Submission #1282119

#	Time	Username	Problem	Language	Result	Execution time	Memory
1282119		Faisal_Saqib	Knapsack (NOI18_knapsack)	C++20	73 / 100	1097 ms	2796 KiB

knapsack

#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define int ll
const int N=1e5+100;
const ll inf=1e18;
int w[N],v[N],k[N];
ll dp[N];
vector<ll> vec[N];
int32_t main()
{
    ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    int s,n;
    cin>>s>>n;
    for(int i=0;i<n;i++)
    {
        cin>>v[i]>>w[i]>>k[i];
        k[i]=min(2000ll,k[i]);
    }
    // dp[i][s] = max value 
    // dp[i][s]  = dp[i-1][s] take no elements
    // dp[i][s] = dp[i-1][s-w[i]]+v[i] 1 ele
    // dp[i][s] = max(dp[i-1][s-k*w[i]]+v[i]*k)
    for(int i=0;i<n;i++)
    {
        // dp[x] = max(dp[x-w[i]])
        for(int x=0;x<=s;x++)
        {
            vec[x%w[i]].push_back(dp[x]);
        }
        for(int x=0;x<w[i];x++)
        {
            multiset<ll> cur={-inf};
            ll ad=0;
            for(int j=0;j<vec[x].size();j++)
            {
                ad+=v[i]; // add v[i] to each element in cur
                if(j-1-k[i]>=0)
                {
                    cur.erase(cur.find(vec[x][j-1-k[i]]+(k[i]+1)*v[i]-ad));
                }
                cur.insert(vec[x][j]-ad);
                ll idp=w[i]*j+x;
                dp[idp]=max((*rbegin(cur))+ad,0ll);
                // vec[x][j-k]+(k+1)v -ad 
                // 
                // vec[x][j] vec[x][j-1]+v vec[x][j-2]+2v .. vec[x][j-k]+kv
                // vec[x][j+1] vec[x][j]+v vec[x][j-1]+2v .. vec[x][j+1-l]+kv vec[x][j-k]+(k+1)v
            }
            vec[x].clear();
        }
    }
    ll mx=0;
    for(int i=0;i<=s;i++)mx=max(mx,dp[i]);
    cout<<mx<<endl;
}

• Subtask 1: 12 / 12
• Subtask 2: 17 / 17
• Subtask 3: 20 / 20
• Subtask 4: 24 / 24
• Subtask 5: 0 / 27