| # |
Submission time |
Handle |
Problem |
Language |
Result |
Execution time |
Memory |
| 529287 |
2022-02-22T16:42:37 Z |
blue |
Bodyguard (JOI21_bodyguard) |
C++17 |
|
6814 ms |
1235208 KB |
#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
{
ll e;
ll a;
ll b;
};
bool operator < (slope_line A, slope_line B)
{
return A.a < B.a;
}
struct point_line
{
ll 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 ll(b1 - b2) / ll(a2 - a1);
}
bool good(ll a0, ll b0, ll a, ll b, ll a1, ll b1)
{
return ll(b0 - b) / ll(a - a0) < ll(b - b1) / ll(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({ll(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});
}
ll 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 = ll(nxt->b - b) / ll(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 = ll(prv->b - b) / ll(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';
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
6302 ms |
715272 KB |
Output is correct |
| 2 |
Correct |
6613 ms |
724652 KB |
Output is correct |
| 3 |
Correct |
2200 ms |
281480 KB |
Output is correct |
| 4 |
Correct |
873 ms |
108696 KB |
Output is correct |
| 5 |
Correct |
6814 ms |
1235208 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
5991 ms |
1153888 KB |
Output is correct |
| 2 |
Correct |
6005 ms |
1153996 KB |
Output is correct |
| 3 |
Correct |
5785 ms |
1138860 KB |
Output is correct |
| 4 |
Correct |
23 ms |
48260 KB |
Output is correct |
| 5 |
Correct |
5712 ms |
1154008 KB |
Output is correct |
| 6 |
Correct |
4147 ms |
1153928 KB |
Output is correct |
| 7 |
Correct |
4073 ms |
1152576 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
5991 ms |
1153888 KB |
Output is correct |
| 2 |
Correct |
6005 ms |
1153996 KB |
Output is correct |
| 3 |
Correct |
5785 ms |
1138860 KB |
Output is correct |
| 4 |
Correct |
23 ms |
48260 KB |
Output is correct |
| 5 |
Correct |
5712 ms |
1154008 KB |
Output is correct |
| 6 |
Correct |
4147 ms |
1153928 KB |
Output is correct |
| 7 |
Correct |
4073 ms |
1152576 KB |
Output is correct |
| 8 |
Incorrect |
5919 ms |
1154032 KB |
Output isn't correct |
| 9 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
5991 ms |
1153888 KB |
Output is correct |
| 2 |
Correct |
6005 ms |
1153996 KB |
Output is correct |
| 3 |
Correct |
5785 ms |
1138860 KB |
Output is correct |
| 4 |
Correct |
23 ms |
48260 KB |
Output is correct |
| 5 |
Correct |
5712 ms |
1154008 KB |
Output is correct |
| 6 |
Correct |
4147 ms |
1153928 KB |
Output is correct |
| 7 |
Correct |
4073 ms |
1152576 KB |
Output is correct |
| 8 |
Incorrect |
5919 ms |
1154032 KB |
Output isn't correct |
| 9 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
6302 ms |
715272 KB |
Output is correct |
| 2 |
Correct |
6613 ms |
724652 KB |
Output is correct |
| 3 |
Correct |
2200 ms |
281480 KB |
Output is correct |
| 4 |
Correct |
873 ms |
108696 KB |
Output is correct |
| 5 |
Correct |
6814 ms |
1235208 KB |
Output is correct |
| 6 |
Correct |
5991 ms |
1153888 KB |
Output is correct |
| 7 |
Correct |
6005 ms |
1153996 KB |
Output is correct |
| 8 |
Correct |
5785 ms |
1138860 KB |
Output is correct |
| 9 |
Correct |
23 ms |
48260 KB |
Output is correct |
| 10 |
Correct |
5712 ms |
1154008 KB |
Output is correct |
| 11 |
Correct |
4147 ms |
1153928 KB |
Output is correct |
| 12 |
Correct |
4073 ms |
1152576 KB |
Output is correct |
| 13 |
Incorrect |
5919 ms |
1154032 KB |
Output isn't correct |
| 14 |
Halted |
0 ms |
0 KB |
- |
