Submission #227812

#	Time	Username	Problem	Language	Result	Execution time	Memory
227812		caoash	Split the sequence (APIO14_sequence)	C++14	100 / 100	921 ms	87652 KiB

sequence

/*

*/

#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <cmath>
#include <vector>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <queue>
#include <ctime>
#include <cassert>
#include <complex>
#include <string>
#include <cstring>
#include <random>
#include <queue>
#include <bitset>
 
// #define int long long
#define ll long long
#define ld long double
#define pb push_back
#define str string
using namespace std;
const int M = 998244353;
ll dp[100009];
int par[100009][209];
int zzz;
 
ld intersec(pair<pair<ll, ll>, int> w1, pair<pair<ll, ll>, int> w2) {
    ld k1 = w1.first.first, b1 = w1.first.second;
    ld k2 = w2.first.first, b2 = w2.first.second;
    ld x = (b2 - b1) / (k1 - k2);
    return x;
}
 
vector<pair<pair<ll, ll>, int>> s;
 
void add_line(ll k, ll b, int index) {
    while (s.size() >= 2) {
        ld x1 = intersec(s[s.size() - 2], s[s.size() - 1]);
        ld x2 = intersec(s[s.size() - 2], {{k, b}, index});
        if (x1 >= x2) {
            s.pop_back();
        } else {
            break;
        }
    }
    s.pb({{k, b}, index});
}
 
pair<ll, int> my_lower_bound(ll h) {
    int left = zzz;
    int right = (int) s.size();
    int f = 0;
    for (int mid = left + 1; mid < right; mid++) {
        ld lol = intersec(s[mid - 1], s[mid]);
        if (lol >= h) {
            left = mid - 1;
            f = 1;
            break;
        }
    }
    if (f == 0) left = s.size() - 1;
    zzz = left;
    return {h * s[left].first.first + s[left].first.second, s[left].second};
}
 
signed main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);
    int n, k;
    cin >> n >> k;
    vector<ll> A(n + 1);
    for (int i = 1; i <= n; i++) cin >> A[i];
    vector<ll> pref = A;
    for (int i = 1; i <= n; i++) pref[i] += pref[i - 1];
    for (int i = 1; i <= n; i++) {
        dp[i] = 0;
    }
    for (int t = 1; t <= k; t++) {
        add_line(pref[t], dp[t] - pref[t] * pref[t], t);
        zzz = 0;
        for (int i = t + 1; i <= n; i++) {
            pair<ll, int> kek = my_lower_bound(pref[i]);
            add_line(pref[i], dp[i] - pref[i] * pref[i], i);
            dp[i] = kek.first;
            par[i][t] = kek.second;
        }
        s = {};
    }
    cout << dp[n] << '\n';
    int i = n;
    int t = k;
    vector<ll> ans;
    while (t >= 1) {
        cout << par[i][t] << ' ';
        i = par[i][t];
        t--;
    }
 
}

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