Submission #538448

#	Time	Username	Problem	Language	Result	Execution time	Memory
538448		Lobo	Split the sequence (APIO14_sequence)	C++17	100 / 100	1799 ms	88180 KiB

sequence

#include<bits/stdc++.h>
using namespace std;

const long long inf = (long long) 1e13 + 10;
const int inf1 = (int) 1e9 + 10;
#define int long long   
#define ll long long
#define dbl long double
#define endl '\n'
#define sc second
#define fr first
#define mp make_pair
#define pb push_back
#define all(x) x.begin(), x.end()

#define maxn 100010

int n, k, a[maxn], ps[maxn];
int dp[maxn][2];
int32_t ant[maxn][202];
vector<pair<pair<int,int>,pair<pair<int,int>,int>>> cht;
//cht -> a,b,l,r
//chtlr -> l,r,a,b

int f(int a, int b, int x) {
    return a*x + b;
}

dbl interx(int a1, int b1, int a2, int b2) {
    return (dbl) (b2-b1)/(a1-a2);
}

void resetcht() {
    cht.clear();

    cht.pb(mp(mp(-inf1,+inf1),mp(mp(0,0),0)));
}

void attcht(int a, int b, int id) {
    // so vai tirar para a esquerda
    // vai tirando enquanto valer a pena

    int ansl = inf;
    while(cht.size()) {
        int a1 = cht.back().sc.fr.fr;
        int b1 = cht.back().sc.fr.sc;
        int l = cht.back().fr.fr;    
        int r = cht.back().fr.sc;
        int id1 = cht.back().sc.sc;

        if(f(a,b,l) >= f(a1,b1,l)) {
            cht.pop_back();
            ansl = l;
        }
        else if(f(a,b,r) >= f(a1,b1,r)) {
            int x = ceil(interx(a,b,a1,b1));

            cht.pop_back();
            cht.pb(mp(mp(l,x-1),mp(mp(a1,b1),id1)));
            ansl = x;
            break;
        }
        else {
            break;
        }
    }

    if(ansl <= inf1) {
        cht.pb(mp(mp(ansl,inf1),mp(mp(a,b),id)));
    }
}

int idq;
pair<int,int> qrr(int x) {
    idq = min(idq,(int) cht.size()-1);

    while(idq+1 != cht.size()) {
        int a = cht[idq].sc.fr.fr;
        int b = cht[idq].sc.fr.sc;
        int a1 = cht[idq+1].sc.fr.fr;
        int b1 = cht[idq+1].sc.fr.sc;

        if(f(a1,b1,x) >= f(a,b,x)) idq++;
        else break;
    }

    int a = cht[idq].sc.fr.fr;
    int b = cht[idq].sc.fr.sc;
    return mp(f(a,b,x),cht[idq].sc.sc);
}

void solve() {
    cin >> n >> k;
    for(int i = 1; i <= n; i++) {
        cin >> a[i];
        ps[i] = ps[i-1] + a[i];
    }

    for(int j = 1; j <= k; j++) {
        resetcht();
        //dp[0][j] = 0
        idq = 0;
        for(int i = j; i <= n; i++) {
            auto qr = qrr(ps[i]);
            dp[i][j&1] = qr.fr;
            ant[i][j] = qr.sc;
            attcht(ps[i],dp[i][j&1^1]-ps[i]*ps[i],i);
        }
    }

    //dp[i][k] = max(dp[j-1][k-1] + ps[j-1]*(ps[i]-ps[j-1]))
    //dp[j-1][k-1] - ps[j-1]² + ps[j-1]*ps[i]
    //a ordem que vai colocando é crescente entao é só usar um vector bem mais simples
    

    int id = n;
    vector<int> ans;
    for(int j = k; j >= 1; j--) {
        ans.pb(ant[id][j]);
        id = ant[id][j];
    }

    reverse(all(ans));

    cout << dp[n][k&1] << endl;
    for(auto x : ans) cout << x << " ";
    cout << endl;
}

int32_t main() {
    ios::sync_with_stdio(false); cin.tie(0);

    // freopen("in.in", "r", stdin);
    // freopen("out.out", "w", stdout);

    int tt = 1;
    // cin >> tt;
    while(tt--) solve();

}

Compilation message (stderr)

sequence.cpp: In function 'std::pair<long long int, long long int> qrr(long long int)':
sequence.cpp:77:17: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<std::pair<std::pair<long long int, long long int>, std::pair<std::pair<long long int, long long int>, long long int> > >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   77 |     while(idq+1 != cht.size()) {
      |           ~~~~~~^~~~~~~~~~~~~
sequence.cpp: In function 'void solve()':
sequence.cpp:107:33: warning: suggest parentheses around arithmetic in operand of '^' [-Wparentheses]
  107 |             attcht(ps[i],dp[i][j&1^1]-ps[i]*ps[i],i);
      |                                ~^~

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