Submission #529450

#	Time	Username	Problem	Language	Result	Execution time	Memory
529450		blue	Bodyguard (JOI21_bodyguard)	C++17	6 / 100	7159 ms	1234428 KiB

bodyguard

#include <iostream>
#include <vector>
#include <algorithm>
#include <set>
#include <cassert>
#include <map>
using namespace std;
 
using ll = long long;
using vll = vector<ll>;
using vvll = vector<vll>;
using vi = vector<int>;
using vvi = vector<vi>;
 
 
const int maxN = 2'800;
 
int N;
 
vll T(1 + maxN), A(1 + maxN), B(1 + maxN), C(1 + maxN);
 
 
 
const int maxQ = 3'000'000;
 
int Q;
 
vll P(1 + maxQ), X(1 + maxQ);
 
 
 
 
 
 
 
 
const ll INF = 1'000'000'000'000'000'000LL;
 
struct slope_line
{
	double e;
 
	ll a;
	ll b;
};
 
bool operator < (slope_line A, slope_line B)
{
	return A.a < B.a;
}
 
struct point_line
{
	double e;
 
	ll a;
	ll b;
};
 
bool operator < (point_line A, point_line B)
{
	return A.e < B.e;
}
 
ll get_intersect(ll a1, ll b1, ll a2, ll b2)
{
	return double(b1 - b2) / double(a2 - a1);
}
 
 
bool good(ll a0, ll b0, ll a, ll b, ll a1, ll b1)
{
	return double(b0 - b) / double(a - a0) < double(b - b1) / double(a1 - a);
}
 
 
struct cht
{	
	multiset<slope_line> sl;
	multiset<point_line> pl;
 
	ll query(ll x)
	{
		if(pl.empty()) return 0;
 
		auto it = pl.lower_bound({double(x), 0, 0});
 
		if(it == pl.end()) while(1);
 
 
		return it->a * x  +  it->b;
	}
 
	void insert(ll a, ll b)
	{
		// cerr << "inserting " << a << ' ' << b << '\n';
		multiset<slope_line>::iterator it, nxt, prv, nxt2, prv2;
 
		it = sl.lower_bound({-1, a, b});
 
		if(it != sl.end() && it->a == a && it->b >= b) return;
 
		// cerr << "check\n";
 
		if(it != sl.end() && it->a == a) 
		{
			pl.erase({it->e, it->a, it->b});
			sl.erase(it);
		}
 
		sl.insert({-1, a, b});
 
		// cerr << "hello\n";
 
		// cerr << "check A\n";
// 
 
 
 
		it = sl.find({-1, a, b});
		nxt = it;
		nxt++;
 
		// cerr << "why\n";
 
		if(nxt != sl.end())
		{
			prv = it;
			if(prv != sl.begin())
			{
				prv--;
 
				ll a0 = prv->a, b0 = prv->b;
				ll a1 = nxt->a, b1 = nxt->b;
 
				if(!good(a0, b0, a, b, a1, b1))
				{
					return;
				}
				// cerr << "passed\n";
			}
		}
 
 
 
 
		while(1)
		{
			// cerr << "check B1\n";
			nxt = sl.find({-1, a, b});
			nxt++;
 
			if(nxt == sl.end()) break;
 
			// cerr << "B2\n";
 
			nxt2 = nxt;
			nxt2++;
 
			if(nxt2 == sl.end()) break;
 
			// cerr << "B3\n";
 
			if(good(a, b, nxt->a, nxt->b, nxt2->a, nxt2->b)) break;
 
			// cerr << "hello\n";
 
			pl.erase({nxt->e, nxt->a, nxt->b});
			sl.erase(nxt);
 
			// cerr << "B4\n";
		}
 
		// cerr << "check C\n";
 
		while(1)
		{
			prv = sl.find({-1, a, b});
			
			if(prv == sl.begin()) break;
			prv--;
 
 
			prv2 = prv;
			if(prv2 == sl.begin()) break;
			prv2--;
 
			if(good(prv2->a, prv2->b, prv->a, prv->b, a, b)) break;
 
			ll prv2a = prv2->a;
			ll prv2b = prv2->b;
			ll prv2e = get_intersect(a, b, prv2->a, prv2->b);
 
			pl.erase({prv->e, prv->a, prv->b});
			sl.erase(prv);
 
			pl.erase({prv2->e, prv2->a, prv2->b});
			sl.erase(prv2);
 
			sl.insert({prv2e, prv2a, prv2b});
			pl.insert({prv2e, prv2a, prv2b});
		}
 
 
		double endv, startv;
 
