import pandas as pd

# Auxiliary functions (unchanged)
def aggregate_data(data, interval):
    all_minutes = pd.DataFrame({'interval_group': range(0, 1440, interval)})
    result = []
    for date in data['date'].unique():
        day_data = data[data['date'] == date].copy()
        day_data['interval_group'] = (day_data['minute_of_day'] // interval) * interval
        agg = day_data.groupby('interval_group').size().reset_index(name='tweet_count')
        complete_data = all_minutes.merge(agg, on='interval_group', how='left').fillna({'tweet_count': 0})
        complete_data['date'] = date
        result.append(complete_data)
    return pd.concat(result, ignore_index=True)


def generate_xticks(interval):
    if interval <= 5:
        tick_step = 60
    elif interval <= 10:
        tick_step = 60
    elif interval <= 30:
        tick_step = 120
    else:
        tick_step = 240
    ticks = list(range(0, 1440, tick_step))
    tick_labels = [f"{m // 60:02d}:{m % 60:02d}" for m in ticks]
    return ticks, tick_labels


def minutes_to_time(minutes):
    hours = minutes // 60
    mins = minutes % 60
    return f"{hours:02d}:{mins:02d}"