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Submission #101024

# Submission time Handle Problem Language Result Execution time Memory
101024 2019-03-16T04:35:05 Z Retro3014 Split the sequence (APIO14_sequence) C++17
100 / 100
 827 ms 84800 KB 
#include <bits/stdc++.h>

#define pb push_back
#define all(v) ((v).begin(), (v).end())
#define sortv(v) sort(all(v))
#define sz(v) ((int)(v).size())
#define uniqv(v) (v).erase(unique(all(v)), (v).end())
#define umax(a, b) (a)=max((a), (b))
#define umin(a, b) (a)=min((a), (b))
#define FOR(i,a,b) for(int i = (a); i <= (b); i++)
#define rep(i,n) FOR(i,1,n)
#define rep0(i,n) FOR(i,0,(int)(n)-1)
#define FI first
#define SE second
#define INF 2000000000
#define INFLL 1000000000000000000LL


using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef long double ld;

const int MAX_N = 100010;
const int MAX_K = 210;
int N, K;
vector<ll> v;
ll S[MAX_N+1];
ll dp[2][MAX_N+1];
int from[MAX_K+1][MAX_N+1];
pll pr[MAX_N+1];
vector<int> st;
int k;

ll calc(int x, int y){
	pll tmp = {S[x], dp[0][x] - S[x]*S[x]};
	return tmp.first * S[y] + tmp.second;
}

bool chk(int x){
	ld x1 = -(ld)(pr[x].second - pr[st.back()].second) / (ld)(pr[x].first - pr[st.back()].first);
	ld x2 = -(ld)(pr[st.back()].second - pr[st[st.size()-2]].second) / (ld)(pr[st.back()].first - pr[st[st.size()-2]].first);
	if(x1<=x2)	return true;
	return false;
}

int main(){
	scanf("%d%d", &N, &K);
	v.push_back(0);
	for(int i=1; i<=N; i++){
		ll x; scanf("%lld", &x); v.push_back(x);
		S[i] = S[i-1] + v[i];
	}
	int idx = 0;
	for(k=1; k<=K; k++){
		idx = 0; 
		while(!st.empty())	st.pop_back();
		st.pb(k);
		pr[k] = {S[k], dp[0][k] - S[k]*S[k]};
		for(int i=k+1; i<=N; i++){
			while(st.size() > idx + 1 && calc(st[idx], i) < calc(st[idx+1], i))	idx++;
			dp[1][i] = calc(st[idx], i);
			from[k][i] = st[idx];
			pr[i] = {S[i], dp[0][i] - S[i]*S[i]};
			if(pr[i].first==pr[st.back()].first){
				if(pr[i].second>pr[st.back()].second){
					if(idx==st.size()-1)	idx--;
					st.pop_back();
				}else{
					continue;
				}
			}
			while(st.size()>1 && chk(i)){
				if(idx==st.size()-1)	idx--;
				st.pop_back();
			}
			st.push_back(i);
			idx = max(idx, 0);
			//cout<<k<<" "<<i<<" "<<dp[k][i]<<" "<<from[k][i]<<endl;
		}
		for(int i=1; i<=N; i++){
			dp[0][i] = dp[1][i];
		}
	}
	printf("%lld\n", dp[0][N]);
	vector<int> ans;
	idx = N;
	while(K>=1){
		idx = from[K][idx];
		K--;
		ans.pb(idx);
	}
	while(!ans.empty()){
		printf("%d ", ans.back());
		ans.pop_back();
	}
	return 0;
}

Compilation message

sequence.cpp: In function 'int main()':
sequence.cpp:62:20: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
    while(st.size() > idx + 1 && calc(st[idx], i) < calc(st[idx+1], i)) idx++;
          ~~~~~~~~~~^~~~~~~~~
sequence.cpp:68:12: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
      if(idx==st.size()-1) idx--;
         ~~~^~~~~~~~~~~~~
sequence.cpp:75:11: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
     if(idx==st.size()-1) idx--;
        ~~~^~~~~~~~~~~~~
sequence.cpp:49:7: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
  scanf("%d%d", &N, &K);
  ~~~~~^~~~~~~~~~~~~~~~
sequence.cpp:52:14: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
   ll x; scanf("%lld", &x); v.push_back(x);
         ~~~~~^~~~~~~~~~~~

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 384 KB contestant found the optimal answer: 108 == 108
2 Correct 2 ms 384 KB contestant found the optimal answer: 999 == 999
3 Correct 2 ms 384 KB contestant found the optimal answer: 0 == 0
4 Correct 3 ms 384 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 3 ms 384 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 2 ms 512 KB contestant found the optimal answer: 1 == 1
7 Correct 2 ms 384 KB contestant found the optimal answer: 1 == 1
8 Correct 2 ms 384 KB contestant found the optimal answer: 1 == 1
9 Correct 2 ms 384 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 2 ms 384 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 3 ms 384 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 2 ms 384 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 2 ms 384 KB contestant found the optimal answer: 140072 == 140072
14 Correct 2 ms 384 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 2 ms 384 KB contestant found the optimal answer: 805 == 805
16 Correct 2 ms 384 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 2 ms 384 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 384 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 3 ms 384 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 3 ms 640 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 3 ms 384 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 2 ms 384 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 2 ms 384 KB contestant found the optimal answer: 933702 == 933702
7 Correct 2 ms 512 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 3 ms 384 KB contestant found the optimal answer: 687136 == 687136
9 Correct 2 ms 384 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 2 ms 384 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 384 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 2 ms 384 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 3 ms 1536 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 2 ms 428 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 4 ms 1152 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 4 ms 1408 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 4 ms 1536 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 2 ms 640 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 3 ms 512 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 3 ms 640 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 384 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 2 ms 384 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 9 ms 2048 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 2 ms 384 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 11 ms 2048 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 8 ms 1792 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 9 ms 2048 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 10 ms 2048 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 4 ms 768 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 6 ms 1152 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 1152 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 5 ms 1152 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 51 ms 9592 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 5 ms 1024 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 40 ms 6136 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 71 ms 6964 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 68 ms 7416 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 46 ms 6264 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 48 ms 7036 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 56 ms 8696 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 25 ms 7020 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 25 ms 7060 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 570 ms 84800 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 41 ms 7528 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 827 ms 84464 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 526 ms 60804 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 627 ms 65136 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 467 ms 54180 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 472 ms 61272 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 538 ms 76696 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845