Submission #1209288

#	Time	Username	Problem	Language	Result	Execution time	Memory
1209288		Zbyszek99	Split the sequence (APIO14_sequence)	C++20	100 / 100	995 ms	82504 KiB

sequence

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ll long long
#define ld long double
#define ull unsigned long long
#define ff first
#define ss second
#define pii pair<int,int>
#define pll pair<long long, long long>
#define vi vector<int>
#define vl vector<long long>
#define pb push_back
#define rep(i, b) for(int i = 0; i < (b); ++i)
#define rep2(i,a,b) for(int i = a; i <= (b); ++i)
#define rep3(i,a,b,c) for(int i = a; i <= (b); i+=c)
#define count_bits(x) __builtin_popcountll((x))
#define all(x) (x).begin(),(x).end()
#define siz(x) (int)(x).size()
#define forall(it,x) for(auto& it:(x))
using namespace __gnu_pbds;
using namespace std;
typedef tree<int, null_type, less<int>, rb_tree_tag,tree_order_statistics_node_update> ordered_set;
//mt19937 mt;void random_start(){mt.seed(chrono::time_point_cast<chrono::milliseconds>(chrono::high_resolution_clock::now()).time_since_epoch().count());}
//ll los(ll a, ll b) {return a + (mt() % (b-a+1));}
const int INF = 1e9+50;
const ll INF_L = 1e18+40;
const ll MOD = 1e9+7;

struct line
{
    ll a,b,ind;
    ll operator()(ll x)
    {
        return a + b*x;
    }
    pll operator*(line& other)
    {
        return {other.a - a,b - other.b};
    }
};

deque<line> hull;
ll arr[100001];
ll pref[100001];

void add_line(line l)
{
    while(siz(hull) >= 2)
    {
        line l1 = hull.front();
        hull.pop_front();
        line l2 = hull.front();
        hull.pop_front();
        pll com = l1*l2;
        pll com2 = l1*l;
        if(com.ss < 0)
        {
            com.ff *= -1;
            com.ss *= -1;
        }
        if(com2.ss < 0)
        {
            com2.ff *= -1;
            com2.ss *= -1;
        }
        if(com.ff * com2.ss < com2.ff * com.ss && (com2.ss != 0 || l.b < l1.b))
        {
            hull.push_front(l2);
            hull.push_front(l1);
            break;
        }
        else
        {
            hull.push_front(l2);
        }
    }

    if(siz(hull) == 0)
    {
        hull.push_front(l);
    }
    else
    {
        if(hull.front().b != l.b)
        {
            hull.push_front(l);
        }
        else
        {
            if(hull.front().a < l.a)
            {
                hull.pop_front();
                hull.push_front(l);
            }
        }
    }
    if(siz(hull) == 2)
    {
        line l1 = hull.front();
        hull.pop_front();
        line l2 = hull.front();
        hull.pop_front();
        if(l1.b < l2.b) swap(l1,l2);
        hull.push_front(l2);
        hull.push_front(l1);
    }
}

pll get_best(ll x)
{
    if(siz(hull) == 0) return {-1e18,-1};
    while(siz(hull) >= 2)
    {
        line fl = hull.back();
        hull.pop_back();
        line f2 = hull.back();
        hull.pop_back();
        if(f2(x) >= fl(x))
        {
            hull.push_back(f2);
        }
        else
        {
            hull.push_back(f2);
            hull.push_back(fl);
            break;
        }
    }
    return {hull.back()(x),hull.back().ind};
}

ll dp[100001];
int best[100001][201];

int main()
{
    ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
    //random_start();
    int n,k;
    cin >> n >> k;
    rep2(i,1,n) cin >> arr[i];
    rep2(i,1,n) pref[i] = pref[i-1] + arr[i];
    ll sum = 0;
    rep2(i,1,n) sum += arr[i];
    rep(i,n+1) dp[i] = -1;
    dp[0] = 0;
    k++;
    rep(kk,k)
    {
        hull = {};
        rep(i,n+1)
        {
            ll prev_dp = dp[i];
            pll b = get_best(pref[i]);
            dp[i] = -b.ff + pref[i] * pref[i];
            if(b.ff == -1e18) dp[i] = -1;
            best[i][kk] = b.ss;
            if(prev_dp != -1)
            {
                add_line({-pref[i]*pref[i]-prev_dp,2*pref[i],i});
            }
        }
    }
    cout << (sum*sum - dp[n])/2 << "\n";
    vi ans;
    int z = k-1;
    int cur = n;
    rep(i,k-1)
    {
        ans.pb(best[cur][z]);
        cur = best[cur][z];
        z--;
    }
    reverse(all(ans));
    forall(it,ans) cout << it << " ";
}

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