编写 DBSCAN密度聚类算法，绘制数据集的聚类结果

好的，下面是代码实现和聚类结果的绘制：

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import make_moons

# 生成数据集
X, y = make_moons(n_samples=200, noise=0.05, random_state=0)

# 计算两个点之间的距离
def euclidean_distance(x1, x2):
    return np.sqrt(np.sum((x1 - x2)**2))

# DBSCAN聚类算法
def dbscan(X, eps, min_samples):
    # 初始化簇标记数组
    labels = np.zeros(len(X))
    # 初始化簇编号
    cluster = 0
    # 遍历数据集中的每个点
    for i in range(len(X)):
        # 如果该点已经被分配到某个簇中，则跳过
        if labels[i] != 0:
            continue
        # 获取该点的邻居
        neighbors = get_neighbors(X, i, eps)
        # 如果邻居数量小于min_samples，则将该点标记为噪声
        if len(neighbors) < min_samples:
            labels[i] = -1
        # 否则，创建一个新簇，并将该点及其邻居分配给该簇
        else:
            cluster += 1
            labels[i] = cluster
            expand_cluster(X, labels, i, neighbors, cluster, eps, min_samples)
    return labels

# 获取某个点的邻居
def get_neighbors(X, i, eps):
    neighbors = []
    for j in range(len(X)):
        if i == j:
            continue
        dist = euclidean_distance(X[i], X[j])
        if dist <= eps:
            neighbors.append(j)
    return neighbors

# 将某个簇扩展为所有可达的点
def expand_cluster(X, labels, i, neighbors, cluster, eps, min_samples):
    # 遍历邻居中的每个点
    for j in neighbors:
        # 如果该点未被分配到任何簇中，则将其分配给当前簇
        if labels[j] == 0:
            labels[j] = cluster
            # 获取该点的邻居
            new_neighbors = get_neighbors(X, j, eps)
            # 如果该点的邻居数量大于等于min_samples，则将其邻居加入当前簇
            if len(new_neighbors) >= min_samples:
                neighbors += new_neighbors
        # 如果该点被标记为噪声，则将其重新分配给当前簇
        elif labels[j] == -1:
            labels[j] = cluster

# 设置eps和min_samples参数
eps = 0.3
min_samples = 5

# 运行DBSCAN算法
labels = dbscan(X, eps, min_samples)

# 绘制聚类结果
plt.scatter(X[:, 0], X[:, 1], c=labels, cmap='viridis')
plt.title('DBSCAN Clustering')
plt.show()

运行结果如下图所示：