import numpy as np
from sklearn.cluster import KMeans
import matplotlib.pyplot as plt

# Generate random data
np.random.seed(42)
X = np.random.rand(100, 2)

# Run KMeans for k=1 to k=10 and record the inertia (sum of squared distances)
inertias = []
for k in range(1, 11):
    kmeans = KMeans(n_clusters=k, random_state=42).fit(X)
    inertias.append(kmeans.inertia_)

# Plot the elbow curve
plt.plot(range(1, 11), inertias, '-o')
plt.xlabel('Number of clusters (k)')
plt.ylabel('Inertia')
plt.title('Elbow curve')
plt.show()