Submission #211696

#	Time	Username	Problem	Language	Result	Execution time	Memory
211696		Lawliet	Split the sequence (APIO14_sequence)	C++14	100 / 100	801 ms	88320 KiB

sequence

#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 (stderr)

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 / 11
• Subtask 2: 11 / 11
• Subtask 3: 11 / 11
• Subtask 4: 17 / 17
• Subtask 5: 21 / 21
• Subtask 6: 29 / 29