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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#722001 | #9520. Concave Hull | zzfs# | RE | 1ms | 3728kb | C++17 | 4.4kb | 2024-11-07 17:25:39 | 2024-11-07 17:25:40 |
Judging History
answer
#include <bits/stdc++.h>
using namespace std;
#define int int64_t
struct point
{
int x, y;
int ind;
point() {}
point(int xx, int yy)
{
x = xx, y = yy;
}
point operator+(const point& r) const
{
return point(x + r.x, y + r.y);
}
point operator-(const point& r) const
{
return point(x - r.x, y - r.y);
}
int operator*(const point& r) const
{
return x * r.x + y * r.y;
}
bool operator<(const point& r) const
{
return make_pair(x, y) < make_pair(r.x, r.y);
}
int operator^(const point& r) const
{
return x * r.y - y * r.x;
}
int len2() const
{
return (*this) * (*this);
}
int dis2(const point& r) const
{
return (r - (*this)).len2();
}
int toleft(const point& r) const
{
const auto t = (*this) ^ r;
return (t > 0) - (t < 0);
}
};
struct polygon
{
vector<point> p;
polygon() = default;
polygon(vector<point> _p) : p(_p) {};
int nxt(const int i) const
{
return i == p.size() - 1 ? 0 : i + 1;
}
int pre(const int i) const
{
return i == 0 ? p.size() - 1 : i - 1;
}
int area_m2() const
{
int sum = 0;
for (int i = 0; i < p.size(); i++)
{
sum += p[i] ^ p[nxt(i)];
}
return sum;
}
};
polygon convexhull(vector<point> p, vector<bool>& is_use)
{
for (int i = 0; i < p.size(); i++)
{
p[i].ind = i;
}
is_use.clear();
is_use.assign(p.size(), false);
vector<point> st;
if(p.empty()) return polygon{st};
sort(p.begin(), p.end());
const auto check = [] (const vector<point> &st, const point &u)
{
const auto back1 = st.back(), back2 = *prev(st.end(), 2);
return (back1 - back2).toleft(u - back2) <= 0;
};
for (const point& u : p)
{
while (st.size() > 1 && check(st, u))
{
st.pop_back();
}
st.push_back(u);
}
int k = st.size();
p.pop_back();
reverse(p.begin(), p.end());
for(const point& u : p)
{
while (st.size() > k && check(st, u))
{
st.pop_back();
}
st.push_back(u);
}
st.pop_back();
for (const point& u : st)
{
is_use[u.ind] = true;
}
return polygon{st};
}
struct line
{
point p, v;
line() = default;
line(point beg, point end)
{
p = beg;
v = end - beg;
}
long double dis(const point &a) const
{
return abs(v ^ (a - p)) / sqrt(v.len2());
}
};
void sol()
{
vector<point> parr;
int N;
cin >> N;
for (int i = 0; i < N; i++)
{
int x, y;
cin >> x >> y;
parr.push_back(point(x, y));
}
vector<bool> point_is_use;
auto pol_hull_outsite = convexhull(parr, point_is_use);
vector<point> p_insite;
assert(point_is_use.size() == N);
for (int i = 0; i < parr.size(); i++)
{
if(point_is_use[i] == false)
{
p_insite.push_back(parr[i]);
}
}
if(p_insite.size() == 0)
{
cout << "-1\n";
return;
}
auto pol_hull_in = convexhull(p_insite, point_is_use);
int p_in = 0;
int outsite_Sm2 = abs(pol_hull_outsite.area_m2());
int min_sub_Sm2 = outsite_Sm2;
for (int i = 0; i < pol_hull_outsite.p.size(); i++)
{
auto op1 = pol_hull_outsite.p[i];
auto op2 = pol_hull_outsite.p[pol_hull_outsite.nxt(i)];
for(; ; p_in = pol_hull_in.nxt(p_in))
{
auto ip0 = pol_hull_in.p[pol_hull_in.pre(p_in)];
auto ip1 = pol_hull_in.p[p_in];
auto ip2 = pol_hull_in.p[pol_hull_in.nxt(p_in)];
auto dis0 = line(op1, op2).dis(ip0);
auto dis1 = line(op1, op2).dis(ip1);
auto dis2 = line(op1, op2).dis(ip2);
if(dis1 <= dis0 && dis1 <= dis2)
{
break;
}
}
auto p_3jx = polygon({op1, op2, pol_hull_in.p[p_in]});
min_sub_Sm2 = min(min_sub_Sm2, abs(p_3jx.area_m2()));
}
cout << outsite_Sm2 - min_sub_Sm2 << "\n";
}
int32_t main()
{
int T;
cin >> T;
while (T--)
{
sol();
}
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 0ms
memory: 3728kb
input:
2 6 -2 0 1 -2 5 2 0 4 1 2 3 1 4 0 0 1 0 0 1 1 1
output:
40 -1
result:
ok 2 lines
Test #2:
score: 0
Accepted
time: 1ms
memory: 3568kb
input:
10 243 -494423502 -591557038 -493438474 -648991734 -493289308 -656152126 -491185085 -661710614 -489063449 -666925265 -464265894 -709944049 -447472922 -737242534 -415977509 -773788538 -394263365 -797285016 -382728841 -807396819 -373481975 -814685302 -368242265 -818267002 -344482838 -833805545 -279398...
output:
2178418010787347715 1826413114144932145 1651687576234220014 1883871859778998985 2119126281997959892 894016174881844630 2271191316922158910 1998643358049669416 1740474221286618711 1168195646932543192
result:
ok 10 lines
Test #3:
score: -100
Runtime Error
input:
1000 125 64661186 -13143076 302828013 -185438065 -418713797 -191594241 430218126 -397441626 354327250 -836704374 149668812 -598584998 311305970 66790541 199720625 -592356787 468137 -584752683 258775829 96211747 -358669612 -134890109 -129221188 -998432368 -277309896 -140056561 356901185 420557649 -51...
output:
1986320445246155278 1900093336073022078 1612088392301142476 2012259136539173407 1819942017252118749 1772230185841892196 1164835025329039520 1527446155241140517 1807368432185303666 1236918659444944569 1306839249967484778 1984123720246784099 1868728080720036006 667458140583450322 2127932992585026491