给定数据集，设计程序计算数据集的熵和信息增益

以下是Python代码，可以计算数据集的熵和信息增益：

import math

# 计算数据集的熵
def entropy(data):
    total = len(data)
    label_counts = {}
    for row in data:
        label = row[-1]
        if label not in label_counts:
            label_counts[label] = 0
        label_counts[label] += 1
    entropy = 0.0
    for label in label_counts:
        prob = float(label_counts[label]) / total
        entropy -= prob * math.log(prob, 2)
    return entropy

# 计算数据集在某个特征下的信息增益
def information_gain(data, feature):
    total = len(data)
    feature_counts = {}
    for row in data:
        value = row[feature]
        if value not in feature_counts:
            feature_counts[value] = 0
        feature_counts[value] += 1
    feature_entropy = 0.0
    for value in feature_counts:
        prob = float(feature_counts[value]) / total
        subset = [row for row in data if row[feature] == value]
        feature_entropy += prob * entropy(subset)
    return entropy(data) - feature_entropy

其中，`data`是一个二维列表，每行代表一个样本，最后一列是样本的标签；`entropy`函数计算数据集的熵，`information_gain`函数计算数据集在某个特征下的信息增益。可以通过调用这两个函数来计算数据集的熵和每个特征的信息增益。