0-1 Knapsack problem (Small quantity)
(Mylib/Typical/knapsack_small_quantity.cpp)

• View this file on GitHub
• Last update: 2021-04-23 23:44:44+09:00
• Link: View error logs on GitHub Actions

Operations

• knapsack_small_quantity(int N, Weight cap, Weight w[N], Value v[N])
  • 0-1ナップサック問題を解く。
  • Time complexity $O(2^{N/2} N)$

Requirements

Notes

Problems

• AOJ DPL_1_H Huge Knapsack Problem

References

Verified with

• test/aoj/DPL_1_H/main.test.cpp

Code

#pragma once
#include <algorithm>
#include <iterator>
#include <map>
#include <vector>

namespace haar_lib {
  template <typename Weight, typename Value>
  Value knapsack_small_quantity(int N, Weight cap, const std::vector<Weight> &w, const std::vector<Value> &v) {
    const int p = N / 2;
    const int q = N - p;

    std::vector<std::pair<Weight, Value>> a, b;
    a.reserve(1 << p);
    b.reserve(1 << q);

    a.emplace_back(0, 0);
    b.emplace_back(0, 0);

    for (int i = 0; i < p; ++i) {
      const int k      = a.size();
      const auto begin = a.begin();
      const auto end   = a.end();

      for (auto it = begin; it != end; ++it) {
        a.emplace_back(it->first + w[i], it->second + v[i]);
      }

      std::inplace_merge(a.begin(), a.begin() + k, a.end());
    }

    for (int i = p; i < p + q; ++i) {
      const int k      = b.size();
      const auto begin = b.begin();
      const auto end   = b.end();

      for (auto it = begin; it != end; ++it) {
        b.emplace_back(it->first + w[i], it->second + v[i]);
      }

      std::inplace_merge(b.begin(), b.begin() + k, b.end());
    }

    for (size_t i = 1; i < a.size(); ++i) {
      a[i].second = std::max(a[i].second, a[i - 1].second);
    }

    for (size_t i = 1; i < b.size(); ++i) {
      b[i].second = std::max(b[i].second, b[i - 1].second);
    }

    Value ret = 0;

    for (int i = 0, j = (int) b.size() - 1; i < (int) a.size(); ++i) {
      while (j >= 0 and a[i].first + b[j].first > cap) --j;
      if (j < 0) break;
      ret = std::max(ret, a[i].second + b[j].second);
    }

    return ret;
  }
}  // namespace haar_lib

#line 2 "Mylib/Typical/knapsack_small_quantity.cpp"
#include <algorithm>
#include <iterator>
#include <map>
#include <vector>

namespace haar_lib {
  template <typename Weight, typename Value>
  Value knapsack_small_quantity(int N, Weight cap, const std::vector<Weight> &w, const std::vector<Value> &v) {
    const int p = N / 2;
    const int q = N - p;

    std::vector<std::pair<Weight, Value>> a, b;
    a.reserve(1 << p);
    b.reserve(1 << q);

    a.emplace_back(0, 0);
    b.emplace_back(0, 0);

    for (int i = 0; i < p; ++i) {
      const int k      = a.size();
      const auto begin = a.begin();
      const auto end   = a.end();

      for (auto it = begin; it != end; ++it) {
        a.emplace_back(it->first + w[i], it->second + v[i]);
      }

      std::inplace_merge(a.begin(), a.begin() + k, a.end());
    }

    for (int i = p; i < p + q; ++i) {
      const int k      = b.size();
      const auto begin = b.begin();
      const auto end   = b.end();

      for (auto it = begin; it != end; ++it) {
        b.emplace_back(it->first + w[i], it->second + v[i]);
      }

      std::inplace_merge(b.begin(), b.begin() + k, b.end());
    }

    for (size_t i = 1; i < a.size(); ++i) {
      a[i].second = std::max(a[i].second, a[i - 1].second);
    }

    for (size_t i = 1; i < b.size(); ++i) {
      b[i].second = std::max(b[i].second, b[i - 1].second);
    }

    Value ret = 0;

    for (int i = 0, j = (int) b.size() - 1; i < (int) a.size(); ++i) {
      while (j >= 0 and a[i].first + b[j].first > cap) --j;
      if (j < 0) break;
      ret = std::max(ret, a[i].second + b[j].second);
    }

    return ret;
  }
}  // namespace haar_lib

Back to top page