		// cerr << "check D\n";
 
 
 
		nxt = sl.find({-1, a, b});
		nxt++;
 
		if(nxt == sl.end()) endv = 2'000'000'005;
		else
		{
			// cerr << "#\n";
			// cerr << a << ' ' << b << " : " << nxt->a << ' ' << nxt->b << '\n';
			endv = double(nxt->b - b) / double(a - nxt->a);
 
			// cerr << endv << '\n';
		}
 
		// cerr << "endv = " << endv << '\n';
 
 
		prv = sl.find({-1, a, b});
		if(prv != sl.begin())
		{
			// cerr << "entered\n";
			prv--;
 
			startv = double(prv->b - b) / double(a - prv->a);
 
			slope_line new_prev = {startv, prv->a, prv->b};
 
 
			pl.erase({prv->e, prv->a, prv->b});
			// cerr << "checking\n";
 
			sl.erase(prv);
 
 
			sl.insert(new_prev);
			pl.insert({new_prev.e, new_prev.a, new_prev.b});
		}
 
		// cerr << "check E\n";
 
 
		sl.erase({-1, a, b});
		sl.insert({endv, a, b});
		pl.insert({endv, a, b});
 
		// cerr << "final line = " << endv << ' ' << a << ' ' << b << '\n';
	}
};
 
 
 
 
 
 
 
 
 
int main()
{
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
 
	cin >> N >> Q;
	for(int i = 1; i <= N; i++)
	{
		cin >> T[i] >> A[i] >> B[i] >> C[i];
 
		T[i] *= 2;
		A[i] *= 2;
		B[i] *= 2;
		C[i] /= 2;
	}
 
	for(int j = 1; j <= Q; j++)
	{
		cin >> P[j] >> X[j];
		P[j] *= 2;
		X[j] *= 2;
	}
 
	// if(Q > 40'000) assert(0);
 
 
	map<ll, ll> ypx_map, ymx_map;
	for(int i = 1; i <= N; i++)
	{
		ypx_map[T[i] + A[i]] = 0;
		ymx_map[T[i] - A[i]] = 0;
 
		ypx_map[(T[i] + abs(A[i] - B[i])) + B[i]] = 0;
		ymx_map[(T[i] + abs(A[i] - B[i])) - B[i]] = 0;
	}
 
	ll pct = 0, mct = 0;
 
	vll ypx{-2'000'000'002LL};
	vll ymx{-2'000'000'002LL};
 
	for(auto& z : ypx_map) 
	{
		z.second = ++pct;
		ypx.push_back(z.first);
	}
 
	for(auto& z : ymx_map) 
	{
		z.second = ++mct;
		ymx.push_back(z.first);
	}
 
	vi start_ypx(1 + N), start_ymx(1 + N), end_ypx(1 + N), end_ymx(1 + N);
	for(int i = 1; i <= N; i++)
	{
		start_ypx[i] = ypx_map[T[i] + A[i]];
		start_ymx[i] = ymx_map[T[i] - A[i]];
 
		end_ypx[i] = ypx_map[T[i] + abs(A[i] - B[i]) + B[i]];
		end_ymx[i] = ymx_map[T[i] + abs(A[i] - B[i]) - B[i]];
	}
 
 
 
 
	//i = ypx, j = ymx
 
	vvll horiz(1 + pct, vll(1 + mct, 0)); //(i, j) -> (i, j+1)
	vvll vert(1 + pct, vll(1 + mct, 0)); //(i, j) - (i+1, j)
 
	vvll horiz_basic(1 + pct, vll(1 + mct, 0)); //(i, j) -> (i, j+1)
	vvll vert_basic(1 + pct, vll(1 + mct, 0)); //(i, j) - (i+1, j)
 
	for(int i = 1; i <= N; i++)
	{
		if(B[i] < A[i])
		{
			for(int j = start_ymx[i]; j < end_ymx[i]; j++)
			{
				// cerr << start_ypx[i] << " ! " << j << '\n';
				horiz_basic[ start_ypx[i] ][j] = max(horiz_basic[ start_ypx[i] ][j], C[i]);
				// horiz[ start_ypx[i] ][j] = max(horiz[start_ypx[i]][j], (ymx[j+1] - ymx[j])/2  *  C[i]);
				horiz[start_ypx[i]][j] = horiz_basic[start_ypx[i]][j] * (ymx[j+1] - ymx[j]) / 2;
 
