSum-1

	// Use binary search to find the next song
	left = 0
	right = SongNumber-1
	While (left < right) Do
		i = left + ((left + right) / 2)
		If (Tickets[i] > rnd)
			right = i-1
		Else
			left = i

		If (left == right)
			next_song = i

	// Update the ticket sum
	If (next_song == SongNumber-1)
		TicketSum = TicketSum + TicketSum - Tickets[next_song]
	Else
		TicketSum = TicketSum + Tickets[next_song+1] - Tickets[next_song]
	TicketSum = TicketSum + RatingSum

	// Update the individual tickets
	For (i=1 to next_song)
		Tickets[i] = Min(Tickets[i] + Rating(i-1) - Tickets[i-1] , MaxTickets) + Tickets[i-1]
	If (next_song < SongNumber-1)
		Tickets[next_song+1] = Tickets[next_song]
	For (i=next_song+2 to SongNumber-1)
		Tickets[i] = Min(Tickets[i] + Rating(i-1) - Tickets[i-1] , MaxTickets) + Tickets[i-1]

	Return next_song