Submission #653073

#	Time	Username	Problem	Language	Result	Execution time	Memory
653073		ssense	Split the sequence (APIO14_sequence)	C++14	100 / 100	990 ms	97304 KiB

sequence

#include <bits/stdc++.h>
#define startt ios_base::sync_with_stdio(false);cin.tie(0);
typedef long long  ll;
using namespace std;
#define vint vector<int>
#define aint(v) v.begin(), v.end()
#define MOD 1000000007
#define MOD2 998244353
#define MX 1000000000
#define MXL 1000000000000000000
#define PI (ld)2*acos(0.0)
#define pb push_back
#define sc second
#define fr first
//#define int long long
#define endl '\n'
#define ld long double
#define NO cout << "NO" << endl
#define YES cout << "YES" << endl
int ceildiv(int one, int two) {if (one % two == 0) {return one / two;}else {return one / two + 1;}} int power(int n, int pow, int m) {if (pow == 0) return 1;if (pow % 2 == 0) {int x = power(n, pow / 2, m);return (x * x) % m;}else return (power(n, pow - 1, m) * n) % m;} int gcd(int a, int b) { if (!b)return a; return gcd(b, a % b);} int factorial(int n, int mod) {if (n > 1)return (n * factorial(n - 1, mod)) % mod; else return 1;} int lcm(int a, int b) {return (a * b) / gcd(a, b);} vector<ll> read(ll n) {vector<ll> a; for (int i = 0; i < n; i++) { int x; cin >> x; a.pb(x);} return a;}struct prefix_sum{vector<ll> pref;void build(vector<ll> a){pref.pb(0LL);for(int i = 0; i < a.size(); i++){pref.pb(pref.back()+a[i]);}}ll get(ll l, ll r){return pref[r]-pref[l-1];}};//mesanu

const int K = 200;
const int N = 1e5;

int best[N+5][K+5];

deque<pair<pair<ll, ll>, ll>> lines[K+5];

const double eps = 1e-5;

long double intersection_point(ll first_slope, ll first_b, ll second_slope, ll second_b)
{
    return (long double)(second_b-first_b)/(long double)(first_slope-second_slope);
}

void insert(ll m, ll b, ll k, ll index)
{
    if(m == lines[k].front().fr.fr)
    {
        if(b > lines[k].front().fr.sc)
        {
            lines[k].pop_front();
        }
        else
        {
            return;
        }
    }
    while(lines[k].size() > 1 && intersection_point(m, b, lines[k].front().fr.fr, lines[k].front().fr.sc)+eps > intersection_point(lines[k].front().fr.fr, lines[k].front().fr.sc, lines[k][1].fr.fr, lines[k][1].fr.sc))
    {
        lines[k].pop_front();
    }
    lines[k].push_front({{m, b}, index});
}

pair<ll, int> get_line(ll x, ll k)
{
    while(lines[k].size() >= 2 && lines[k].back().fr.fr*x+lines[k].back().fr.sc <= lines[k][lines[k].size()-2].fr.fr*x + lines[k][lines[k].size()-2].fr.sc)
    {
        lines[k].pop_back();
    }
    return {lines[k].back().fr.fr*x+lines[k].back().fr.sc, lines[k].back().sc};
}

void solve()
{
    int n, k;
    cin >> n >> k;
    vector<ll> a = read(n);
    prefix_sum pref;
    pref.build(a);
    for(int i = 0; i <= k; i++)
    {
        deque<pair<pair<ll, ll>, ll>> x;
        x.push_back({{0, 0}, 0});
        lines[i] = x;
    }
    ll ans = 0;
    int start = 0;
    for(int i = 0; i < n-1; i++)
    {
        vector<ll> now_vals(k+1);
        for(int j = min(k, i+1); j >= 1; j--)
        {
            pair<ll, int> best_line = get_line(pref.get(i+2, n), j-1);
            now_vals[j] = best_line.fr+pref.get(1, i+1)*pref.get(i+2, n);
            best[i+1][j] = best_line.sc;
            if(now_vals[j] >= ans && j == k)
            {
                start = i+1;
                ans = now_vals[j];
            }
            insert(-pref.get(1, i+1), now_vals[j], j, i+1);
        }
    }
    cout << ans << endl;
    while(k != 0)
    {
        cout << start << " ";
        start = best[start][k--];
    }
    cout << endl;
}
 
int32_t main(){
    startt
    int t = 1;
    //cin >> t;
    while (t--) {
        solve();
    }
}
/*
7 3
4 1 3 4 0 2 3
 */
/*
 introduci o linie - m = -sum 0..i b = dp[i][k]
 get o linie - k = k-1 coordonatul sum i..n
 */

Compilation message (stderr)

sequence.cpp: In member function 'void prefix_sum::build(std::vector<long long int>)':
sequence.cpp:20:679: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   20 | int ceildiv(int one, int two) {if (one % two == 0) {return one / two;}else {return one / two + 1;}} int power(int n, int pow, int m) {if (pow == 0) return 1;if (pow % 2 == 0) {int x = power(n, pow / 2, m);return (x * x) % m;}else return (power(n, pow - 1, m) * n) % m;} int gcd(int a, int b) { if (!b)return a; return gcd(b, a % b);} int factorial(int n, int mod) {if (n > 1)return (n * factorial(n - 1, mod)) % mod; else return 1;} int lcm(int a, int b) {return (a * b) / gcd(a, b);} vector<ll> read(ll n) {vector<ll> a; for (int i = 0; i < n; i++) { int x; cin >> x; a.pb(x);} return a;}struct prefix_sum{vector<ll> pref;void build(vector<ll> a){pref.pb(0LL);for(int i = 0; i < a.size(); i++){pref.pb(pref.back()+a[i]);}}ll get(ll l, ll r){return pref[r]-pref[l-1];}};//mesanu
      |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     ~~^~~~~~~~~~

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