How do I check date ranges for overlap and save them for later, when i need to filter?

Question

Hey guys i'm relatively new to python and i have this problem that i cant solve. i need to create a python code which works like a scheduler for a hotel reception. it has to search in a list which contain the single bookings. these specific bookings contain the arrival and departure date but i dont know how to check and compare those ranges. i have limited amount of room, so thats another criteria.

rooms = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
booking = []
booking_id = 0

def make_booking():

    bframe = Tk()
    bframe.geometry('200x150+150+150')
    bframe.title('New booking')
    nameLabel = Label(bframe, text='Name').grid(row=0, column=0)
    name = Entry(bframe)
    name.grid(row=0, column=1)
    ArrivalLabel = Label(bframe, text='Arrival in: DD.MM.YYYY').grid(row=2, column=0)
    arrival = Entry(bframe)
    arrival.grid(row=2, column=1)
    deptLabel = Label(bframe, text='Departure in: DD.MM.YYYY').grid(row=3, column=0)
    dept = Entry(bframe)
    dept.grid(row=3, column=1)

def save_booking():
    arrival = time.strptime(arrival.get(), "%d.%m.%y")
    dept = time.strptime(dept.get(), "%d.%m.%y")
    global booking_id
    booking_id += 1
    b = [booking_id, name.get(), arrival, dept]
    booking.append(b)




    else:
        messagebox.showinfo(title="Whops", message="""
    Something went wrong with your booking entry. Did you check the room availability?""")
    bframe.destroy()
saveButton = Button(bframe, text="Save", command=save_booking).grid(row=4, column=0)

this is my code atm. the else case is from my older version which kinda worked but didnt check for the room availabilty for a certain date range

def save_booking():
    b = (name.get(), room_number.get(), arrival.get(), dept.get())
    if rooms[int(room_number.get())] == 0:
        global booking_id
        booking_id += 1
        b.append(booking_id)
        rooms[int(room_number.get())] = b

any ideas on how to solve this?