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Submission #211696

# Submission time Handle Problem Language Result Execution time Memory
211696 2020-03-21T02:29:42 Z Lawliet Split the sequence (APIO14_sequence) C++14
100 / 100
 801 ms 88320 KB 
#include <bits/stdc++.h>
 
using namespace std;
typedef long long int lli;
typedef pair<int,int> pii; 

const int MAXK = 210;
const int MAXN = 100010;
const lli INF = 1000000000000000000LL;
 
class ConvexHullTrick
{
	public:
 
		bool canRemove(lli a, lli b, lli c, lli d)
		{
			if( b == 0 ) return true;

			if( a/b != c/d ) return a/b < c/d;

			a %= b;
			c %= d;

			if( a == 0 ) return true;
			if( c == 0 ) return false;

			return canRemove( d , c , b , a );
		}
 
		void add(lli a, lli b, int i)
		{
			if( !A.empty() && A.back() == a && B.back() >= b ) return;
			
			while( sz > 1 && canRemove(B[sz] - b , a - A[sz] , B[sz - 1] - B[sz] , A[sz] - A[sz - 1]) )
			{
				A.pop_back();
				B.pop_back();
				ind.pop_back();

				sz--;
			}
 
			sz++;
 
			A.push_back( a );
			B.push_back( b );
			ind.push_back( i );
		}
 
		lli getFunction(int i, lli x) { return A[i]*x + B[i]; }
 
		lli query(int x)
		{
			if( opt > sz ) opt = sz;
 
			while( opt < sz && getFunction(opt , x) <= getFunction(opt + 1 , x) ) opt++;
 
			return ind[opt];
		}
 
		void clear()
		{
			A.clear(); B.clear();
			ind.clear();
 
			sz = -1;
			opt = 0;
		}
 
		ConvexHullTrick() : sz( -1 ), opt( 0 ) {}
 
	private:
 
		int sz;
		int opt;
 
		vector<lli> A;
		vector<lli> B;
 
		vector<int> ind;
};
 
int n, k;
 
int v[MAXN];
int opt[MAXN][MAXK];
 
lli sv[MAXN];
lli dp[MAXN][2];
 
ConvexHullTrick CHT;
 
int main()
{
	scanf("%d %d",&n,&k);
 
	for(int i = 1 ; i <= n ; i++)
		scanf("%d",&v[i]);

	for(int i = 1 ; i <= n ; i++)
		sv[i] = sv[i - 1] + v[i];
 
	for(int j = 1 ; j <= k ; j++)
	{
		CHT.add( sv[j] , dp[j][1 - j%2] - sv[j]*sv[j] , j );
 
		for(int i = j + 1 ; i <= n ; i++)
		{
			int& l = opt[i][j];
			opt[i][j] = CHT.query( sv[i] );
  
			dp[i][j%2] = dp[ l ][1 - j%2] - sv[l]*sv[l] + sv[l]*sv[i];
  
			CHT.add( sv[i] , dp[i][1 - j%2] - sv[i]*sv[i] , i );
 		}
  
		CHT.clear();
	}
 
	printf("%lld\n",dp[n][k%2]);
 
	int cur = n;
 
	for(int i = k ; i > 0 ; i--)
	{
		printf("%d ",opt[cur][i]);
		cur = opt[cur][i];
	} 
}
 
//dp(i,k) = dp(j - 1 , k) + sv[j - 1]*(sv[i] - sv[j - 1]) = dp(j - 1 , k) - (sv[j - 1]*sv[j - 1]) + (sv[j - 1]*sv[i])

Compilation message

sequence.cpp: In function 'int main()':
sequence.cpp:95:7: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
  scanf("%d %d",&n,&k);
  ~~~~~^~~~~~~~~~~~~~~
sequence.cpp:98:8: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
   scanf("%d",&v[i]);
   ~~~~~^~~~~~~~~~~~

Subtask #1
11.0 / 11.0

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

Subtask #2
11.0 / 11.0

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

Subtask #3
11.0 / 11.0

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

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 1280 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 5 ms 1152 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 9 ms 1152 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 6 ms 1280 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 11 ms 1280 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 10 ms 1152 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 12 ms 1280 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 9 ms 1280 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 6 ms 1152 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 8 ms 1152 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 11 ms 9088 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 10 ms 9088 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 61 ms 9344 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 13 ms 9344 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 50 ms 9088 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 57 ms 9088 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 62 ms 9344 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 46 ms 9344 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 49 ms 9216 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 66 ms 9216 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 61 ms 87540 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 61 ms 87540 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 717 ms 88320 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 66 ms 88304 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 801 ms 87540 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 604 ms 87664 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 637 ms 88180 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 486 ms 88180 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 533 ms 88052 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 637 ms 87920 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845