Submission #530219

#	Time	Username	Problem	Language	Result	Execution time	Memory
530219		blue	Bodyguard (JOI21_bodyguard)	C++17	7 / 100	4793 ms	1154052 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>;
#define sz(x) int(x.size())
 
 
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);

bool dbg = 0;
 
 
 
 
const ll INF = 1'000'000'000'000'000'000LL;
 
 
 
 
struct lct
{
	vll xv;
 
	// vector<bool> good;
	vector<ll> a;
	vector<ll> b;
 
	lct(vll& xv_)
	{
		// if(dbg)
		// {
		// 	// cerr << "creating LCT : ";
		// 	// for(ll xv__ : xv_) cerr << xv__ << ' ';
		// 	// 	cerr << '\n';
		// }

		xv = xv_;
 
		// good = vector<bool>((sz(xv) << 2) + 5, 0);
		a = b = vector<ll>((sz(xv) << 2) + 5, 0);
 
		// good[1] = 1;
	}
 
	void insert(ll na, ll nb, int i, int xi, int xj)
	{
		// if(dbg)cerr << "insert line " << na << ' ' << nb << " : " << xv[xi] << ' ' << xv[xj] << '\n';
		if(na * xv[xi] + nb <= a[i] * xv[xi] + b[i] && na * xv[xj] + nb <= a[i] * xv[xj] + b[i]) return;
 
		if(na * xv[xi] + nb >= a[i] * xv[xi] + b[i] && na * xv[xj] + nb >= a[i] * xv[xj] + b[i]) 
		{
			// if(dbg)
				// cerr << "direct\n";
			a[i] = na;
			b[i] = nb;
			// good[i] = 1;
 
		}
		else
		{
			// if(good[i])
			// 	insert(a[i], b[i], 2*i, xi, (xi+xj)/2);
			// insert(na, nb, 2*i, xi, (xi+xj)/2);
			
 
			// if(good[i])
			// 	insert(a[i], b[i], 2*i+1, (xi+xj)/2, xj);
			// insert(na, nb, 2*i+1, (xi+xj)/2+1, xj);
 
			// good[i] = 0;

			// if(dbg) cerr << na * xv[xi] + nb << " --- " << a[i] * xv[xi] + b[i] << '\n';
			// if(dbg) cerr << na * xv[xi] + nb - (a[i] * xv[xi] + b[i]) << '\n';
			// if(dbg) cerr << na * xv[xi] + nb - (a[i] * xv[xi] + b[i]) << ' ' << 0 << " : " << int(na * xv[xi] + nb - (a[i] * xv[xi] + b[i]) >= 0) << '\n';

			if(na * xv[xi] + nb >= a[i] * xv[xi] + b[i])
			{
				// cerr << "!!! " << na * xv[xi] + nb << ' ' << a[i] + xv[xi]

				if(na * xv[(xi+xj)/2] + nb >= a[i] + xv[(xi+xj)/2] + b[i])
				{
					// if(dbg)cerr << "Case A\n";
					insert(a[i], b[i], 2*i+1, (xi+xj)/2+1, xj);
					a[i] = na;
					b[i] = nb;
				}
				else
				{
					// if(dbg)cerr << "case B\n";
					insert(na, nb, 2*i, xi, (xi+xj)/2);
				}
			}
			else
			{
				if(na * xv[(xi+xj)/2 + 1] + nb >= a[i] + xv[(xi + xj) / 2 + 1] + b[i])
				{
					// if(dbg)cerr << "case C\n";
					insert(a[i], b[i], 2*i, xi, (xi+xj)/2);
					a[i] = na;
					b[i] = nb;
				}
				else
				{
					// if(dbg)cerr << "case D\n";
					insert(na, nb, 2*i + 1, (xi+xj)/2 + 1, xj);
				}
			}
		}
	}
 
	void insert(ll na, ll nb)
	{
		// if(dbg)cerr << "\n\n\n xv size = " << sz(xv) << '\n';
		insert(na, nb, 1, 0, sz(xv) - 1);
	}
 
	ll query(ll x, int i, int xi, int xj)
	{
		// if(good[i]) return a[i] * x + b[i];
		// else if(x <= xv[(xi+xj)/2]) return query(x, 2*i, xi, (xi+xj)/2);
		// else return query(x, 2*i+1, (xi+xj)/2+1, xj);

		ll cr = a[i] * x + b[i];

		if(xi != xj)
		{
			if(x <= xv[(xi+xj)/2]) cr = max(cr, query(x, 2*i, xi, (xi+xj)/2));
			else cr = max(cr, query(x, 2*i+1, (xi+xj)/2+1, xj));
		}

		return cr;
	}
 
	ll query(ll x)
	{
		return query(x, 1, 0, sz(xv) - 1);
	}
};
 
 
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;

		// cerr << "query " << j << " : " << (P[j]+X[j])/2 << '\n';
	}
 
	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);


		// cerr << "ypx : " << z.first / 2 << '\n';
	}
 
	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]];
	}
 
	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++)
			{
				horiz_basic[ start_ypx[i] ][j] = max(horiz_basic[ start_ypx[i] ][j], C[i]);
			
				horiz[start_ypx[i]][j] = horiz_basic[start_ypx[i]][j] * (ymx[j+1] - ymx[j]) / 2;
 
			}
		}
		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]);
 
		}
	}
 
 
	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 << j << " <> " << plo << ' ' << ypx[plo]/2 << '\n';
  
		queries[plo][mlo].push_back(j);
	}
	for(int mi = 1; mi <= mct; mi++)
	{
		set<ll> xv;
 
		for(int pi = pct; pi >= 1; pi--)
		{
			for(int qr : queries[pi][mi])
			{
				xv.insert((ymx[mi] - (P[qr] - X[qr]))/2);
			}
		}
 
		vll xvv;
 
		for(ll kv : xv) xvv.push_back(kv);
 
		if(xvv.empty()) continue;
 
		lct CHT(xvv);
 
 
		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 << qr << " : " << pi << ' ' << mi << '\n';
			}
		}
	}


	// cerr << pct << ' ' << mct << '\n';

	for(int pi = 1; pi <= pct; pi++)
	{
		// cerr << "\n\n\n\n pi = " << pi << '\n'; 
		// if(pi == 3) dbg = 1;
		// else dbg = 0;
		set<ll> xv;
 
		for(int mi = mct; mi >= 1; mi--)
		{
			for(int qr : queries[pi][mi])
			{
				xv.insert((ypx[pi] - (P[qr] + X[qr]))/2);

				// if(pi == 3) cerr << "query query " << qr << '\n';
			}
		}
 
		vll xvv;
 
		for(ll kv : xv) xvv.push_back(kv);
 
		if(xvv.empty()) continue;
 
		lct CHT(xvv);
 
		for(int mi = mct; mi >= 1; mi--)
		{
			// if(pi == 3) cerr << "add line " << vert_basic[pi - 1][mi] << ' ' << dp[pi][mi] << '\n';
			CHT.insert(vert_basic[pi - 1][mi], dp[pi][mi]);
 
			for(int qr : queries[pi][mi])
			{
				res[qr] = max(res[qr], CHT.query((ypx[pi] - (P[qr] + X[qr]))/2));
				// if(pi == 3) cerr << "query = " << qr << " : " << "x = " << (ypx[pi] - (P[qr] + X[qr]))/2 << '\n';
			}
		}
	}
	for(int j = 1; j <= Q; j++) cout << res[j] << '\n';
}

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