DP(Dynamic Programming) demo: optimal substructure(recursion) + overlapping structure(memo)

#quote from 'introduction to computation and programming using python,# revised edition, MIT'class Item(object):      def __init__(self, n, v, w):          self.name = n          self.value = float(v)          self.weight = float(w)      def getName(self):          return self.name      def getValue(self):          return self.value      def getWeight(self):          return self.weight      def __str__(self):          result = '<' + self.name + ', ' + str(self.value)\                 + ', ' + str(self.weight) + '>'          return result          def fastMaxVal(toConsider, avail, memo = {}):         """Asumes toConsider a list of items, avail a weight         memo used only by recursive calls       Returns a tuple of the total weight of a solution to the         0/1 knapsack problem and the items of that solution"""    if (len(toConsider), avail) in memo:         result = memo[(len(toConsider), avail)]    elif toConsider == [] or avail == 0:        result = (0, ())    elif toConsider[0].getWeight() > avail:        #Explore right branch only        result = fastMaxVal(toConsider[1:], avail, memo)    else:        nextItem = toConsider[0]        #Explore left branch        withVal, withToTake =\                 fastMaxVal(toConsider[1:],                            avail - nextItem.getWeight(), memo)        withVal += nextItem.getValue()        #Explore right branch        withoutVal, withoutToTake = fastMaxVal(toConsider[1:],                                            avail, memo)        #Choose better branch        if withVal > withoutVal:            result = (withVal, withToTake + (nextItem,))        else:            result = (withoutVal, withoutToTake)    memo[(len(toConsider), avail)] = result    return result               def smallTest():    names = ['a', 'b', 'c', 'd']    vals = [6, 7, 8, 9]    weights = [3, 3, 2, 5]    Items = []    for i in range(len(vals)):        Items.append(Item(names[i], vals[i], weights[i]))    val, taken = fastMaxVal(Items, 5)    for item in taken:        print item    print 'Total value of items taken =', val