一个背包算法的源代码

在工作中遇到一个奇怪的要求，给定空间和时间，要求将特定设备的配置最佳化，这就用到了“背包”算法，很有趣，我写了一个比较通用的算法（原理就是穷举），下面是源代码：

#include <vector>#include <cassert>#include <cmath>#include <iostream>template <typename _W, typename _V>class Choice{public:_W weight;_V value;Choice(_W _weight, _V _value): weight(_weight), value(_value){}};template <typename _W, typename _V>class Item: public std::vector< Choice<_W, _V> >{};template <typename _W, typename _V>class ItemList: public std::vector< Item<_W, _V> >{};class ItemChoiceIndexList: public std::vector<size_t>{};template <typename _W, typename _V>bool CalculateBestItemChoiceList(_W capacity,typename ItemList<_W, _V>::const_iterator item_begin,typename ItemList<_W, _V>::const_iterator item_end,ItemChoiceIndexList & retItemChoiceList,_W & retTotalWeight,_V & retTotalValue){assert(retItemChoiceList.empty());// 深度检测if(item_begin == item_end){retTotalWeight = 0;retTotalValue = 0;return true;}bool findMinChoiceList = false;_V maxTotalValue = 0;for(size_t choice_i = 0; choice_i < item_begin->size(); choice_i++){const Choice<_W, _V> & choice = (*item_begin)[choice_i];assert(choice.value > 0);// 如果当前选项大于总空间，本次组合不可选if(choice.weight > capacity){continue;}// 获取剩下总空间的最佳背包组合ItemChoiceIndexList retRemainingItemChoiceList;_W retRemainingTotalWeight;_V retRemainingTotalValue;if(!CalculateBestItemChoiceList(capacity - choice.weight,item_begin + 1,item_end,retRemainingItemChoiceList,retRemainingTotalWeight,retRemainingTotalValue)){continue;}// 如果这次的组合获得的剩余空间最小，这保存这次的组合if(retRemainingTotalValue + choice.value > maxTotalValue){findMinChoiceList = true;maxTotalValue = retRemainingTotalValue + choice.value;retItemChoiceList.clear();retItemChoiceList.push_back(choice_i);retItemChoiceList.insert(retItemChoiceList.end(), retRemainingItemChoiceList.begin(), retRemainingItemChoiceList.end());retTotalValue = maxTotalValue;retTotalWeight = retRemainingTotalWeight + choice.weight;}}// 没有找到合适的组合if(!findMinChoiceList){return false;}assert(!retItemChoiceList.empty());return true;}int main(int argc, char ** argv){typedef unsigned int WeightType;typedef float ValueType;// 初始化ItemList用以测试ItemList<WeightType, ValueType> itemList;const int item_count = 9;const int choice_count = 3;for(int i = 0; i < item_count; i++){Item<WeightType, ValueType> item;for(int w = 1; w < 2 * choice_count; w += 2){item.push_back(Choice<WeightType, ValueType>(w, sqrt((float)w)));}itemList.push_back(item);}// 设置总空间const WeightType capacity = 35;// 测试，并获得最小剩余空间ItemChoiceIndexList itemChoiceList;WeightType totalWeight;ValueType totalValue;if(!CalculateBestItemChoiceList(capacity,itemList.begin(),itemList.end(),itemChoiceList,totalWeight,totalValue)){std::cout << "cannot calculate best item choice list" << std::endl;}else{std::cout << "the best choice list: total = "<< capacity << ", remaining = " << capacity - totalWeight << std::endl;for(size_t i = 0; i < itemList.size(); i++){std::cout << "item [" << i << "]:";Item<WeightType, ValueType>::const_iterator choice_iter = itemList[i].begin();for(; choice_iter != itemList[i].end(); choice_iter++){std::cout << " (" << choice_iter->weight << ", " << choice_iter->value << ")";}std::cout << " choice: " << itemChoiceList[i] + 1 << std::endl;}}return 0;}