def calcShannonEnt(dataSet): 
 #calculate the shannon value 
 numEntries = len(dataSet) 
 labelCounts = {} 
 for featVec in dataSet:  #create the dictionary for all of the data 
  currentLabel = featVec[-1] 
  if currentLabel not in labelCounts.keys(): 
   labelCounts[currentLabel] = 0 
  labelCounts[currentLabel] += 1 
 shannonEnt = 0.0 
 for key in labelCounts: 
  prob = float(labelCounts[key])/numEntries 
  shannonEnt -= prob*log(prob,2) #get the log value 
 return shannonEnt 

def createDataSet(): 
 dataSet = [[1,1,'yes'], 
    [1,1, 'yes'], 
    [1,0,'no'], 
    [0,1,'no'], 
    [0,1,'no']] 
 labels = ['no surfacing','flippers'] 
 return dataSet, labels 

def splitDataSet(dataSet, axis, value): 
 retDataSet = [] 
 for featVec in dataSet: 
  if featVec[axis] == value:  #abstract the fature 
   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)) 
   newEntropy +=prob * calcShannonEnt(subDataSet) 
  infoGain = baseEntropy - newEntropy 
  if(infoGain > bestInfoGain): 
   bestInfoGain = infoGain 
   bestFeature = i 
 return bestFeature 

def majorityCnt(classList): 
 classCount = {} 
 for vote in classList: 
  if vote not in classCount.keys(): classCount[vote] = 0 
  classCount[vote] += 1 
 sortedClassCount = sorted(classCount.iteritems(), key=operator.itemgetter(1), reverse=True) 
 return sortedClassCount[0][0] 

def createTree(dataSet, labels): 
 classList = [example[-1] for example in dataSet] 
 # the type is the same, so stop classify 
 if classList.count(classList[0]) == len(classList): 
  return classList[0] 
 # traversal all the features and choose the most frequent feature 
 if (len(dataSet[0]) == 1): 
  return majorityCnt(classList) 
 bestFeat = chooseBestFeatureToSplit(dataSet) 
 bestFeatLabel = labels[bestFeat] 
 myTree = {bestFeatLabel:{}} 
 del(labels[bestFeat]) 
 #get the list which attain the whole properties 
 featValues = [example[bestFeat] for example in dataSet] 
 uniqueVals = set(featValues) 
 for value in uniqueVals: 
  subLabels = labels[:] 
  myTree[bestFeatLabel][value] = createTree(splitDataSet(dataSet, bestFeat, value), subLabels) 
 return myTree 

myDat, labels = trees.createDataSet() 
myTree = trees.createTree(myDat,labels) 
print myTree 

def classify(inputTree, featLabels, testVec): 
 firstStr = inputTree.keys()[0] 
 secondDict = inputTree[firstStr] 
 featIndex = featLabels.index(firstStr) 
 for key in secondDict.keys(): 
  if testVec[featIndex] == key: 
   if type(secondDict[key]).__name__ == 'dict': 
    classLabel = classify(secondDict[key], featLabels, testVec) 
   else: classLabel = secondDict[key] 
 return classLabel