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Submission #135274

# Submission time Handle Problem Language Result Execution time Memory
135274 2019-07-24T01:26:50 Z Lawliet Split the sequence (APIO14_sequence) C++14
33 / 100
 2000 ms 87664 KB 
#include <bits/stdc++.h>
 
#define MAXK 210
#define MAXN 100010
#define INF 1000000000000000000LL
 
using namespace std;
typedef long long int lli;
typedef pair<int,int> pii; 

class ConvexHullTrick
{
	public:

		bool canRemove(lli a, lli b, lli c, lli d)
		{
			double aa = (double) a;
			double cc = (double) c;

			return aa/b <= cc/d;
		}

		void add(lli a, lli b, int i)
		{
			//printf("ADD %lld %lld\n",a,b);
			while(size > 1 && canRemove(B[size] - b , a - A[size] , B[size] - B[size - 1] , A[size - 1] - A[size]))
			{
				A.pop_back();
				B.pop_back();
				ind.pop_back();

				size--;
				//printf("POP\n");
			}

			A.push_back( a );
			B.push_back( b );
			ind.push_back( i );

			size++;
		}

		lli equation(int i, lli x) { return A[i]*x + B[i]; }

		lli query(lli x)
		{
			if(optLine >= size) optLine = size - 1;

			while(optLine < size - 1 && equation(optLine , x) <= equation(optLine + 1 , x))
				optLine++;

			//printf("---- opt = %d\n",optLine);

			return ind[ optLine ];
		}

		void clear()
		{
			A.clear(); B.clear();
			ind.clear();

			size = optLine = 0;
		}

		ConvexHullTrick() : size(0), optLine(0) {}

	private:

		int size;
		int optLine;

		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 g = 1 ; g <= n ; g++)
	{
		scanf("%d",&v[g]);
 
		sv[g] = sv[g - 1] + v[g];
	}
 
	dp[0][0] = dp[0][1] = -INF;
 
	for(int j = 1 ; j <= k ; j++)
	{
		CHT.add(0 , -INF , 0);

		for(int i = 1 ; i <= n ; i++)
		{
			opt[i][j] = CHT.query( sv[i] );

			int l = opt[i][j];

			dp[i][j%2] = dp[ l ][1 - j%2] - sv[l]*sv[l] + sv[l]*sv[i];

			//printf("dp(%d,%d) = %lld         %lld\n",i,j,dp[i][j%2],dp[i][1 - j%2] - sv[i]*sv[i]);
			//printf("\n");

			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 g = k ; g > 0 ; g--)
	{
		printf("%d ",opt[cur][g]);
 
		cur = opt[cur][g];
	} 
}

//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:90:7: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
  scanf("%d %d",&n,&k);
  ~~~~~^~~~~~~~~~~~~~~
sequence.cpp:94:8: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
   scanf("%d",&v[g]);
   ~~~~~^~~~~~~~~~~~

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 376 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 380 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 376 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 376 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 376 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 2 ms 504 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 2 ms 504 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 3 ms 504 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 2 ms 504 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 3 ms 504 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 3 ms 504 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 4 ms 504 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 2 ms 504 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 3 ms 504 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 2 ms 504 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 1272 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 3 ms 1272 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 7 ms 1144 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 3 ms 1144 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 9 ms 1272 KB contestant found the optimal answer: 679388326 == 679388326
6 Incorrect 8 ms 1272 KB contestant didn't find the optimal answer: 4698985920 < 4699030287
7 Halted 0 ms 0 KB -

Subtask #5
0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 10 ms 9080 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 10 ms 9080 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 82 ms 9208 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 11 ms 9208 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 60 ms 9080 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Incorrect 63 ms 9080 KB contestant didn't find the optimal answer: 69688202167 < 514790755404
7 Halted 0 ms 0 KB -

Subtask #6
0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 106 ms 87284 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 107 ms 87356 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Execution timed out 2075 ms 87664 KB Time limit exceeded
4 Halted 0 ms 0 KB -