程式碼：

import numpy as np
import operator
#計算夏農熵,度量資料集的無序程度
def calcShannonEnt(dataSet):
    numEntries = len(dataSet)
    labelCountes = {}
    for featureVect in dataSet:
        currentLable = featureVect[-1]
        labelCountes[currentLable] = labelCountes.get(currentLable,0)+1
    shannonEnt = 0.0
    for key in labelCountes:
        prob = float(labelCountes[key]/numEntries)
        shannonEnt -= prob*np.log2(prob)
    return shannonEnt

#根據給定的特徵和該特徵的相應取值，劃分資料集
def splitDataSet(dataSet,axis,value):
    retDataSet = []
    for featVec in dataSet:
        if featVec[axis] == value:
            reducedFeatVec = featVec[:axis]
            reducedFeatVec.extend(featVec[axis+1:])
            retDataSet.append(reducedFeatVec)
    return retDataSet

def chooseBestFeatureToSplit(dataSet):
    numFeatures = len(dataSet[0]) - 1
    baseEntropy = calcShannonEnt(dataSet)
    bestInfoGain = 0.0
    bestFeature = -1
    for i in range(numFeatures):
        featList = [example[i] for example in dataSet]
        uniqueVals =set(featList)
        newEntropy = 0.0
        for value in uniqueVals:
            subDataSet = splitDataSet(dataSet,i,value)
            prob = len(subDataSet)/float(len(dataSet))
            #在熵函式裡面已經加過負號了
            newEntropy += prob*calcShannonEnt(subDataSet)
        infoGain = baseEntropy - newEntropy
        if infoGain > bestInfoGain:
            bestInfoGain = infoGain
            bestFeature = i
    return bestFeature

#如果用完所有特徵後，還有葉子節點裡面沒有統一的分類，則返回最多數對應的分類
def maiorityCnt(classList):
    classCount = {}
    for vote in classList:
        classCount[vote] = classCount.get(vote,0) + 1
    sortedClassCount = sorted(classCount.items(),operator.itemgetter(1),reverse=True)
    return sortedClassCount[0][0]

#建立樹函式程式碼,labels為特徵名
def createTree(dataSet,labels):
    classList = [example[-1] for example in dataSet]
    #如果全都是一個分類了，到達了遞迴終點,返回
    if classList.count(classList[0]) == len(classList):
        return classList[0]
    #遍歷完所有特徵後返回葉子節點中例項數目最多的類別，到達遞迴終點返回
    if len(dataSet[0]) == 1:
        return maiorityCnt(classList)
    #chooseBestFeatureToSplit 返回最好的特徵對應於資料集的列下標
    bestFeat = chooseBestFeatureToSplit(dataSet)
    bestFeatLable = labels[bestFeat]
    myTree = {bestFeatLable:{}}
    del(labels[bestFeat])
    featValues = [example[bestFeat] for example in dataSet]
    uniquVals =set(featValues)
    for value in uniquVals:
        subLables = labels[:]
        myTree[bestFeatLable][value] = createTree(splitDataSet(dataSet,bestFeat,value),subLables)
    return myTree



def createDataSet():
    dataSet = [[1,1,'yes'],[1,1,'yes'],[1,0,'no'],[0,1,'no'],[0,1,'no']]
    labels = ['水下能生存','有腳蹼']
    return dataSet,labels

if __name__ == '__main__':
    # dataset,labels = createDataSet()
    # shannonEnt = calcShannonEnt(dataset)
    # print(shannonEnt)
    # p = 1/5
    # a = p*np.log2(p)
    # print(-a*5)
    # vocabset = set([])
    # vocabset |= set(['a','b','c'])
    # print(vocabset)
    dataSet,labels = createDataSet()
    print(createTree(dataSet,labels))

 

 執行結果：