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답안 #1017188

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
1017188 2024-07-09T05:45:47 Z Gray 수열 (APIO14_sequence) C++17
100 / 100
 854 ms 96044 KB 
#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
11.0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 43 ms 80720 KB contestant found the optimal answer: 108 == 108
2 Correct 34 ms 80712 KB contestant found the optimal answer: 999 == 999
3 Correct 35 ms 80716 KB contestant found the optimal answer: 0 == 0
4 Correct 35 ms 80724 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 34 ms 80612 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 34 ms 80724 KB contestant found the optimal answer: 1 == 1
7 Correct 34 ms 80724 KB contestant found the optimal answer: 1 == 1
8 Correct 35 ms 80720 KB contestant found the optimal answer: 1 == 1
9 Correct 35 ms 80720 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 36 ms 80736 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 33 ms 80732 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 33 ms 80724 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 34 ms 80600 KB contestant found the optimal answer: 140072 == 140072
14 Correct 49 ms 80724 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 36 ms 80796 KB contestant found the optimal answer: 805 == 805
16 Correct 43 ms 80724 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 35 ms 80720 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 35 ms 80732 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 34 ms 80720 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 34 ms 80732 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 36 ms 80728 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 36 ms 80724 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 38 ms 80720 KB contestant found the optimal answer: 933702 == 933702
7 Correct 34 ms 80684 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 34 ms 80728 KB contestant found the optimal answer: 687136 == 687136
9 Correct 35 ms 80724 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 34 ms 80728 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 34 ms 80768 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 35 ms 80720 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 35 ms 80732 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 38 ms 80724 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 40 ms 80724 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 35 ms 80728 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 34 ms 80724 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 33 ms 80732 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 34 ms 80732 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 37 ms 80720 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# 결과 실행 시간 메모리 Grader output
1 Correct 34 ms 80732 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 35 ms 80720 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 43 ms 80976 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 35 ms 80664 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 39 ms 80928 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 40 ms 80888 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 42 ms 80720 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 41 ms 81240 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 36 ms 80732 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 37 ms 80720 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# 결과 실행 시간 메모리 Grader output
1 Correct 37 ms 80976 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 37 ms 81152 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 99 ms 82216 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 37 ms 81256 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 81 ms 82080 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 83 ms 81492 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 91 ms 81996 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 83 ms 82256 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 82 ms 82000 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 98 ms 82004 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# 결과 실행 시간 메모리 Grader output
1 Correct 51 ms 84304 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 52 ms 84560 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 717 ms 96044 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 54 ms 85580 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 854 ms 93824 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 584 ms 89172 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 624 ms 94528 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 538 ms 93780 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 561 ms 93324 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 696 ms 93920 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845