Submission #987820

#	Time	Username	Problem	Language	Result	Execution time	Memory
987820		Gray	Split the sequence (APIO14_sequence)	C++17	22 / 100	99 ms	131072 KiB

sequence

#include <algorithm>
#include <bits/stdc++.h>

#define ll long long
#define ld long double
#define ff first
#define ss second
#define ln "\n"

using namespace std;
const ll MOD = 1e9+7;
const unsigned long long INF = 1e19;

struct line{
	ll m, c;
	pair<ll, ll> id;
	line(ll m, ll c, pair<ll, ll> id):m(m),c(c),id(id){}
	ll eval(ll x){
		return m*x+c;
	}
	long double inter(const line &alt){
		return (ld)(c-alt.c)/(ld)(alt.m-m);
	}
};

struct CHT{
	deque<line> lc;
	void add(ll m, ll c, ll i, ll j){
		while (lc.size()>1 and lc.front().inter(line(m, c, {i, j}))>=lc[1].inter(lc.front())) lc.pop_front();
		lc.push_front(line(m, c, {i, j}));
	}
	pair<ll, pair<ll, ll>> query(ll x){
		while (lc.size()>1 and lc.back().eval(x)<=lc[lc.size()-2].eval(x)) lc.pop_back();
		return {lc.back().eval(x), lc.back().id};
	}
};

// dp[i] = dp[j]+(suff[j]-suff[i])*suff[i];
// dp[i] = dp[j]+suff[j]*suff[i]-suff[i]*suff[i];

void solve(){
	ll n, k; cin >> n >> k;
	vector<ll> a(n);
	vector<ll> suff(n+1, 0);
	for (ll i=0; i<n; i++) cin >> a[i];
	for (ll i=n-1; i>=0; i--){
		suff[i]=suff[i+1]+a[i];
	}
	vector<vector<ll>> dp(n, vector<ll>(k+1));
	vector<vector<pair<ll, ll>>> con(n, vector<pair<ll, ll>>(k+1));
	vector<CHT> chts(k+1);
	chts[0].add(suff[0], 0, -1, -1);
	ll mx = -1;
	pair<ll, ll> mxi = {-1, -1};
	for (ll i=1; i<n; i++){
		for (ll j=1; j<=min(i, k); j++){
			auto ret = chts[j-1].query(suff[i]);
			dp[i][j] = ret.ff-suff[i]*suff[i];
			con[i][j] = ret.ss;
			chts[j].add(suff[i], dp[i][j], i, j);
			if (j==k and mx<dp[i][j]){
				mx=dp[i][j];
				mxi = {i, j};
			}
		}
	}
	cout << mx << ln;
	vector<ll> ans;
	while (make_pair(-1LL, -1LL)!=mxi){
		ans.push_back(mxi.ff);
		mxi = con[mxi.ff][mxi.ss];
	}
	for (ll i=k-1; i>=0; i--){
		cout << ans[i] << " ";
	}
	cout << ln;
}

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

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