Backpack template

01 knapsack

int dp[10000]; 
int v[100]; 
int p[100]; 
int main()
{   int n,w;cin>>n>>w;
	 
	for(int i=1;i<=n;i++){
    		cin>>v[i]>>p[i];
	}
	 for(int i=1;i<=n;i++){
	 	for(int j=w;j>=0;j--){
		 	if(j>=v[i])dp[j]=max(dp[j],dp[j-v[i]]+p[i]);
		 }
	 }
	 
	cout<<dp[w];
}

Completely backpack

ll dp[60000]; 
ll v[60000]; 
ll p[20000]; 
int main()
{   ll n,w;scanf("%lld%lld",&n,&w);
	 
	for(ll i=1;i<=n;i++){
    	scanf("%lld%lld",&v[i],&p[i]);
	}
	 for(ll i=1;i<=n;i++){
	 	for(ll j=v[i];j<=w;j++){
		 	if(j>=v[i])dp[j]=max(dp[j],dp[j-v[i]]+p[i]);
		 }
	 }
	 
	cout<<dp[w];
}

Multiple backpack （ A monotonous queue ）

int dp[60000],zu[60000], x[60000],n,m;
int main() {
    cin >> n >> m;
    for (int i = 0; i < n; ++i) {
        int v, w, s;
        cin >> v >> w >> s;
        memcpy(zu, dp, sizeof dp);                 
        for (int j = 0; j < v; ++j) {            
            int a = 0, b = -1;                
            for (int k = j; k <= m; k += v) {   
            if (a <= b && x[a]<k-s* v) a ++;   
            while (a <= b && zu[x[b]]-(x[b] - j) / v * w <= zu[k] - (k - j) / v * w) b --;
            if (a <= b) dp[k] = max(dp[k], zu[x[a]] + (k - x[a]) / v * w); x[++b] = k;                 
            }
        }
    }
    cout<<dp[m];
    return 0;
}