knapsack_test.cc

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/*
                          Aleph_w
 
  Data structures & Algorithms
  version 2.0.0b
  https://github.com/lrleon/Aleph-w
 
  This file is part of Aleph-w library
 
  Copyright (c) 2002-2026 Leandro Rabindranath Leon
 
  Permission is hereby granted, free of charge, to any person obtaining a copy
  of this software and associated documentation files (the "Software"), to deal
  in the Software without restriction, including without limitation the rights
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  copies of the Software, and to permit persons to whom the Software is
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  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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*/
 
 
# include <gtest/gtest.h>
 
# include <algorithm>
# include <cstdint>
# include <limits>
# include <random>
 
# include <Knapsack.H>
 
using namespace Aleph;
 
using Item = Knapsack_Item<int, int>;
 
namespace
{
  int selected_value(const Array<Item> & items,
                     const Array<size_t> & selected)
  {
    int total = 0;
    for (size_t i = 0; i < selected.size(); ++i)
      total += items[selected[i]].value;
    return total;
  }
 
  int selected_weight(const Array<Item> & items,
                      const Array<size_t> & selected)
  {
    int total = 0;
    for (size_t i = 0; i < selected.size(); ++i)
      total += items[selected[i]].weight;
    return total;
  }
 
  int brute_force_knapsack_01(const Array<Item> & items, const int capacity)
  {
    const size_t n = items.size();
    const uint64_t total_masks = uint64_t(1) << n;
    int best = 0;
 
    for (uint64_t mask = 0; mask < total_masks; ++mask)
      {
        int w = 0, v = 0;
        for (size_t i = 0; i < n; ++i)
          if (mask & (uint64_t(1) << i))
            {
              w += items[i].weight;
              v += items[i].value;
            }
        if (w <= capacity and v > best)
          best = v;
      }
 
    return best;
  }
 
  int brute_force_bounded(const Array<Item> & items, const Array<size_t> & counts,
                          const int capacity, const size_t i = 0)
  {
    if (i == items.size())
      return 0;
 
    int best = brute_force_bounded(items, counts, capacity, i + 1);
    const int wi = items[i].weight;
    const int vi = items[i].value;
 
    if (wi == 0)
      {
        if (vi > 0 and counts[i] > 0)
          best = std::max(best,
                          static_cast<int>(counts[i]) * vi
                          + brute_force_bounded(items, counts, capacity, i + 1));
        return best;
      }
 
    for (size_t take = 1; take <= counts[i]; ++take)
      {
        const int weight = static_cast<int>(take) * wi;
        if (weight > capacity)
          break;
        best = std::max(best,
                        static_cast<int>(take) * vi
                        + brute_force_bounded(items, counts,
                                              capacity - weight, i + 1));
      }
 
    return best;
  }
 
  int brute_force_unbounded(const Array<Item> & items,
                            const int capacity, const size_t i = 0)
  {
    if (i == items.size())
      return 0;
 
    int best = brute_force_unbounded(items, capacity, i + 1);
    const int wi = items[i].weight;
    const int vi = items[i].value;
 
    if (wi <= 0)
      return best;
 
    for (int take = 1; take * wi <= capacity; ++take)
      best = std::max(best,
                      take * vi + brute_force_unbounded(items,
                                                        capacity - take * wi,
                                                        i + 1));
 
    return best;
  }
} // namespace
 
 
TEST(Knapsack01, EmptyItems)
{
  Array<Item> items;
  auto r = knapsack_01(items, 10);
  EXPECT_EQ(r.optimal_value, 0);
  EXPECT_EQ(r.selected_items.size(), 0u);
}
 
TEST(Knapsack01, ZeroCapacity)
{
  Array<Item> items = {{5, 10}, {3, 7}};
  auto r = knapsack_01(items, 0);
  EXPECT_EQ(r.optimal_value, 0);
}
 
TEST(Knapsack01, ClassicExample)
{
  // Items: (weight, value): (2,3), (3,4), (4,5), (5,6)
  // Capacity = 8
  // Best: items 1,2,3 (w=3+4+5=12 too heavy), items 0,1,2 (w=2+3+4=9 too heavy)
  // items 0,2 (w=2+4=6, v=3+5=8), items 1,3 (w=3+5=8, v=4+6=10)
  Array<Item> items = {{2, 3}, {3, 4}, {4, 5}, {5, 6}};
  auto r = knapsack_01(items, 8);
  EXPECT_EQ(r.optimal_value, 10);
 
