Submission #762544

#	Time	Username	Problem	Language	Result	Execution time	Memory
762544		Ahmed57	Split the sequence (APIO14_sequence)	C++17	71 / 100	2067 ms	92348 KiB

sequence

#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
using namespace std;
#define ll long long
const ll is_query = -(1LL<<62);
struct Line {
    ll m,b,idx;
    mutable function<const Line*()> succ;
    bool operator<(const Line& rhs) const {
        if (rhs.b != is_query) return m < rhs.m;
        const Line* s = succ();
        if (!s) return 0;
        ll x = rhs.m;
        return b - s->b < (s->m - m) * x;
    }
};
struct HullDynamic : public multiset<Line> { // will maintain upper hull for maximum
    bool bad(iterator y) {
        auto z = next(y);
        if (y == begin()) {
            if (z == end()) return 0;
            return y->m == z->m && y->b <= z->b;
        }
        auto x = prev(y);
        if (z == end()) return y->m == x->m && y->b <= x->b;
        return (x->b - y->b)*(z->m - y->m) >= (y->b - z->b)*(y->m - x->m);
    }
    void insert_line(ll m, ll b,int idx) {
        auto y = insert({ m, b,idx });
        y->succ = [=] { return next(y) == end() ? 0 : &*next(y); };
        if (bad(y)) { erase(y); return; }
        while (next(y) != end() && bad(next(y))) erase(next(y));
        while (y != begin() && bad(prev(y))) erase(prev(y));
    }
    pair<ll,ll> eval(ll x) {
        auto l = *lower_bound((Line) { x, is_query });
        return {l.m * x + l.b , l.idx};
    }
};
long long dp[100001][2];
int lol[100001][204];
signed main(){
    ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
    long long n,k;
    cin>>n>>k;
    long long arr[n+1] = {0};
    for(int i = 1;i<=n;i++){
        cin>>arr[i];
        arr[i]+=arr[i-1];
    }
    if(n==1){
        cout<<0<<endl;
        return 0;
    }
    for(int j = 1;j<=k+1;j++){
        HullDynamic cht;
        cht.insert_line(arr[j-1],(dp[j-1][!(j&1)]-arr[j-1]*arr[n]),j-1);
        for(int i = j;i<=n;i++){
            dp[i][j&1] = arr[i]*arr[n]-arr[i]*arr[i]+cht.eval(arr[i]).first;
            lol[i][j] = cht.eval(arr[i]).second;
            cht.insert_line(arr[i],(dp[i][!(j&1)]-arr[i]*arr[n]),i);
        }
    }
    k++;
    cout<<dp[n][k&1]<<endl;
    int x = n;
    vector<ll> ha;
    while(k>1){
        ha.push_back(max(1,lol[x][k]));
        x = lol[x][k];k--;
    }
    for(int i = ha.size()-1;i>=0;i--){
        cout<<ha[i]<<" ";
    }
}

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