题目描述
完全背包问题
朴素dp
c++代码 $O(n^3)$
#include <iostream>
using namespace std;
const int N = 1050;
int n, m;
int v[N], w[N];
int f[N][N];
int main()
{
cin >> n >> m;
for (int i = 1; i <= n; i++) cin >> v[i] >> w[i];
for (int i = 1; i <= n; i++)
{
for (int j = 1; j <= m; j++)
{
for (int k = 0; j - k * v[i] >= 0; k++)
{
f[i][j] = max(f[i][j], f[i-1][j-k*v[i]] + k*w[i]);
}
}
}
cout << f[n][m] << endl;
return 0;
}
时间优化dp
C++ 代码 $O(n^2)$
#include <iostream>
using namespace std;
const int N = 1050;
int n, m;
int v[N], w[N];
int f[N][N];
int main()
{
cin >> n >> m;
for (int i = 1; i <= n; i++) cin >> v[i] >> w[i];
for (int i = 1; i <= n; i++)
{
for (int j = 1; j <= m; j++)
{
f[i][j] = f[i-1][j];
if (j >= v[i])
f[i][j] = max(f[i][j], f[i][j-v[i]] + w[i]);
}
}
cout << f[n][m] << endl;
return 0;
}
空间优化
c++代码
#include <iostream>
using namespace std;
const int N = 1050;
int n, m;
int v[N], w[N];
int f[N];
int main()
{
cin >> n >> m;
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 <= m; j++)
{
f[j] = f[j]; // f[i][j] = f[i-1][j];
f[j] = max(f[j], f[j-v[i]] + w[i]); // f[i][j] = max(f[i][j], f[i][j-v[i]] + w[i]);
}
}
cout << f[m] << endl;
return 0;
}