Submission #1202518

#	Time	Username	Problem	Language	Result	Execution time	Memory
1202518		adiyer	Split the sequence (APIO14_sequence)	C++20	0 / 100	0 ms	328 KiB

sequence

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

const int N = 1e5 + 11;
const ll is_query = -(1ll << 62);

ll n, k;
ll a[N], p[N], s[N], sz[201];

pair < ll, ll > ans;
pair < ll, ll > dp[N][201];


struct convex_hull{

	ll l = 1, r;

	struct line {
	
		ll m, b, i;

		ll get(ll x){
			return m * x + b;
		}

	};

	vector < line > c;

	double slope(line a, line b){
		return 1.0 * (b.b - a.b) / (a.m - b.m);
	}

	pair < ll, ll > eval(ll x){
		if(l >= c.size()) return {0, 0};
		while(l + 1 < c.size() && c[l].get(x) < c[l + 1].get(x)) l++;
		return {c[l].get(x), c[l].i};
	}

	void insert_line(line nw){
		if(c.empty()) c.push_back({0, 0});
		while(l + 1 < c.size() && slope(c[c.size() - 2], nw) < slope(c[c.size() - 2], c[c.size() - 1])) c.pop_back();
		// for(auto it : c) cout << it.i << ' ' << it.m << '\n';
		// cout << '\n';
		c.push_back(nw);
	}

} hull[201];


void solve(){
	cin >> n >> k;
	for(ll i = 0; i <= 200; i++) sz[i] = 1;
	for(ll i = 1; i <= n; i++) cin >> a[i];
	for(ll i = 1; i <= n; i++) p[i] = p[i - 1] + a[i];
	for(ll i = n; i >= 1; i--) s[i] = s[i + 1] + a[i];
	hull[0].insert_line({0, 0, 0});
	for(ll i = 1; i < n; i++){
		for(ll lay = 1; lay <= min(i, k); lay++){
			dp[i][lay] = hull[lay - 1].eval(-(s[i + 1]));
			dp[i][lay].first += p[i] * s[i + 1];
			// cout << i << ' ' << lay << ' ' << dp[i][lay].first << ' ' << dp[i][lay].second << '\n';
		}
		for(ll lay = 1; lay <= min(i, k); lay++){
			hull[lay].insert_line({p[i], dp[i][lay].first, i});
			if(dp[i][lay].first >= ans.first) ans = {dp[i][lay].first, i};
		}
	}
	cout << ans.first << '\n';
	while(k > 0){
		cout << ans.second << ' ';
		ans = dp[ans.second][k];
		k--;
	}
}

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

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