Submission #500800

#	Time	Username	Problem	Language	Result	Execution time	Memory
500800		pancankes	Knapsack (NOI18_knapsack)	C++17	100 / 100	174 ms	17420 KiB

knapsack

#include <iostream>
#include <vector>
#include <set>
#include <map>
#include <algorithm>
using namespace std;
#define ll long long

const int MAXN=1e5+2;
const int MOD=1e9+7;

int main()
{
    ll s,n;
    cin >> s >> n;
    // since s<=2000, and n<=1000000
    // there will inevitably be repeated weights, so we can group them together
    map<int, vector<pair<int,int> > >weights; 
    for (int i=0; i<n; i++)
    {
        int p,w,n;
        cin >> p >> w >> n;
        weights[w].push_back({p,n});
    }
    vector<vector<int>> dp(weights.size()+1,vector<int>(s+1,0));
    dp[0][0]=0;
    int at=1;
    for (auto& [w, items] : weights)
    {
        sort(items.rbegin(),items.rend());
        for (int i=0; i<=s; i++)
        {
            dp[at][i]=dp[at-1][i];
            int copies=0, j=0, cur=0;
            ll profit=0;

            // while there are items and while it is within the usable weight
            // we can use copies since all groups of items are of the same weight
            while ((copies+1) * w <= i && j<(int)items.size())
            {
                copies++;
                profit+=items[j].first;
                dp[at][i]=max((ll)dp[at][i],dp[at-1][i-copies*w]+profit);
                cur++;
                if (cur==items[j].second)
                {
                    cur=0;
                    j++;
                }
            } 
        }
        at++;
    }
    // max_element gives a ptr to the value of the max element in a vector
    cout << *max_element(dp.back().begin(),dp.back().end()) << endl;
}

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