Submission #1000757

#	Time	Username	Problem	Language	Result	Execution time	Memory
1000757		dimashhh	Split the sequence (APIO14_sequence)	C++17	100 / 100	919 ms	93896 KiB

sequence

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

const int  N = 1e5 + 30, MOD = 1e9 + 7;
int n,k;
int a[N];
ll pref[N],sf[N];
int p[N][203];
ll dp[N],tdp[N];
struct line{
    ll k,b;
    int pos = 0;
    ll get(ll x){
        return k * x + b;
    }
};

long double cross(line a,line b){
    return ((a.b - b.b) * 1.0 / ((b.k - a.k) * 1.0));
}
void add(vector<line> &st,line l){
    while((int)st.size() > 1 && cross(l,st[(int)st.size() - 2]) <= cross(l,st.back())){
        st.pop_back();
    }
    st.push_back(l);
}
pair<ll,ll> get(vector<line> &st,ll x){
    int l = -1,r = (int)st.size() - 1;
    while(r - l > 1){
        int mid = (l + r) >> 1;
        if(mid == (int)st.size() - 1 || (st[mid].b - st[mid + 1].b) * 1.0 >= x * 1.0 * (st[mid + 1].k - st[mid].k)){
            r = mid;
        }else{
            l = mid;
        }
    }
    return {st[r].get(x),st[r].pos};
}
set<int> St;
void test(){
    cin >> n >> k;
    for(int i = 1;i <= n;i++){
        cin >> a[i];
        St.insert(i);
    }
    for(int i = 1;i <= n;i++){
        pref[i] = pref[i - 1] + a[i];
    }
    for(int i = n;i >= 1;i--){
        sf[i] = sf[i + 1] + a[i];
    }
    for(int i = 1;i <= k;i++){
        vector<line> st;
        add(st,{0,0});
        int it = 1;
        auto ok = [&](int mid,int j){
            return (mid == (int)st.size() - 1 || (st[mid].b - st[mid + 1].b) * 1.0 >= sf[j + 1] * 1.0 * (st[mid + 1].k - st[mid].k));
        };
        for(int j = 1;j <= n;j++){
            while(it < (int)st.size() - 1 && !ok(it + 1,j)){
                it++;
            }
            while(it >= 0 && (it == (int)st.size() - 1 || (st[it].b - st[it + 1].b) * 1.0 >= sf[j + 1] * 1.0 * (st[it + 1].k - st[it].k))){
                it--;
            }
            pair<ll,ll> G = {st[it + 1].get(sf[j + 1]),st[it + 1].pos};
            dp[j] = G.first+ pref[j] * sf[j + 1];
            p[j][i] = G.second;
            if(!p[j][i] && i != 1){
                p[j][i] = j - 1;
            }
            line nv = {-pref[j],tdp[j],j};
            add(st,nv);
            it = min(it,(int)st.size() - 1);
        }
        for(int j = 1;j <= n;j++){
            tdp[j] = dp[j];
            dp[j] =0 ;
        }
    }
    ll res = 0;
    int ps = 0;
    for(int i = 1;i < n;i++){
        if(tdp[i] >= res){
            res = tdp[i];
            ps = i;
        }
    }
    vector<int> f;
    cout << res << '\n';
    int k1 = k;
    while(ps){
        f.push_back(ps);
        St.erase(ps);
        ps = p[ps][k--];
    }
    for(int i = 1;i <= n - 1;i++){
        if(St.find(i) != St.end()&&(int)f.size() < k1){
            f.push_back(i);
        }
    }
    sort(f.begin(),f.end());
    for(int j:f){
        cout << j << ' ';
    }
}
int main() {
    ios_base::sync_with_stdio(false);cin.tie(0);
    int t = 1;
    // cin >> t;
    while(t--){
        test();
    }
}

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