0-1 Knapsack problem (Small weight)
(Mylib/Typical/knapsack_small_weight.cpp)

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• Last update: 2021-04-23 23:44:44+09:00
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Operations

• knapsack_small_weight(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 $O(N * cap)$

Requirements

Notes

Problems

• EDPC D - Knapsack 1

References

Verified with

• test/aoj/DPL_1_B/main.test.cpp

Code

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

namespace haar_lib {
  template <typename Weight, typename Value>
  Value knapsack_small_weight(int N, Weight cap, const std::vector<Weight> &w, const std::vector<Value> &v) {
    std::vector<std::vector<Value>> dp(N + 1, std::vector<Value>(cap + 1));

    for (int i = 0; i < N; ++i) {
      for (int j = 0; j <= cap; ++j) {
        dp[i + 1][j] = std::max(dp[i + 1][j], dp[i][j]);
        if (j + w[i] <= cap) dp[i + 1][j + w[i]] = std::max(dp[i + 1][j + w[i]], dp[i][j] + v[i]);
      }
    }

    return dp[N][cap];
  }
}  // namespace haar_lib

#line 2 "Mylib/Typical/knapsack_small_weight.cpp"
#include <algorithm>
#include <vector>

namespace haar_lib {
  template <typename Weight, typename Value>
  Value knapsack_small_weight(int N, Weight cap, const std::vector<Weight> &w, const std::vector<Value> &v) {
    std::vector<std::vector<Value>> dp(N + 1, std::vector<Value>(cap + 1));

    for (int i = 0; i < N; ++i) {
      for (int j = 0; j <= cap; ++j) {
        dp[i + 1][j] = std::max(dp[i + 1][j], dp[i][j]);
        if (j + w[i] <= cap) dp[i + 1][j + w[i]] = std::max(dp[i + 1][j + w[i]], dp[i][j] + v[i]);
      }
    }

    return dp[N][cap];
  }
}  // namespace haar_lib

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