import math

def logBaseB (B,N):
   """ Return the log of N to the base B
   >>> logBaseB(2,16) 
   4.0
   """
   if N == 0: return 1
   else:    return math.log(N) / math.log(B)

def entropy(classes,examples):
   """ Return the entropy of a set of examples.
       classes is a list of the classes
       examples is a list of the class values of the examples
   """
   print("Examples:",examples)
   classProbs = {}
   for c in classes:
      classProbs[c] = 0
   for c in examples:
      classProbs[c] += 1
   for c in classes:
      classProbs[c] = classProbs[c] / float(len(examples))
   n = len(classes)
   print("The maximum entropy is logBaseB(2,",end="",sep="")
   print(n,")=",format(logBaseB(2,n),".3f"),sep="")
   ent = 0
   for c in classes:
      #print "c:", c, "p(c):", classProbs[c],"log(p(c))",logBaseB(2,classProbs[c])
      ent = ent + -1 * classProbs[c] * logBaseB(2,classProbs[c])
   print("Entropy:",format(ent,".3f"))
   return ent

def entropy1(classProbs):
   """ Returns entropy given the class probabilities.
       classProbs is a list, where classProb[i] is the proportion
        of the examples that have the ith class value
   """
   print("")
   p = [format(c,".3f") for c in classProbs]
   p.sort()
   print("Probabilities:", p)
   n = len(classProbs)
   print("The maximum entropy is logBaseB(2,",n,")=",format(logBaseB(2,n),".3f"),sep="")
   ent = 0
   for c in classProbs:
      #print "c", c, "log(c)",logBaseB(2,c)
      ent = ent + -1 * c * logBaseB(2,c)
   print("Entropy:",format(ent,".3f"))      
   return ent

print("==")
x = entropy([1,2],[1,1,1,1,1,1,1,1,1,1,1])
x = entropy1([1.0,0.0])
print("==")
x = entropy([1,2,3,4,5],[1,1,2,2,3,3,4,4,5,5])
x = entropy1([.2,.2,.2,.2,.2])
print("==")
x = entropy([1,2,3,4,5,6,7,8],[1,1,1,2,3,4,4,5,5,6,6,7,7,8,8])
x = entropy1([3.0/15.0,1.0/15.0,1.0/15.0,2.0/15.0,2.0/15.0,2.0/15.0,2.0/15.0,2.0/15.0])
print("==")
x = entropy([1,2],[1,1,1,2,2,2,2,2,2,2,2,2])
x = entropy1([3.0/12.0,9.0/12.0])
print("==")
x = entropy([1,2],[1,1,1,1,1,1,1,2])
x = entropy1([7.0/8.0,1.0/8.0])
print("==")
x = entropy([1,2],[1,1,1,1,1,1,1,1,1,1,2])
x = entropy1([10.0/11.0,1.0/11.0])
print("==")
x = entropy([1,2,3],[1,1,1,1,1,1,2,2,3,3,3,3])
x = entropy1([6/12.0,2/12.0,4/12.0])
print("==")
x = entropy([1,2,3],[1,1,1,1,3,3,3,2,3,3,3,3])
x = entropy1([4/12.0,1/12.0,7/12.0])
print("==")
x = entropy([1,2],[1,1,1,1,2,2])
x = entropy1([4/6,2/6])