  // Verify selected items have correct total weight and value
  int total_w = 0, total_v = 0;
  for (size_t k = 0; k < r.selected_items.size(); ++k)
    {
      const auto & it = items[r.selected_items[k]];
      total_w += it.weight;
      total_v += it.value;
    }
  EXPECT_EQ(total_v, r.optimal_value);
  EXPECT_LE(total_w, 8);
}
 
TEST(Knapsack01, AllFit)
{
  Array<Item> items = {{1, 10}, {1, 20}, {1, 30}};
  auto r = knapsack_01(items, 100);
  EXPECT_EQ(r.optimal_value, 60);
  EXPECT_EQ(r.selected_items.size(), 3u);
}
 
TEST(Knapsack01, ValueOnly)
{
  Array<Item> items = {{2, 3}, {3, 4}, {4, 5}, {5, 6}};
  EXPECT_EQ(knapsack_01_value(items, 8), 10);
}
 
TEST(Knapsack01, NegativeCapacity)
{
  Array<Item> items = {{1, 1}};
  EXPECT_THROW(knapsack_01(items, -1), std::domain_error);
  EXPECT_THROW(knapsack_01_value(items, -1), std::domain_error);
}
 
TEST(Knapsack01, ZeroWeightItemsAtZeroCapacity)
{
  Array<Item> items = {{0, 5}, {0, 2}, {2, 7}};
  const auto r = knapsack_01(items, 0);
  EXPECT_EQ(r.optimal_value, 7);
  EXPECT_EQ(selected_weight(items, r.selected_items), 0);
  EXPECT_EQ(selected_value(items, r.selected_items), 7);
  EXPECT_EQ(knapsack_01_value(items, 0), 7);
}
 
TEST(Knapsack, NegativeWeightRejected)
{
  Array<Item> bad = {{-1, 10}, {2, 3}};
  Array<size_t> counts = {1, 1};
 
  EXPECT_THROW(knapsack_01(bad, 10), std::domain_error);
  EXPECT_THROW(knapsack_01_value(bad, 10), std::domain_error);
  EXPECT_THROW(knapsack_unbounded(bad, 10), std::domain_error);
  EXPECT_THROW(knapsack_bounded(bad, counts, 10), std::domain_error);
}
 
TEST(KnapsackUnbounded, Classic)
{
  // Items: (weight, value): (1,1), (3,4), (4,5)
  // Capacity = 7
  // Best unbounded: 2 * item1 (w=6,v=8) + 1 * item0 (w=1,v=1) = v=9
  // Or: 1 * item2 (w=4,v=5) + 1 * item1 (w=3,v=4) = v=9
  Array<Item> items = {{1, 1}, {3, 4}, {4, 5}};
  auto r = knapsack_unbounded(items, 7);
  EXPECT_EQ(r.optimal_value, 9);
 
  // Verify weight
  int total_w = 0;
  for (size_t k = 0; k < r.selected_items.size(); ++k)
    total_w += items[r.selected_items[k]].weight;
  EXPECT_LE(total_w, 7);
}
 
TEST(KnapsackUnbounded, ZeroWeightPositiveValueRejected)
{
  Array<Item> items = {{0, 1}, {3, 4}};
  EXPECT_THROW(knapsack_unbounded(items, 7), std::domain_error);
}
 
TEST(KnapsackUnbounded, Empty)
{
  Array<Item> items;
  auto r = knapsack_unbounded(items, 10);
  EXPECT_EQ(r.optimal_value, 0);
}
 
TEST(KnapsackBounded, Classic)
{
  // Item 0: w=2, v=3, count=2
  // Item 1: w=3, v=5, count=1
  // Capacity = 7
  // Best: 2 * item0 (w=4,v=6) + 1 * item1 (w=3,v=5) = w=7, v=11
  Array<Item> items = {{2, 3}, {3, 5}};
  Array<size_t> counts = {2, 1};
  auto r = knapsack_bounded(items, counts, 7);
  EXPECT_EQ(r.optimal_value, 11);
 
