Submission #142566

#	Time	Username	Problem	Language	Result	Execution time	Memory
142566		12tqian	Split the sequence (APIO14_sequence)	C++14	71 / 100	457 ms	131072 KiB

sequence

#pragma comment(linker, "/stack:200000000")
//#pragma GCC optimize("Ofast")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")
#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>

using namespace std;
using namespace __gnu_pbds;
template <class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag,tree_order_statistics_node_update>;

const double PI = 4 * atan(1);

#define sz(x) (int)(x).size()
#define ll long long
#define ld long double
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define pii pair <int, int>
#define vi vector<int>
#define f first
#define s second
#define lb lower_bound
#define ub upper_bound
#define all(x) x.begin(), x.end()
#define vpi vector<pair<int, int>>
#define vpd vector<pair<double, double>>
#define pd pair<double, double>

#define f0r(i,a) for(int i=0;i<a;i++)
#define f1r(i,a,b) for(int i=a;i<b;i++)
#define trav(a, x) for (auto& a : x)

void fast_io(){
    ios_base::sync_with_stdio(0);
    cin.tie(NULL);
    cout.tie(NULL);
}
void io(string taskname){
    string fin = taskname + ".in";
    string fout = taskname + ".out";
    const char* FIN = fin.c_str();
    const char* FOUT = fout.c_str();
    freopen(FIN, "r", stdin);
    freopen(FOUT, "w", stdout);
    fast_io();
}
const int MAXN = 1e5 + 5;
const int MAXK = 2e2 + 5;
ll dp[MAXK][MAXN];
ll pre[MAXN];
vector<ll> a;
ll get(int l, int r){return pre[r] - (l == 0? 0: pre[l-1]);}
int bef[MAXK][MAXN];

pair<pair<long long, long long> , int> f(pair<pair<long long, long long>, int> a, pair<pair<long long, long long>, int> b) {
    /* point of intersection */
    long long x = ((long long)(b.f.second-a.f.second))/(a.f.first-b.f.first);
    long long y = a.f.first * x + a.f.second;
    return mp(make_pair(x, y), b.s);
}

struct cht {
    vector<long long> pts;
    vector<pair<pair<long long, long long>, int> > taken;
    void add(ll m, ll b, int idx){
        addLine(mp(mp(m, b), idx));
    }
    void addLine(pair<pair<long long, long long>, int> i) {
        if (taken.size() <= 1) {
            if (taken.empty()) { taken.push_back(i); }
            else {
                if (i.first.f == taken.back().first.f) {
                    if (taken.back().f.second > i.f.second) {
                        taken.pop_back();
                        taken.push_back(i);
                    }
                }
                else {
                    pts.push_back(f(i, taken.back()).first.f);
                    taken.push_back(i);
                }
            }
        }
        else {
            if (i.f.first == taken.back().first.f) {
                if (taken.back().second > i.f.second) {
                    taken.pop_back(); pts.pop_back();
                    pts.push_back(f(i, taken.back()).f.first);
                    taken.push_back(i);
                }
            }
            else {
                while (taken.size() >= 2) {
                    pair<pair<long long, long long>, int> l1 = taken[taken.size()-1];
                    pair<pair<long long, long long>, int> l2 = taken[taken.size()-2];
                    if (f(i, l2) > f(l1, l2)) { break; }
                    else { taken.pop_back(); pts.pop_back(); }
                }
                pts.push_back(f(i, taken.back()).f.first);
                taken.push_back(i);
            }
        }
    }

    pair<ll, int> query(long long x) {
        int idx = lower_bound(pts.begin(), pts.end(), x) - pts.begin();
        return mp(taken[idx].f.first * x + taken[idx].f.second, taken[idx].s);
    }
};
cht hull[MAXK];
int main(){
    fast_io();
    int n, k;
    cin >> n >> k;
    k++;
    f0r(i, n){
        int ai;
        cin >> ai;
        a.eb(ai);
        if(i == 0) pre[i] = ai;
        else pre[i] = pre[i-1] + ai;
    }
    ll res = pre[n-1]*pre[n-1];
    f0r(i, n){
        dp[1][i] = get(0, i)*get(0, i);
        bef[1][i] = -1;
        hull[1].add(-2*pre[i], pre[i]*pre[i] + dp[1][i], i);
    }
    f1r(i, 2, k+1){
        int best = i-2;

        f1r(j,i-1, n){
            if(j == i-1){
                bef[i][j] = i-2;
                dp[i][j] = dp[i-1][i-2] + get(i-1, i-1)*get(i-1, i-1);
                bef[i][j] = i-2;
                hull[i].add(-2*pre[j], pre[j]*pre[j] + dp[i][j], j);
            }
            else{
                pair<ll, int> q = hull[i-1].query(pre[j]);
                dp[i][j] = q.f + pre[j]*pre[j];
                bef[i][j] = q.s;
                hull[i].add(-2*pre[j], pre[j]*pre[j]+ dp[i][j], j);
            }
            //bef[i][j] = best;
        }
    }
    res -= dp[k][n-1];
    res/=2;
   // cout << dp[3][4] << endl;
    cout << res << endl;
    vi ans;
    int f = k;
    int s = n-1;
    while(bef[f][s] != -1){
        ans.eb(bef[f][s]);
        s = bef[f][s];
        f--;

    }
    reverse(all(ans));
    for(int x: ans) cout << x+1 << " ";
    cout << endl;

    return 0;
}

Compilation message (stderr)

sequence.cpp:1:0: warning: ignoring #pragma comment  [-Wunknown-pragmas]
 #pragma comment(linker, "/stack:200000000")
 
sequence.cpp: In function 'int main()':
sequence.cpp:134:13: warning: unused variable 'best' [-Wunused-variable]
         int best = i-2;
             ^~~~
sequence.cpp: In function 'void io(std::__cxx11::string)':
sequence.cpp:47:12: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
     freopen(FIN, "r", stdin);
     ~~~~~~~^~~~~~~~~~~~~~~~~
sequence.cpp:48:12: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
     freopen(FOUT, "w", stdout);
     ~~~~~~~^~~~~~~~~~~~~~~~~~~

• Subtask 1: 11 / 11
• Subtask 2: 11 / 11
• Subtask 3: 11 / 11
• Subtask 4: 17 / 17
• Subtask 5: 21 / 21
• Subtask 6: 0 / 29