请给出C4.5算法的代码，并实现可视化

C4.5算法是一种经典的决策树算法，其代码实现涉及到数据处理和决策树构建等多个方面。这里给出一个简单的Python实现，并提供可视化代码。

首先，我们需要定义一个节点类，用于表示决策树中的每个节点：

class Node:
    def __init__(self, feature=None, threshold=None, label=None, left=None, right=None):
        self.feature = feature  # 划分特征
        self.threshold = threshold  # 划分阈值
        self.label = label  # 叶节点标签
        self.left = left  # 左子树
        self.right = right  # 右子树

接下来，我们需要实现C4.5算法中的关键步骤，包括计算信息熵、计算信息增益、选择最优划分特征等。下面是这些步骤的代码实现：

import numpy as np
from collections import Counter

def calc_entropy(y):
    """计算信息熵"""
    counter = Counter(y)
    probs = [val / len(y) for val in counter.values()]
    return -sum(p * np.log2(p) for p in probs)

def calc_cond_entropy(x, y, threshold):
    """计算条件熵"""
    left_idx = np.where(x <= threshold)[0]
    right_idx = np.where(x > threshold)[0]
    left_probs, right_probs = len(left_idx) / len(x), len(right_idx) / len(x)
    left_entropy, right_entropy = calc_entropy(y[left_idx]), calc_entropy(y[right_idx])
    return left_probs * left_entropy + right_probs * right_entropy

def calc_info_gain(x, y):
    """计算信息增益"""
    base_entropy = calc_entropy(y)
    best_gain, best_feature, best_threshold = 0, None, None
    for feature_idx in range(x.shape[1]):
        for threshold in np.unique(x[:, feature_idx]):
            cond_entropy = calc_cond_entropy(x[:, feature_idx], y, threshold)
            gain = base_entropy - cond_entropy
            if gain > best_gain:
                best_gain, best_feature, best_threshold = gain, feature_idx, threshold
    return best_gain, best_feature, best_threshold

接下来是C4.5算法的核心代码，即递归构建决策树的函数：

def build_tree(x, y, max_depth=None, min_samples_split=2, min_impurity_decrease=0):
    """构建决策树"""
    if max_depth is not None and max_depth == 0:
        return Node(label=Counter(y).most_common(1)[0][0])
    if len(y) < min_samples_split or calc_entropy(y) < min_impurity_decrease:
        return Node(label=Counter(y).most_common(1)[0][0])
    gain, feature_idx, threshold = calc_info_gain(x, y)
    if gain == 0:
        return Node(label=Counter(y).most_common(1)[0][0])
    left_idx, right_idx = np.where(x[:, feature_idx] <= threshold)[0], np.where(x[:, feature_idx] > threshold)[0]
    left = build_tree(x[left_idx], y[left_idx], max_depth=max_depth-1 if max_depth is not None else None,
                      min_samples_split=min_samples_split, min_impurity_decrease=min_impurity_decrease)
    right = build_tree(x[right_idx], y[right_idx], max_depth=max_depth-1 if max_depth is not None else None,
                       min_samples_split=min_samples_split, min_impurity_decrease=min_impurity_decrease)
    return Node(feature=feature_idx, threshold=threshold, left=left, right=right)

最后，我们可以使用graphviz库来可视化决策树。下面是可视化代码的实现：

from graphviz import Digraph

def visualize_tree(tree, dot=None):
    """可视化决策树"""
    if dot is None:
        dot = Digraph()
    if tree.label is not None:
        dot.node(str(id(tree)), label=str(tree.label), shape='box')
    else:
        dot.node(str(id(tree)), label=f'feature {tree.feature}\n<= {tree.threshold:.2f}')
        visualize_tree(tree.left, dot)
        visualize_tree(tree.right, dot)
        dot.edge(str(id(tree)), str(id(tree.left)), label='True')
        dot.edge(str(id(tree)), str(id(tree.right)), label='False')
    return dot

这样，我们就完成了C4.5算法的实现和可视化。完整代码如下：

import numpy as np
from collections import Counter
from graphviz import Digraph

class Node:
    def __init__(self, feature=None, threshold=None, label=None, left=None, right=None):
        self.feature = feature  # 划分特征
        self.threshold = threshold  # 划分阈值
        self.label = label  # 叶节点标签
        self.left = left  # 左子树
        self.right = right  # 右子树

def calc_entropy(y):
    """计算信息熵"""
    counter = Counter(y)
    probs = [val / len(y) for val in counter.values()]
    return -sum(p * np.log2(p) for p in probs)

def calc_cond_entropy(x, y, threshold):
    """计算条件熵"""
    left_idx = np.where(x <= threshold)[0]
    right_idx = np.where(x > threshold)[0]
    left_probs, right_probs = len(left_idx) / len(x), len(right_idx) / len(x)
    left_entropy, right_entropy = calc_entropy(y[left_idx]), calc_entropy(y[right_idx])
    return left_probs * left_entropy + right_probs * right_entropy

def calc_info_gain(x, y):
    """计算信息增益"""
    base_entropy = calc_entropy(y)
    best_gain, best_feature, best_threshold = 0, None, None
    for feature_idx in range(x.shape[1]):
        for threshold in np.unique(x[:, feature_idx]):
            cond_entropy = calc_cond_entropy(x[:, feature_idx], y, threshold)
            gain = base_entropy - cond_entropy
            if gain > best_gain:
                best_gain, best_feature, best_threshold = gain, feature_idx, threshold
    return best_gain, best_feature, best_threshold

def build_tree(x, y, max_depth=None, min_samples_split=2, min_impurity_decrease=0):
    """构建决策树"""
    if max_depth is not None and max_depth == 0:
        return Node(label=Counter(y).most_common(1)[0][0])
    if len(y) < min_samples_split or calc_entropy(y) < min_impurity_decrease:
        return Node(label=Counter(y).most_common(1)[0][0])
    gain, feature_idx, threshold = calc_info_gain(x, y)
    if gain == 0:
        return Node(label=Counter(y).most_common(1)[0][0])
    left_idx, right_idx = np.where(x[:, feature_idx] <= threshold)[0], np.where(x[:, feature_idx] > threshold)[0]
    left = build_tree(x[left_idx], y[left_idx], max_depth=max_depth-1 if max_depth is not None else None,
                      min_samples_split=min_samples_split, min_impurity_decrease=min_impurity_decrease)
    right = build_tree(x[right_idx], y[right_idx], max_depth=max_depth-1 if max_depth is not None else None,
                       min_samples_split=min_samples_split, min_impurity_decrease=min_impurity_decrease)
    return Node(feature=feature_idx, threshold=threshold, left=left, right=right)

def visualize_tree(tree, dot=None):
    """可视化决策树"""
    if dot is None:
        dot = Digraph()
    if tree.label is not None:
        dot.node(str(id(tree)), label=str(tree.label), shape='box')
    else:
        dot.node(str(id(tree)), label=f'feature {tree.feature}\n<= {tree.threshold:.2f}')
        visualize_tree(tree.left, dot)
        visualize_tree(tree.right, dot)
        dot.edge(str(id(tree)), str(id(tree.left)), label='True')
        dot.edge(str(id(tree)), str(id(tree.right)), label='False')
    return dot