01背包 完全背包 多重背包

01背包

#include<iostream>
using namespace std;
int N, V;
int v[1002], w[1002];
int dp[1002];
int main()
{
  cin >> N >> V;
  for (int i = 1; i <= N; i++) {
    cin >> v[i] >> w[i];
  }
  for (int i = 1; i <= N; i++) {
    for (int j = V; j >= v[i]; j--)
      dp[j] = (dp[j] >= dp[j - v[i]] + w[i]) ? dp[j] : dp[j - v[i]] + w[i];
  }
  cout << dp[V] << endl;
  system("pause");
  return 0;
}

完全背包

#include<iostream>
using namespace std;
int N, V;
int v[1002], w[1002];
int dp[1002];
int main()
{
  cin >> N >> V;
  for (int i = 1; i <= N; i++) {
    cin >> v[i] >> w[i];
  }
  for (int i = 1; i <= N; i++) {
    for (int j = v[i]; j<=V; j++)
      dp[j] = (dp[j] >= dp[j - v[i]] + w[i]) ? dp[j] : dp[j - v[i]] + w[i];
  }
  cout << dp[V] << endl;
  system("pause");
  return 0;
}

多重背包

#include<iostream>
using namespace std;
int N, V;
int v[1002], w[1002], s[1002];
int dp[1002];
int main()
{
  cin >> N >> V;
  for (int i = 1; i <= N; i++) {
    cin >> v[i] >> w[i]>>s[i];
  }
  for (int i = 1; i <= N; i++) {
    for (int j = V; j>=1; j--)
      for(int k=1;k<=s[i]&&k*v[i]<=j;k++)
      dp[j] = (dp[j] >= dp[j - k*v[i]] +k*w[i]) ? dp[j] : dp[j - k*v[i]] + k*w[i];
  }
  cout << dp[V] << endl;
  system("pause");
  return 0;
}

数据量大的多重背包

#include<iostream>
#include<vector>
using namespace std;
struct goods{
  int g_v;
  int g_w;

};
vector<goods> good;
int N, V;
int v[1002], w[1002], s[1002];
int dp[1002];

int main()
{
  cin >> N >> V;
  for (int i = 1; i <= N; i++) {
    cin >> v[i] >> w[i] >> s[i];
  }
  for (int i = 1; i <= N; i++) {
    for (int k = 1; k < s[i]; k *= 2) {
      s[i] -= k;
      good.push_back({ k*v[i],k + w[i] });
    }
    if (s[i] > 0)
      good.push_back({ s[i]*v[i],s[i]*w[i] });
  }
  for (vector<goods>::iterator it = good.begin(); it != good.end(); it++)
    for (int j = V; j >= 1; j--)
      dp[j] = (dp[j] > dp[j - it->g_v] + it->g_w) ? dp[j] : dp[j - it->g_v] + it->g_w;
  cout << dp[V] << endl;
  system("pause");
  return 0;
}