Submission #1118107

#	Time	Username	Problem	Language	Result	Execution time	Memory
1118107		urosk	Split the sequence (APIO14_sequence)	C++14	33 / 100	689 ms	131072 KiB

sequence

#define here cerr<<"===========================================\n"
#define dbg(x) cerr<<#x<<": "<<x<<endl;
#include <bits/stdc++.h>
#define llinf 100000000000000000LL // 10^17
#define iinf 2000000000 // 2*10^9
#define pb push_back
#define eb emplace_back
#define popb pop_back
#define fi first
#define sc second
#define endl '\n'
#define all(a) a.begin(),a.end()
#define ceri(a,l,r) {cerr<<#a<<": ";for(ll i_ = l;i_<=r;i_++) cerr<<a[i_]<< " ";cerr<<endl;}
#define cer(a) {cerr<<#a<<": ";for(ll x_ : a) cerr<<x_<< " ";cerr<<endl;}
#define si(a) (ll)(a.size())
using namespace std;
using ld = double;
using ll = long long;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pld = pair<ld,ld>;

#define mod 1
ll add(ll x,ll y){
	x+=y;
	if(x<0){
		x%=mod;
		x+=mod;
	}else{
		if(x>=mod) x%=mod;
	}
	return x;
}
ll mul(ll a,ll b){
	a = add(a,0);
	b = add(b,0);
	ll ans = (a*b)%mod;
	if(ans<0) ans+=mod;
	return ans;
}


const ll maxn = 100005;
const ll maxk = 205;
const ll mx = 1000000000;
ll n,k;
int a[maxn];
ll ps[maxn];
ll dp[maxk][maxn];
int opt[maxk][maxn];
void tc(){
	cin >> n >> k;
	for(ll i = 1;i<=n;i++) cin >> a[i];
	for(ll i = 1;i<=n;i++) ps[i] = ps[i-1] + a[i];
	for(ll j = 1;j<=k;j++) {
		vector<array<ld,4> > v;
		ll t = 0;
		for(ll i = j;i<=n;i++) {
			if(si(v)) {
				t = min(t,si(v)-1);
				t = max(t,0LL);
				while(t+1<si(v)&&ps[i]>=v[t+1][0]) t++;
				while(t>=0&&ps[i]<v[t][0]) t--;
				dp[j][i] = v[t][1]*ps[i]+v[t][2];
				opt[j][i] = v[t][3];
			}
			//lin f(-ps[i]*ps[i]+dp[j-1][i],ps[i]);
			ll k1 = ps[i],m1 = -ps[i]*ps[i]+dp[j-1][i];
			while(si(v)) {
				auto it = v.back();
				ll k2 = it[1],m2 = it[2];
				if(k1==k2) {
					if(m1>m2) {
						v.popb();
						continue;
					}else break;
				}
				ld cx = (m2-m1)*1.0/(k1-k2);
				if(cx<=it[0]) v.popb();
				else {
					v.pb({cx*1.0,1.0*k1,1.0*m1,i*1.0});
					break;
				}
			}
			if(v.empty()) v.pb({-mx*1.0,1.0*k1,1.0*m1,i*1.0});
		}
		//ceri(dp[j],1,n);
	}
	cout<<dp[k][n]<<endl;
	vector<ll> v;
	for(ll i = k;i>=1;i--) {
		n = opt[i][n];
		v.pb(n);
	}
	reverse(all(v));
	for(ll x : v) cout<<x<< " ";
	cout<<endl;
}

int main(){
	ios_base::sync_with_stdio(false);cerr.tie(0);cout.tie(0);cin.tie(0);
	int t; t = 1;
	while(t--){
		tc();
	}
	return (0-0);
}

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