Submission #1272285

#	Time	Username	Problem	Language	Result	Execution time	Memory
1272285		pvb.tunglam	Split the sequence (APIO14_sequence)	C++20	0 / 100	2 ms	1848 KiB

sequence

#include <bits/stdc++.h>
#define hash _hash_
#define y1 _y1_
#define dec _dec_
using namespace std;
using ll = long long;
using ull = unsigned long long;
const ll MOD = 1e9 + 7;	
const ll oo = 1e18;

int N, K;
ll a[100009], pre[100009];
ll dp_prev[100009], dp_cur[100009];
int par[100009][205]; // lưu cut cho từng j

struct Line {
    ll m, b;
    int idx;
};
struct CHT {
    deque<Line> dq;
    void add(ll m, ll b, int idx) {
        Line l = {m,b,idx};
        while(dq.size()>=2){
            auto &l1=dq[dq.size()-2], &l2=dq.back();
            if((l2.b - l1.b)*(l1.m - l.m) >= (l.b - l1.b)*(l1.m - l2.m)) dq.pop_back();
            else break;
        }
        dq.push_back(l);
    }
    pair<ll,int> query(ll x){
        while(dq.size()>=2){
            auto &l1=dq[0], &l2=dq[1];
            if(l2.m*x + l2.b >= l1.m*x + l1.b) dq.pop_front();
            else break;
        }
        return {dq[0].m*x + dq[0].b, dq[0].idx};
    }
};

void solve(){
    cin >> N >> K;
    for(int i=1;i<=N;i++){
        cin >> a[i];
        pre[i] = pre[i-1] + a[i];
    }

    for(int i=0;i<=N;i++) dp_prev[i] = -oo;
    dp_prev[0] = 0;

    for(int j=1;j<=K;j++){
        CHT cht;
        for(int i=0;i<=N;i++) dp_cur[i]=-oo;
        cht.add(0,0,0); // k=0
        for(int i=1;i<=N;i++){
            auto [val,k] = cht.query(pre[i]);
            dp_cur[i] = val;
            par[i][j] = k;
            cht.add(pre[i], dp_prev[i]-pre[i]*pre[i], i);
        }
        swap(dp_prev, dp_cur);
    }

    cout << dp_prev[N] << "\n";

    vector<int> cuts;
    int ci = N, cj = K;
    while(cj > 0){
        int t = par[ci][cj];
        if(t <= 0) break;
        cuts.push_back(t);
        ci = t;
        --cj;
    }
    reverse(cuts.begin(), cuts.end());

    for(size_t i=0;i<cuts.size();i++){
        if(i) cout<<" ";
        cout<<cuts[i];
    }
    cout<<"\n";
}

signed main(){
    ios_base::sync_with_stdio(0);
    cin.tie(nullptr);
    solve();
}

• Subtask 1: 0 / 11
• Subtask 2: 0 / 11
• Subtask 3: 0 / 11
• Subtask 4: 0 / 17
• Subtask 5: 0 / 21
• Subtask 6: 0 / 29