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

最新推荐文章于 2020-04-16 23:20:32 发布

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最新推荐文章于 2020-04-16 23:20:32 发布

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本文介绍了使用Python进行计算和编程的基础知识，通过定义classItem类并实现相关方法，展示如何解决0/1背包问题，提供了简化测试代码的实例。

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#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