import matplotlib.pyplot as plt
import seaborn as sns

def plot_engagement_heatmap(engagement_by_hour):
    """Plot engagement heatmap by time of day."""
    plt.figure(figsize=(10, 6))
    sns.heatmap(engagement_by_hour.pivot_table(index='hour', values='engagement_rate'), annot=True, cmap='YlGnBu')
    plt.title('Engagement Heatmap by Time of Day')
    plt.xlabel('Engagement Rate')
    plt.ylabel('Hour of Day')
    plt.show()

def plot_engagement_over_time(engagement_summary):
    """Plot engagement rate over time."""
    plt.figure(figsize=(10, 6))
    plt.plot(engagement_summary['posting_time'], engagement_summary['engagement_rate'])
    plt.title('Engagement Rate Over Time')
    plt.xlabel('Time')
    plt.ylabel('Engagement Rate')
    plt.show()