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;
}

Python: 

import strformat
import tables


type Item = tuple[name: string; weight, value, pieces: int]


const Items: seq[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),
                           ("suntan cream", 11, 70, 1),
                           ("camera", 32, 30, 1),
                           ("T-shirt", 24, 15, 2),
                           ("trousers", 48, 10, 2),
                           ("umbrella", 73, 40, 1),
                           ("waterproof trousers", 42, 70, 1),
                           ("waterproof 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

  
  Number = range[0..Items.high]

  
  ExpandedItem = tuple[num: Number; weight, value: int]




proc expandedItems(items: seq[Item]): seq[ExpandedItem] =
  
  for idx, item in Items:
    for _ in 1..item.pieces:
      result.add((idx.Number, item.weight, item.value))

const ItemList = expandedItems(Items)

type

  
  ExpandedIndex = 0..ItemList.high

  
  Choice = tuple[indexes: set[ExpandedIndex]; weight, value: int]


var cache: Table[tuple[index, weight: int], Choice]




proc select(idx, weightLimit: int): Choice =
  

  if idx < 0 or weightLimit == 0:
    return

  if (idx, weightLimit) in cache:
    return cache[(idx, weightLimit)]

  let weight = ItemList[idx].weight
  if weight > weightLimit:
    return select(idx - 1, weightLimit)

  
  result = select(idx - 1, weightLimit)

  
  var result1 = select(idx - 1, weightLimit - weight)
  inc result1.value, ItemList[idx].value

  
  if result1.value > result.value:
    result = (result1.indexes + {idx.ExpandedIndex}, result1.weight + weight, result1.value)

  cache[(idx, weightLimit)] = result



let (indexes, weight, value) = select(ItemList.high, 400)


var pieces = newSeq[int](Items.len)
for idx in indexes:
  inc pieces[ItemList[idx].num]

echo "List of items:"
for num in 0..Items.high:
  if pieces[num] > 0:
    echo fmt"– {pieces[num]} of {Items[num].pieces} {Items[num].name}"
echo ""
echo "Total weight: ", weight
echo "Total value: ", value