  // Verify weight and count constraints
  int total_w = 0, total_v = 0;
  Array<size_t> used = Array<size_t>::create(items.size());
  for (size_t i = 0; i < items.size(); ++i)
    used(i) = 0;
 
  for (size_t k = 0; k < r.selected_items.size(); ++k)
    {
      const size_t idx = r.selected_items[k];
      total_w += items[idx].weight;
      total_v += items[idx].value;
      used(idx)++;
    }
  EXPECT_EQ(total_v, r.optimal_value);
  EXPECT_LE(total_w, 7);
  for (size_t i = 0; i < items.size(); ++i)
    EXPECT_LE(used(i), counts[i]);
}
 
TEST(KnapsackBounded, SizeMismatch)
{
  Array<Item> items = {{1, 1}};
  Array<size_t> counts = {1, 2};
  EXPECT_THROW(knapsack_bounded(items, counts, 10), std::invalid_argument);
}
 
TEST(Knapsack01, RandomVsBruteForce)
{
  std::mt19937 rng(123456);
  for (int trial = 0; trial < 80; ++trial)
    {
      const size_t n = 1 + rng() % 10;
      const int capacity = static_cast<int>(rng() % 14);
      Array<Item> items;
      items.reserve(n);
 
      for (size_t i = 0; i < n; ++i)
        {
          const int w = static_cast<int>(rng() % 7);      // includes zero
          const int v = static_cast<int>(rng() % 19) - 4; // may be negative
          items.append(Item{w, v});
        }
 
      const auto r = knapsack_01(items, capacity);
      const int brute = brute_force_knapsack_01(items, capacity);
      const int value_only = knapsack_01_value(items, capacity);
 
      EXPECT_EQ(r.optimal_value, brute);
      EXPECT_EQ(value_only, brute);
      EXPECT_EQ(selected_value(items, r.selected_items), r.optimal_value);
      EXPECT_LE(selected_weight(items, r.selected_items), capacity);
    }
}
 
TEST(KnapsackUnbounded, RandomVsBruteForce)
{
  std::mt19937 rng(424242);
  for (int trial = 0; trial < 60; ++trial)
    {
      const size_t n = 1 + rng() % 7;
      const int capacity = 1 + static_cast<int>(rng() % 16);
      Array<Item> items;
      items.reserve(n);
 
      for (size_t i = 0; i < n; ++i)
        {
          const int w = 1 + static_cast<int>(rng() % 6);  // strictly positive
          const int v = static_cast<int>(rng() % 16) - 3;
          items.append(Item{w, v});
        }
 
      const auto r = knapsack_unbounded(items, capacity);
      const int brute = brute_force_unbounded(items, capacity);
      EXPECT_EQ(r.optimal_value, brute);
      EXPECT_EQ(selected_value(items, r.selected_items), r.optimal_value);
      EXPECT_LE(selected_weight(items, r.selected_items), capacity);
    }
}
 
TEST(KnapsackBounded, RandomVsBruteForce)
{
  std::mt19937 rng(777);
  for (int trial = 0; trial < 60; ++trial)
    {
      const size_t n = 1 + rng() % 8;
      const int capacity = static_cast<int>(rng() % 15);
      Array<Item> items;
      Array<size_t> counts;
      items.reserve(n);
      counts.reserve(n);
 
      for (size_t i = 0; i < n; ++i)
        {
          const int w = static_cast<int>(rng() % 5);      // includes zero
          const int v = static_cast<int>(rng() % 17) - 2;
          const size_t c = static_cast<size_t>(rng() % 4);
          items.append(Item{w, v});
          counts.append(c);
        }
 
      const auto r = knapsack_bounded(items, counts, capacity);
      const int brute = brute_force_bounded(items, counts, capacity);
      EXPECT_EQ(r.optimal_value, brute);
      EXPECT_EQ(selected_value(items, r.selected_items), r.optimal_value);
      EXPECT_LE(selected_weight(items, r.selected_items), capacity);
 
      Array<size_t> used = Array<size_t>::create(n);
      for (size_t i = 0; i < n; ++i)
        used(i) = 0;
      for (size_t i = 0; i < r.selected_items.size(); ++i)
        ++used(r.selected_items[i]);
      for (size_t i = 0; i < n; ++i)
        EXPECT_LE(used(i), counts[i]);
    }
}