背包

1.0/1背包

#include <bits/stdc++.h>

using namespace std;

#define ll long long 
#define INF 0x3f3f3f3f
#define MAXN 300010
#define MAXM 3010

inline int read() {
    int x = 0,ff = 1;char ch = getchar();
    while(!isdigit(ch)) {
        if(ch == '-') ff = -1;
        ch = getchar();
    }
    while(isdigit(ch)) {
        x = (x << 1) + (x << 3) + (ch ^ 48);
        ch = getchar();
    }
    return x * ff;
}

int V,n,ans,weigh[MAXN],value[MAXN],f[MAXN];

int main() {
    V = read(); n = read();
    for(int i = 1; i <= n; ++i) {
        weigh[i] = read();
        value[i] = read();
    }
    for(int i = 1; i <= n; ++i) {
        for(int j = V; j >= weigh[i]; --j) {
            f[j] = max(f[j],f[j - weigh[i]] + value[i]);
        }
    }
    for(int i = 1; i <= V; ++i)
        ans = max(ans,f[i]);
    printf("%d\n",ans);
}

2.完全背包

#include <bits/stdc++.h>

using namespace std;

#define ll long long 
#define INF 0x3f3f3f3f
#define MAXN 300010
#define MAXM 3010

inline int read() {
    int x = 0,ff = 1;char ch = getchar();
    while(!isdigit(ch)) {
        if(ch == '-') ff = -1;
        ch = getchar();
    }
    while(isdigit(ch)) {
        x = (x << 1) + (x << 3) + (ch ^ 48);
        ch = getchar();
    }
    return x * ff;
}

int V,n,ans,f[MAXN],v[MAXN],w[MAXN];

int main() {
    V = read(); n = read();
    for(int i = 1; i <= n; ++i) {
        w[i] = read(); v[i] = read();
    }
    for(int i = 1; i <= n; ++i) {
        for(int j = w[i]; j <= V; ++j) {
            f[j] = max(f[j],f[j - w[i]] + v[i]);
        }
    }
    for(int i = 1; i <= V; ++i) 
        ans = max(ans,f[i]);
    printf("%d\n",ans);
}

3.多重背包

#include <bits/stdc++.h>

using namespace std;

#define ll long long
#define INF 0x3f3f3f3f
#define MAXN 300010
#define MAXM 3010

inline int read() {
    int x = 0,ff = 1;char ch = getchar();
    while(!isdigit(ch)) {
        if(ch == '-') ff = -1;
        ch = getchar();
    }
    while(isdigit(ch)) {
        x = (x << 1) + (x << 3) + (ch ^ 48);
        ch = getchar();
    }
    return x * ff;
}

int N,V,ans,w[MAXN],v[MAXN],n[MAXN],f[MAXM][MAXM];

int main() {
    N = read(); V = read();
    for(int i = 1; i <= N; ++i) {
        n[i] = read();
        w[i] = read();
        v[i] = read();
    } 
    for(int i = 1; i <= N; ++i) {
        for(int k = 0; k <= n[i]; ++k){
            for(int j = k * w[i]; j <= V; ++j) {    
                f[i][j] = max(f[i][j],f[i - 1][j - k * w[i]] + k * v[i]);    
            }
        }
    }
    for(int i = 1; i <= V; ++i) 
        ans = max(ans,f[N][i]);
    printf("%d\n",ans);
    return 0;
}

 二进制优化：

#include <bits/stdc++.h>

using namespace std;

#define ll long long
#define INF 0x3f3f3f3f
#define MAXN 300010
#define MAXM 3010

template <typename T> inline void read(T &x) {
    x = 0;
    T ff = 1;char ch = getchar();
    while(!isdigit(ch)) {
        if(ch == '-') ff = -1;
        ch = getchar();
    }
    while(isdigit(ch)) {
        x = (x << 1) + (x << 3) + (ch ^ 48);
        ch = getchar();
    }
    x *= ff;
}

int N,V,size;
ll w[MAXN],v[MAXN],n[MAXN],f[MAXN],ans;

int main() {
    read(N); read(V);
    for(int i = 1; i <= N; ++i) {
        int x,y,z,t = 1; // n,w,v;
        read(x); read(y); read(z);
        while(t <= x) {
            w[++size] = y * t;
            v[size] = z * t;
            x -= t;
            t <<= 1;
        }
        if(x > 0) {
            w[++size] = y * x;
            v[size] = z * x;
        }
    }
    for(int i = 1; i <= size; ++i) {
        for(int j = V; j >= w[i]; --j) {
            f[j] = max(f[j],f[j - w[i]] + v[i]);
        }
    }
    for(int i = 1; i <= V; ++i)
        ans = max(ans,f[i]);
    printf("%lld\n",ans);
    return 0;
}