Submission #1017188

#	Time	Username	Problem	Language	Result	Execution time	Memory
1017188		Gray	Split the sequence (APIO14_sequence)	C++17	100 / 100	854 ms	96044 KiB

sequence

#include <algorithm>
#include <cassert>
#include <cstring>
#include <deque>
#include <ios>
#include <iostream>
#include <map>
#include <vector>
#define ll long long
#define ull unsigned ll
#define ld long double
#define ff first
#define ss second
#define ln "\n"
#define pll pair<ll, ll>
using namespace std;
struct fun{
	ll m, c, i;
	fun(ll _m, ll _c, ll _i):m(_m), c(_c), i(_i){}
	ll f(ll x){
		return m*x+c;
	}
	ld inter(ll _m, ll _c){
		return ((ld)(_c)-(ld)(c))/((ld)(m)-(ld)(_m));
	}
};
struct CHT{
	deque<fun> que;
	void add(ll m, ll c, ll i){
		if (que.size()<2){
			que.push_back(fun(m, c, i));
		}else{
			while (que.size()>1 and que.back().inter(m, c)<=que[que.size()-2].inter(m, c)) que.pop_back();
			que.push_back(fun(m, c, i));
		}
	}
	pair<ll, ll> query(ll x){
		while (que.size()>1 and que[0].f(x)<=que[1].f(x)) que.pop_front();
		return {que[0].f(x), que[0].i};
	}
};
vector<ll> pref(100001), dp(100001);
vector<CHT> chts(201);
int link[100001][201];
// void get(ll l, ll r, ll optl, ll optr, ll n, ll k){
// 	if (l>r) return;
// 	ll m = (l+r)/2;
// 	pll optm = {-1, -1};
// 	for (ll i=optl; i<=min(m-1, optr); i++){
// 		optm = max(optm, {dep[i]+(pref[m]-pref[i])*(pref[n]-pref[m]), i});
// 	}
// 	wr[m]=optm.ff;
// 	assert(optm.ss!=-1);
// 	link[m][k]=(int)(optm.ss);
// 	get(l, m-1, optl, optm.ss, n, k);
// 	get(m+1, r, optm.ss, optr, n, k);
// }
void solve(){
	memset(link, 0, sizeof(link));
	ll n, k; cin >> n >> k;
	for (ll i=1; i<=n; i++){
		cin >> pref[i];
		pref[i]+=pref[i-1];
	}
	for (ll i=1; i<=n; i++){
		for (ll j=min(i, k); j>=1; j--){
			if (j==1){
				if (j==k) dp[i]=pref[i]*(pref[n]-pref[i]);
				chts[j].add(pref[i],pref[i]*(pref[n]-pref[i])-pref[i]*pref[n], i);
			}else{
				auto rdp = chts[j-1].query(pref[i]);
				if (j==k) dp[i]=rdp.ff+(pref[i]*pref[n]-pref[i]*pref[i]);
				link[i][j]=(int)rdp.ss;
				chts[j].add(pref[i], rdp.ff+(pref[i]*pref[n]-pref[i]*pref[i])-pref[i]*pref[n], i);
			}
		}
	}
	pll best = {-1, -1};
	for (ll i=1; i<n; i++){
		best=max(best, {dp[i], i});
	}
	vector<ll> ans;
	for (ll i=k; i>=1; i--){
		ans.push_back(best.ss);
		best.ss=link[best.ss][i];
	}
	cout << best.ff << ln;
	for (ll i=k-1; i>=0; i--) cout << ans[i] << " ";
	cout << ln;
}
// dp[i][k] = maxj(dp[j][k-1]+(pref[i]-pref[j])*(pref[n]-pref[i]));
// dp[j][k-1]+pref[i]*pref[n]-pref[i]*pref[i]-pref[j]*pref[n]+pref[j]*pref[i];
// (dp[j][k-1]-pref[j]*pref[n])+(pref[j]*pref[i])  +  (pref[i]*pref[n]-pref[i]*pref[i]);

int main(){
  	ios_base::sync_with_stdio(0);
  	cin.tie(nullptr);
  	ll t=1;
  	// cin >> t;
  	while (t--)solve();
}

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