				// cerr << ymx[j+1] << ' ' << ymx[j] << ' ' << C[i] << '\n';
 
				// cerr << horiz[start_ypx[i]][j] << '\n';
			}
		}
		else
		{
			for(int j = start_ypx[i]; j < end_ypx[i]; j++)
			{
 
				vert_basic[j][ start_ymx[i] ] = max(vert_basic[j][start_ymx[i]], C[i]);
				vert[j][ start_ymx[i] ] = (ypx[j+1] - ypx[j])/2  *  vert_basic[ j ][ start_ymx[i] ];
			}
		}
	}
 
 
 
 
 
	vvll dp(1 + pct, vll(1 + mct, 0));
 
 
	for(int i = pct; i >= 1; i--)
	{
		for(int j = mct; j >= 1; j--)
		{
			if(i < pct) dp[i][j] = max(dp[i][j], dp[i+1][j] + vert[i][j]);
 
			if(j < mct) dp[i][j] = max(dp[i][j], dp[i][j+1] + horiz[i][j]);
 
			// cerr << i << ' ' << j << " : " << dp[i][j] << '\n';
		}
	}
 
 
	vll res(1 + Q, 0);
 
	vi queries[1 + pct][1 + mct];
 
	for(int j = 1; j <= Q; j++)
	{
		if(P[j] + X[j] > ypx.back()) continue;
 
		if(P[j] - X[j] > ymx.back()) continue;
 
		int plo = 1, phi = pct;
		while(plo != phi)
		{
			int mid = (plo + phi)/2;
 
			if(ypx[mid] < P[j] + X[j])
				plo = mid+1;
			else
				phi = mid;
		}
 
 
		int mlo = 1, mhi = mct;
		while(mlo != mhi)
		{
			int mid = (mlo + mhi)/2;
 
			if(ymx[mid] < P[j] - X[j])
				mlo = mid+1;
			else
				mhi = mid;
		}
 
		// cerr << plo << ' ' << mlo << " A \n";
 
		queries[plo][mlo].push_back(j);
	}
 
	// cerr << "done\n";
 
 
 
 
	for(int mi = 1; mi <= mct; mi++)
	{
		cht CHT;
 
		for(int pi = pct; pi >= 1; pi--)
		{
			CHT.insert(horiz_basic[pi][mi - 1], dp[pi][mi]);
 
			for(int qr : queries[pi][mi])
			{
				res[qr] = max(res[qr], CHT.query((ymx[mi] - (P[qr] - X[qr]))/2));
				// cerr << " ! " << res[qr] << '\n';
			}
		}
	}
 
	// cerr << "done 1\n";
 
	for(int pi = 1; pi <= pct; pi++)
	{
		cht CHT;
 
		for(int mi = mct; mi >= 1; mi--)
		{
 
			// cerr << "pi mi = " << pi << ' ' << mi << '\n';
			CHT.insert(vert_basic[pi - 1][mi], dp[pi][mi]);
 
			// cerr << "ins done\n";
 
			for(int qr : queries[pi][mi])
			{
				// cerr << "query = " << qr << " : " << pi << ' ' << mi << '\n';
				res[qr] = max(res[qr], CHT.query((ypx[pi] - (P[qr] + X[qr]))/2));
				// cerr << " ! " << res[qr] << '\n';
 
				// cerr << "query done\n";
			}
 
			// c
 
			// cerr << "finished\n";
		}
	}
 
 
	for(int j = 1; j <= Q; j++) cout << res[j] << '\n';
 
 
}

Compilation message (stderr)

bodyguard.cpp: In member function 'void cht::insert(ll, ll)':
bodyguard.cpp:200:15: warning: narrowing conversion of 'prv2e' from 'll' {aka 'long long int'} to 'double' [-Wnarrowing]
  200 |    sl.insert({prv2e, prv2a, prv2b});
      |               ^~~~~
bodyguard.cpp:201:15: warning: narrowing conversion of 'prv2e' from 'll' {aka 'long long int'} to 'double' [-Wnarrowing]
  201 |    pl.insert({prv2e, prv2a, prv2b});
      |               ^~~~~

• Subtask 1: 6 / 6
• Subtask 2: 0 / 7
• Subtask 3: 0 / 15
• Subtask 4: 0 / 20
• Subtask 5: 0 / 52