DP入门——01背包 & 完全背包

01背包：

采药：

https://www.luogu.org/problemnew/show/P1048

#include <iostream>
#include <algorithm>
using namespace std;

int dp[1005];
int weight[105],value[105];

int main() {
    int T, n;
    cin >> T >> n;
    for (int i = 0; i < n; i++) {
        cin >> weight[i] >> value[i];
    }
    for (int i = weight[0]; i <= T; i++) {
        dp[i] = value[0];
    }
    for (int i = 1; i < n; i++) {
        for (int j = T; j >= weight[i]; j--) {
            dp[j] = max(dp[j - weight[i]] + value[i], dp[j]);
        }
    }
    cout << dp[T] << endl;
    return 0;
}

完全背包

疯狂采药：

https://www.luogu.org/problemnew/show/P1616

#include <iostream>
#include <algorithm>
using namespace std;

int dp[100005];
int weight[10005],value[10005];

int main() {
    int T, n;
    cin >> T >> n;
    for (int i = 0; i < n; i++) {
        cin >> weight[i] >> value[i];
    }
    for (int i = weight[0]; i <= T; i++) {
        dp[i] = value[0] * (i / weight[0]);
    }
    for (int i = 1; i < n; i++) {
        for (int j = weight[i]; j <= T; j++) {
            dp[j] = max(dp[j - weight[i]] + value[i], dp[j]);
        }
    }
    cout << dp[T] << endl;
    return 0;
}

区别在于，完全背包的初始化值，以及完全背包，每个东西可以用无限次，第二重循环是从前往后。