Submission #1152877

#	Time	Username	Problem	Language	Result	Execution time	Memory
1152877		KluydQ	Split the sequence (APIO14_sequence)	C++17	71 / 100	2098 ms	111336 KiB

sequence

#include <bits/stdc++.h>
//#include "grader.h"
 
#define respagold ios_base::sync_with_stdio(0), cin.tie(0);
//#define int long long
#define ll long long
#define int2 __int128_t
#define FOR( i, x, n, d ) for( int i = x; i <= n; i += d )
#define FORR( i, x, n, d ) for( int i = x; i >= n; i -= d )
#define F first
#define S second
#define all(x) x.begin(), x.end()
#define sz(x) (int)(x.size())
#define pb push_back
#define ins insert
#define lb lower_bound
#define ub upper_bound
#define pii pair <int, int>
#define pll pair <ll, ll>
#define mkp make_pair
 
using namespace std;
 
const int N = 1e5 + 123;
const ll inf = 1e18;
 
ll a[N], b[N], n, m, k, z, w, x, y, mm[N], cc[N];
ll dp[N];
int par[N][201];

mt19937 rng( chrono::steady_clock::now().time_since_epoch().count());
 
int rand( int l, int r )
{
    uniform_int_distribution <int> uid( l, r );
    return uid( rng );
}
pair <int, pll> t[33 * N], sv[N], sv1[N];
int L[33 * N], R[33 * N], timer = 1;
 
void add( pair <int, pll> nw, int v = 1, int l = 0, int r = 1e9 + 1 )
{
	int md = ( l + r ) >> 1;
	bool lef = ( nw.S.F * l + nw.S.S > t[v].S.F * l + t[v].S.S ), mid = ( nw.S.F * md + nw.S.S > t[v].S.F * md + t[v].S.S );
	
	if( mid ) swap( nw, t[v] );
	
	if( l + 1 == r ) return;
	
	if( lef == mid ) 
	{
		if( !R[v] ) R[v] = ++ timer;
		add( nw, R[v], md, r ); 
	}
	else
	{
		if( !L[v] ) L[v] = ++ timer;
		add( nw, L[v], l, md );
	}
}
pll get( int pos, int v = 1, int l = 0, int r = 1e9 + 1 )
{ 
	int md = ( l + r ) >> 1;
	pll res = { t[v].S.F * pos + t[v].S.S, t[v].F };
	
	if( l + 1 == r ) return res;
	if( pos < md && L[v] ) res = max( res, get( pos, L[v], l, md ));
	if( pos >= md && R[v] ) res = max( res, get( pos, R[v], md, r ));
	return res;
}
void solve()
{
	cin >> n >> k;
	
	FOR( i, 1, n, 1 ) cin >> a[i], b[i] = b[i - 1] + a[i];
	sv1[0] = { 0, { 0, 0 }};
		
	FOR( bl, 1, k, 1 )
	{
		FOR( i, bl, n - k + bl - 1, 1 )
		{
			// for i find k that ( dp[k] + sum(k + 1, i) * sum(i + 1, n) ) is max
			
			// dp[i] = dp[k] + ( b[i] - b[k] ) * ( b[n] - b[i] )
			// dp[i] = dp[k] + b[i] * b[n] - b[i] * b[i] - b[k] * b[n] + b[k] * b[i];
			// dp[i] = ( dp[k] - b[k] * b[n] ) + ( b[i] * b[n] - b[i] * b[i] ) + ( b[k] * b[i] )
			
			add( sv1[i - 1] );
			
			pll j = get(b[i]);
			dp[i] = j.F + b[i] * b[n] - b[i] * b[i];
			sv[i] = { i, { b[i], dp[i] - b[i] * b[n] }};
			par[i][bl] = j.S;
		}
		FOR( i, 1, n, 1 ) sv1[i] = sv[i];
		FOR( i, 1, timer, 1 ) t[i] = { 0, { 0, 0 }}, L[i] = R[i] = 0;
		timer = 1;
	}
	ll ans = -inf, id = 0;
	
	FOR( i, 1, n - 1, 1 )
	{
		if( dp[i] >= ans ) ans = dp[i], id = i;
	}
	vector <int> v;
	FORR( blo, k, 1, 1 ) v.pb( id ), id = par[id][blo];
	reverse( all( v ));
	cout << ans << '\n';
	for( auto i : v ) cout << i << ' ';
}
signed main() 
{
//	freopen("connect.in", "r", stdin);
//	freopen("connect.out", "w", stdout);
	    
    respagold
    
    int test = 1;
    
    if( !test ) cin >> test;
	
	while( test -- )
	{
		solve();
	}
}
// solved by KluydQ

• Subtask 1: 11 / 11
• Subtask 2: 11 / 11
• Subtask 3: 11 / 11
• Subtask 4: 17 / 17
• Subtask 5: 21 / 21
• Subtask 6: 0 / 29