Task: Knapsack problem_Bounded


C++: #include <iostream>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <memory>
#include <sys/time.h>

using std::cout;
using std::endl;

class StopTimer
{
public:
    StopTimer(): begin_(getUsec()) {}
    unsigned long long getTime() const { return getUsec() - begin_; }
private:
    static unsigned long long getUsec()
    {
        timeval tv;
        const int res = ::gettimeofday(&tv, 0);
        if(res)
            return 0;
        return tv.tv_usec + 1000000 * tv.tv_sec;
    }
    unsigned long long begin_;
};

struct KnapsackTask
{
    struct Item
    {
        std::string name;
        unsigned w, v, qty;
        Item(): w(), v(), qty() {}
        Item(const std::string& iname, unsigned iw, unsigned iv, unsigned iqty):
            name(iname), w(iw), v(iv), qty(iqty)
        {}
    };
    typedef std::vector<Item> Items;
    struct Solution
    {
        unsigned v, w;
        unsigned long long iterations, usec;
        std::vector<unsigned> n;
        Solution(): v(), w(), iterations(), usec() {}
    };
    
    KnapsackTask(): maxWeight_(), totalWeight_() {}
    void add(const Item& item)
    {
        const unsigned totalItemWeight = item.w * item.qty;
        if(const bool invalidItem = !totalItemWeight)
            throw std::logic_error("Invalid item: " + item.name);
        totalWeight_ += totalItemWeight;
        items_.push_back(item);
    }
    const Items& getItems() const { return items_; }
    void setMaxWeight(unsigned maxWeight) { maxWeight_ = maxWeight; }
    unsigned getMaxWeight() const { return std::min(totalWeight_, maxWeight_); }

private:
    unsigned maxWeight_, totalWeight_;
    Items items_;
};

class BoundedKnapsackRecursiveSolver
{
public:
    typedef KnapsackTask Task;
    typedef Task::Item Item;
    typedef Task::Items Items;
    typedef Task::Solution Solution;

    void solve(const Task& task)
    {
        Impl(task, solution_).solve();
    }
    const Solution& getSolution() const { return solution_; }
private:
    class Impl
    {
        struct Candidate
        {
            unsigned v, n;
            bool visited;
            Candidate(): v(), n(), visited(false) {}
        };
        typedef std::vector<Candidate> Cache;
    public:
        Impl(const Task& task, Solution& solution):
            items_(task.getItems()),
            maxWeight_(task.getMaxWeight()),
            maxColumnIndex_(task.getItems().size() - 1),
            solution_(solution),
            cache_(task.getMaxWeight() * task.getItems().size()),
            iterations_(0)
        {}
        void solve()
        {
            if(const bool nothingToSolve = !maxWeight_ || items_.empty())
                return;
            StopTimer timer;
            Candidate candidate;
            solve(candidate, maxWeight_, items_.size() - 1);
            convertToSolution(candidate);
            solution_.usec = timer.getTime();
        }
    private:
        void solve(Candidate& current, unsigned reminderWeight, const unsigned itemIndex)
        {
            ++iterations_;

            const Item& item(items_[itemIndex]);

            if(const bool firstColumn = !itemIndex)
            {
                const unsigned maxQty = std::min(item.qty, reminderWeight/item.w);
                current.v = item.v * maxQty;
                current.n = maxQty;
                current.visited = true;
            }
            else
            {
                const unsigned nextItemIndex = itemIndex - 1;
                {
                    Candidate& nextItem = cachedItem(reminderWeight, nextItemIndex);
                    if(!nextItem.visited)
                        solve(nextItem, reminderWeight, nextItemIndex);
                    current.visited = true;
                    current.v = nextItem.v;
                    current.n = 0;
                }
                if(reminderWeight >= item.w)
                {
                    for (unsigned numberOfItems = 1; numberOfItems <= item.qty; ++numberOfItems)
                    {
                        reminderWeight -= item.w;
                        Candidate& nextItem = cachedItem(reminderWeight, nextItemIndex);
                        if(!nextItem.visited)
                            solve(nextItem, reminderWeight, nextItemIndex);

                        const unsigned checkValue = nextItem.v + numberOfItems * item.v;
                        if ( checkValue > current.v)
                        {
                            current.v = checkValue;
                            current.n = numberOfItems;
                        }
                        if(!(reminderWeight >= item.w))
                            break;
                    }
                }
            }
        }
        void convertToSolution(const Candidate& candidate)
        {
            solution_.iterations = iterations_;
            solution_.v = candidate.v;
            solution_.n.resize(items_.size());

            const Candidate* iter = &candidate;
            unsigned weight = maxWeight_, itemIndex = items_.size() - 1;
            while(true)
            {
                const unsigned currentWeight = iter->n * items_[itemIndex].w;
                solution_.n[itemIndex] = iter->n;
                weight -= currentWeight;
                if(!itemIndex--)
                    break;
                iter = &cachedItem(weight, itemIndex);
            }
            solution_.w = maxWeight_ - weight;
        }
        Candidate& cachedItem(unsigned weight, unsigned itemIndex)
        {
            return cache_[weight * maxColumnIndex_ + itemIndex];
        }
        const Items& items_;
        const unsigned maxWeight_;
        const unsigned maxColumnIndex_;
        Solution& solution_;
        Cache cache_;
        unsigned long long iterations_;
    };
    Solution solution_;
};

