Submission #541770

#	Time	Username	Problem	Language	Result	Execution time	Memory
541770		FatihSolak	Split the sequence (APIO14_sequence)	C++17	100 / 100	1034 ms	84312 KiB

sequence

#include <bits/stdc++.h>
#define N 100005
#define K 205
using namespace std;
long long dp[N];
long long ndp[N];
int par[N][K];
long long pre[N];
int n;
struct CHT{
    vector<pair<int,int>> lines;
    void clear(){
        lines.clear();
    }
    long long get(pair<int,long long> a,pair<int,long long> b){
        if(a.first == b.first)
            return 0;
        return (b.second - a.second + (a.first - b.first -1)) / (a.first - b.first);
    }
    long long val(int c){
        return dp[c] - pre[c] * pre[n] - pre[c] * pre[c];
    }
    void add(int c){
        int a = 2*pre[c];
        long long b = val(c);
        if(lines.size() && 2*pre[lines.back().second] == a && val(lines.back().second) >= b)
            return;
        while(lines.size() && get({2*pre[lines.back().second],val(lines.back().second)},{a,b}) <= lines.back().first){
            lines.pop_back();
        }
        if(lines.empty()){
            lines.push_back({0,c});
        }
        else lines.push_back({get({2*pre[lines.back().second],val(lines.back().second)},{a,b}),c});
    }
    pair<int, long long> get(int x){
        pair<int,int> tmp = {x+1,0};
        int pos = lower_bound(lines.begin(),lines.end(),tmp) - lines.begin() - 1;
        return {lines[pos].second,1ll * 2*pre[lines[pos].second] * x + val(lines[pos].second)};
    }
}maxi;
void solve(){
    int k;
    cin >> n >> k;
    k++;
    for(int i = 1;i<=n;i++){
        cin >> pre[i];
        pre[i] += pre[i-1];
    }
    for(int j = 1;j<=k;j++){
        maxi.add(j-1);
        for(int i=j;i<=n;i++){
            auto x = maxi.get(pre[i]);
            par[i][j] = x.first;
            ndp[i] = x.second - pre[i] * pre[i] + pre[i] * pre[n];
            maxi.add(i);
        }
        for(int i=1;i<=n;i++){
            dp[i] = ndp[i];
        }
        maxi.clear();
    }
    cout << dp[n] / 2 << endl;
    while(par[n][k]){
        cout << par[n][k];
        n = par[n][k];
        k--;
        if(k)cout << " ";
    }
}

int32_t main(){
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    #ifdef Local
    freopen("in.txt","r",stdin);
    freopen("out.txt","w",stdout);
    #endif
    int t=1;
    //cin>>t;
    while(t--){
        solve();
    }
    #ifdef Local
    cout<<endl<<fixed<<setprecision(2)<<1000.0 * clock() / CLOCKS_PER_SEC<< " milliseconds ";
    #endif
}

• Subtask 1: 11 / 11
• Subtask 2: 11 / 11
• Subtask 3: 11 / 11
• Subtask 4: 17 / 17
• Subtask 5: 21 / 21
• Subtask 6: 29 / 29