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Submission #96106

# Submission time Handle Problem Language Result Execution time Memory
96106 2019-02-05T21:16:12 Z gs14004 Split the sequence (APIO14_sequence) C++17
100 / 100
 150 ms 6348 KB 
#include <bits/stdc++.h>
using namespace std;
typedef long long lint;
typedef long double llf;
typedef pair<lint, int> pi;
const int MAXN = 100005;

struct line{ lint x, y; int cnt, idx; };

struct cht{
	vector<line> v;
	int p = 0;
	void clear(){ v.clear(); p = 0; }
	bool bad(line x, line y, line z){
		return (llf)(x.y - y.y) / (y.x - x.x) >= (llf)(z.y - y.y) / (y.x - z.x);
	}
	void add(line l){
		if(v.size() > p && v.back().x == l.x){
			if(l.y < v.back().y) l = v.back();
			v.pop_back();
		}
		while(v.size() >= p + 2 && bad(v[v.size()-2], v.back(), l)){
			v.pop_back();
		}
		v.push_back(l);
	}
	tuple<lint, int, int> query(lint x){
		while(p + 1 < v.size() && v[p].x * x + v[p].y <= v[p+1].x * x + v[p+1].y) p++;
		return make_tuple(v[p].x * x + v[p].y, v[p].cnt, v[p].idx);
	}
}cht;

int n, k, a[MAXN], trk[MAXN];
pi dp[MAXN];

pi trial(lint l){
	cht.clear();
	for(int i=1; i<=n; i++){
		cht.add({a[i-1], dp[i-1].first - l, dp[i-1].second, i-1});
		lint x; int y, z; 
		tie(x, y, z) = cht.query(2 * (a[i] - a[n]));
		dp[i] = pi(x + 2ll * (a[n] - a[i]) * a[i], y + 1);
		trk[i] = z;
	}
	return dp[n];
}

vector<int> trace(lint l){
	trial(l);
	vector<int> v;
	for(int i=n; i; i=trk[i]){
		v.push_back(i);
	}
	v.push_back(0);
	return vector<int>(v.rbegin(), v.rend());
}

void printv(vector<int> v){
	lint ret = 0;
	for(int i=1; i<v.size(); i++){
		ret += 1ll * (a[v[i]] - a[v[i-1]]) * (a[n] - a[v[i]]);
	}
	printf("%lld\n", ret);
	for(int i=1; i+1<v.size(); i++) printf("%d ", v[i]);
	exit(0);
}

int main(){
	scanf("%d %d",&n,&k); k++;
	for (int i=0; i<n; i++) {
		int t;
		scanf("%d",&t);
		a[i+1] = a[i] + t;
	}
	lint s = 0, e = 1e17;
	while(s != e){
		lint m = (s+e)/2;
		if(trial(2 * m + 1).second <= k) e = m;
		else s = m + 1;
	}
	vector<int> l = trace(2 * s + 1);
	vector<int> r = trace(2 * s - 1);
	if(l.size() == k + 1) printv(l);
	if(r.size() == k + 1) printv(r);
	for(int i=0; i+1<r.size(); i++){
		auto idx = upper_bound(l.begin(), l.end(), r[i]) - l.begin();
		if(l[idx] >= r[i+1] && (i + 1) + (l.size() - idx) == k + 1){
			vector<int> v;
			for(int j=0; j<=i; j++) v.push_back(r[j]);
			for(int j=idx; j<l.size(); j++) v.push_back(l[j]);
			printv(v);
		}
	}
	assert(0);
}

Compilation message

sequence.cpp: In member function 'void cht::add(line)':
sequence.cpp:18:15: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   if(v.size() > p && v.back().x == l.x){
      ~~~~~~~~~^~~
sequence.cpp:22:18: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   while(v.size() >= p + 2 && bad(v[v.size()-2], v.back(), l)){
         ~~~~~~~~~^~~~~~~~
sequence.cpp: In member function 'std::tuple<long long int, int, int> cht::query(lint)':
sequence.cpp:28:15: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   while(p + 1 < v.size() && v[p].x * x + v[p].y <= v[p+1].x * x + v[p+1].y) p++;
         ~~~~~~^~~~~~~~~~
sequence.cpp: In function 'void printv(std::vector<int>)':
sequence.cpp:60:16: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  for(int i=1; i<v.size(); i++){
               ~^~~~~~~~~
sequence.cpp:64:18: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  for(int i=1; i+1<v.size(); i++) printf("%d ", v[i]);
               ~~~^~~~~~~~~
sequence.cpp: In function 'int main()':
sequence.cpp:83:14: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  if(l.size() == k + 1) printv(l);
     ~~~~~~~~~^~~~~~~~
sequence.cpp:84:14: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  if(r.size() == k + 1) printv(r);
     ~~~~~~~~~^~~~~~~~
sequence.cpp:85:18: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  for(int i=0; i+1<r.size(); i++){
               ~~~^~~~~~~~~
sequence.cpp:87:53: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   if(l[idx] >= r[i+1] && (i + 1) + (l.size() - idx) == k + 1){
                          ~~~~~~~~~~~~~~~~~~~~~~~~~~~^~~~~~~~
sequence.cpp:90:20: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
    for(int j=idx; j<l.size(); j++) v.push_back(l[j]);
                   ~^~~~~~~~~
sequence.cpp:69:7: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
  scanf("%d %d",&n,&k); k++;
  ~~~~~^~~~~~~~~~~~~~~
sequence.cpp:72:8: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
   scanf("%d",&t);
   ~~~~~^~~~~~~~~

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 376 KB contestant found the optimal answer: 108 == 108
2 Correct 2 ms 376 KB contestant found the optimal answer: 999 == 999
3 Correct 2 ms 376 KB contestant found the optimal answer: 0 == 0
4 Correct 2 ms 376 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 2 ms 380 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 2 ms 376 KB contestant found the optimal answer: 1 == 1
7 Correct 2 ms 376 KB contestant found the optimal answer: 1 == 1
8 Correct 2 ms 376 KB contestant found the optimal answer: 1 == 1
9 Correct 2 ms 376 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 2 ms 256 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 2 ms 376 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 2 ms 376 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 2 ms 376 KB contestant found the optimal answer: 140072 == 140072
14 Correct 2 ms 376 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 2 ms 376 KB contestant found the optimal answer: 805 == 805
16 Correct 2 ms 256 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 2 ms 376 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 376 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 2 ms 376 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 2 ms 376 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 2 ms 376 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 2 ms 380 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 2 ms 376 KB contestant found the optimal answer: 933702 == 933702
7 Correct 2 ms 376 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 2 ms 376 KB contestant found the optimal answer: 687136 == 687136
9 Correct 2 ms 376 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 2 ms 376 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 376 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 2 ms 376 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 2 ms 376 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 2 ms 376 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 2 ms 380 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 2 ms 376 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 2 ms 376 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 2 ms 376 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 2 ms 376 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 2 ms 376 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 376 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 3 ms 376 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 3 ms 348 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 3 ms 376 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 3 ms 380 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 3 ms 376 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 3 ms 376 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 3 ms 376 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 3 ms 376 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 3 ms 376 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 12 ms 760 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 14 ms 952 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 14 ms 1208 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 13 ms 888 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 15 ms 888 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 16 ms 888 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 25 ms 1072 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 15 ms 1080 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 24 ms 1080 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 18 ms 1080 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 129 ms 4336 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 132 ms 4332 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 116 ms 5836 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 129 ms 5872 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 149 ms 5932 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 138 ms 5864 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 150 ms 6348 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 139 ms 6248 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 129 ms 6248 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 125 ms 6248 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845