void populateDataset(KnapsackTask& task)
{
    typedef KnapsackTask::Item Item;
    task.setMaxWeight( 400 );
    task.add(Item("map",9,150,1));
    task.add(Item("compass",13,35,1));
    task.add(Item("water",153,200,2));
    task.add(Item("sandwich",50,60,2));
    task.add(Item("glucose",15,60,2));
    task.add(Item("tin",68,45,3));
    task.add(Item("banana",27,60,3));
    task.add(Item("apple",39,40,3));
    task.add(Item("cheese",23,30,1));
    task.add(Item("beer",52,10,3));
    task.add(Item("suntancream",11,70,1));
    task.add(Item("camera",32,30,1));
    task.add(Item("T-shirt",24,15,2));
    task.add(Item("trousers",48,10,2));
    task.add(Item("umbrella",73,40,1));
    task.add(Item("w-trousers",42,70,1));
    task.add(Item("w-overclothes",43,75,1));
    task.add(Item("note-case",22,80,1));
    task.add(Item("sunglasses",7,20,1));
    task.add(Item("towel",18,12,2));
    task.add(Item("socks",4,50,1));
    task.add(Item("book",30,10,2));
}

int main()
{
    KnapsackTask task;
    populateDataset(task);

    BoundedKnapsackRecursiveSolver solver;
    solver.solve(task);
    const KnapsackTask::Solution& solution = solver.getSolution();

    cout << "Iterations to solve: " << solution.iterations << endl;
    cout << "Time to solve: " << solution.usec << " usec" << endl;
    cout << "Solution:" << endl;
    for (unsigned i = 0; i < solution.n.size(); ++i)
    {
        if (const bool itemIsNotInKnapsack = !solution.n[i])
            continue;
        cout << "  " << solution.n[i] << ' ' << task.getItems()[i].name << " ( item weight = " << task.getItems()[i].w << " )" << endl;
    }

    cout << "Weight: " << solution.w << " Value: " << solution.v << endl;
    return 0;
}



Go: package main

import "fmt"

type Item struct {
	name               string
	weight, value, qty int
}

var items = []Item{
	{"map",			9,	150,	1},
	{"compass",		13,	35,	1},
	{"water",		153,	200,	2},
	{"sandwich",		50,	60,	2},
	{"glucose",		15,	60,	2},
	{"tin",			68,	45,	3},
	{"banana",		27,	60,	3},
	{"apple",		39,	40,	3},
	{"cheese",		23,	30,	1},
	{"beer",		52,	10,	3},
	{"suntancream",		11,	70,	1},
	{"camera",		32,	30,	1},
	{"T-shirt",		24,	15,	2},
	{"trousers",		48,	10,	2},
	{"umbrella",		73,	40,	1},
	{"w-trousers",		42,	70,	1},
	{"w-overclothes",	43,	75,	1},
	{"note-case",		22,	80,	1},
	{"sunglasses",		7,      20,	1},
	{"towel",		18,	12,	2},
	{"socks",		4,      50,	1},
	{"book",		30,	10,	2},
}

type Chooser struct {
	Items []Item
	cache map[key]solution
}

type key struct {
	w, p int
}

type solution struct {
	v, w int
	qty  []int
}

func (c Chooser) Choose(limit int) (w, v int, qty []int) {
	c.cache = make(map[key]solution)
	s := c.rchoose(limit, len(c.Items)-1)
	c.cache = nil 
	return s.v, s.w, s.qty
}

func (c Chooser) rchoose(limit, pos int) solution {
	if pos < 0 || limit <= 0 {
		return solution{0, 0, nil}
	}

	key := key{limit, pos}
	if s, ok := c.cache[key]; ok {
		return s
	}

	best_i, best := 0, solution{0, 0, nil}
	for i := 0; i*items[pos].weight <= limit && i <= items[pos].qty; i++ {
		sol := c.rchoose(limit-i*items[pos].weight, pos-1)
		sol.v += i * items[pos].value
		if sol.v > best.v {
			best_i, best = i, sol
		}
	}

	if best_i > 0 {
		
		
		
		old := best.qty
		best.qty = make([]int, len(items))
		copy(best.qty, old)
		best.qty[pos] = best_i
		best.w += best_i * items[pos].weight
	}
	c.cache[key] = best
	return best
}

func main() {
	v, w, s := Chooser{Items: items}.Choose(400)

	fmt.Println("Taking:")
	for i, t := range s {
		if t > 0 {
			fmt.Printf("  %d of %d %s\n", t, items[i].qty, items[i].name)
		}
	}
	fmt.Printf("Value: %d; weight: %d\n", v, w)
}