一维数组（滚动数组）

和01背包很像，就是背包的遍历顺序不一样
https://www.bilibili.com/video/BV11K411i7od (结合y总讲的)

#include <iostream>
#include <algorithm>

using namespace std;

const int N = 1010;

int n, m;
int v[N], w[N];
int dp[N];

int main() {
    // 输入数据
    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++) // 每个物品随便取，所以要更新所以程序
            dp[j] = max(dp[j], dp[j - v[i]] + w[i]);

    cout << dp[m] << endl;

    return 0;
}

超级暴力（三重循环）(现在会TLE)

#include <iostream>
#include <algorithm>

using namespace std;

const int N = 1010;

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 = 0; j <= m; j++)
            for (int k = 0; k * v[i] <= j; k++)
                f[i][j] = max(f[i][j], f[i - 1][j - v[i] * k] + w[i] * k);

    cout <<  f[n][m] << endl;

    return 0;

}

进化一下两重循环的

#include <iostream>
#include <algorithm>

using namespace std;

const int N = 1010;
int w[N], v[N];
int n, m;
int dp[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 = 0; j <= m; j++) {
            dp[i][j] = dp[i - 1][j]; // 拷贝上一层数据
            if (j >= v[i]) {   // 满足条件
                dp[i][j] = max(dp[i][j], dp[i][j - v[i]] + w[i]);  // 同一层的比较，这也是优化为一维数组的一个重要条件，即为什么可以从头遍历
            }
        }
    }

    cout << dp[n][m] << endl;

    return 0;
}