QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#690487 | #9520. Concave Hull | kinuru | AC ✓ | 130ms | 15072kb | C++23 | 6.5kb | 2024-10-30 22:28:14 | 2024-10-30 22:28:23 |
Judging History
answer
#include<bits/stdc++.h>
#define L(i, l, r) for(int i = l; i <= r; i ++)
#define R(i, l, r) for(int i = l; i >= r; i --)
#define fi first
#define se second
#define ll long long
#define ld long double
#define vi vector <int>
#define vl vector <long long>
#define endl '\n'
#define sz(a) ((int) (a).size())
#define me(f, x) memset(f, x, sizeof(f))
#define ull unsigned long long
using namespace std;
const double eps = 1e-8;
const double pi = 3.141592653589793284l;
template <typename T> struct point{
T x, y;
bool operator == (const point &a) const{
return abs(x - a.x) <= eps && abs(y - a.y) <= eps;
}
bool operator < (const point &a) const{
if(fabs(x - a.x) <= eps){
return y < a.y;
}
return x < a.x;
}
point operator + (const point &a) const{
return {x + a.x, y + a.y};
}
point operator - (const point &a) const{
return {x - a.x, y - a.y};
}
point operator * (const T k) const{
return {x * k, y * k};
}
point operator / (const T k) const{
return {x / k, y / k};
}
point operator - () const{
return {- x, - y};
}
T operator * (const point &a) const{ // Dot
return x * a.x + y * a.y;
}
T operator ^ (const point &a) const{ // Cross
return x * a.y - y * a.x;
}
int to_left(const point &a) const{
const auto t = (*this) ^ a;
return (t > eps) - (t < -eps); // 1: this 在 a left // 0:this 与 a 共线 // -1 this 在a right
}
int area() const {
if (y > 0 || y == 0 && x > 0)
return 0;
return 1;
}
// 极角排序2 : bool operator <(const Point& rhs) const { return area() < rhs.area() || area() == rhs.area() && cross(rhs) > 0; }
T length2() const{
return (*this) * (*this);
}
T dist2(const point &a) const{
return (a - (*this)).length2();
}
double length() const{
return sqrt(length2());
}
double dist(const point &a) const{
return (a - (*this)).length();
}
friend auto &operator<<(ostream &os, point p) {
return os << "(" << p.x << ", " << p.y << ")";
}
};
// 这里看情况换double || long long || long double
using Point = point<ll>;
typedef Point Vector;
typedef vector<Point> Polygon;
bool argcmp(const Point &a, const Point &b){
// 下半 < 原点 < +x轴 < 上半 < -x轴
auto quad =[](const Point &a){
if(a.y < -eps) return 1; // 下半平面,三四象限。
if(a.y > eps) return 4; // 上半平面,一二象限。
if(a.x < -eps) return 5; // -x轴
if(a.x > eps) return 3; // +x轴
return 2; // 原点
};
int qa = quad(a), qb = quad(b);
if(qa != qb) return qa < qb;
auto t = a ^ b;
if(t == 0) return a * a < b * b - eps; // 如果共线,则近的在前面。
return t > eps; // 同一半平面内to_left测试, 大于0表示a在b的左边,排前面。
}
int sgn(double x){
if(fabs(x) <= eps) return 0;
return x > 0 ? 1 : -1;
}
// 两点距离
double dis(Point a, Point b){
return sqrt((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y));
}
//叉积
ll cross(Vector v1, Vector v2){
return v1.x * v2.y - v1.y * v2.x;
}
// to_left测试
int to_left(Point &a, Point &o, Point &b){
int t = (a - o) ^ (b - o);
if(sgn(t) == 0) return 0;
return t > 0 ? 1 : -1;
}
// 求凸包
Polygon Andrew(vector<Point> s){
vector<Point> a, b;
if(s.size() <= 2) return s;
sort(s.begin(), s.end());
int sz = s.size();
a.push_back(s[0]), a.push_back(s[1]);
b.push_back(s[sz - 1]), b.push_back(s[sz - 2]);
for(int i = 2; i < sz; i ++){
for(int j = a.size(); j >= 2; j --){
Vector v1 = a[j - 1] - a[j - 2], v2 = s[i] - a[j - 1];
if( (v1 ^ v2) >= 0) a.pop_back();
else break;
}
a.push_back(s[i]);
}
for(int i = sz - 3; i >= 0; i --){
for(int j = b.size(); j >= 2; j --){
Vector v1 = b[j - 1] - b[j - 2], v2 = s[i] - b[j - 1];
if( (v1 ^ v2) >= 0) b.pop_back();
else break;
}
b.push_back(s[i]);
}
reverse(b.begin(), b.end());
int len = a.size();
for(int i = len - 2; i >= 1; i --) b.push_back(a[i]);
return b;
}
void solve(){
int n; cin >> n;
vector <Point> vec;
for(int i = 1; i <= n; i ++){
ll x, y; cin >> x >> y;
vec.push_back({x, y});
}
Polygon out = Andrew(vec);
ll ans = 0;
for(int i = 0; i < sz(out); i ++){
ans += cross(out[i], out[(i + 1) % sz(out)]);
}
map <pair<ll, ll>, int> mp;
for(auto [x, y] : out){
mp[{x, y}] = 1;
}
vector <Point> A;
for(auto [x, y] : vec){
if(!mp[{x, y}]) A.push_back({x, y});
}
if(A.empty()){
cout << -1 << endl;
return ;
}
// {
// // bf
// ll mn = 5e18;
// ll m = sz(in);
// out.push_back(out[0]);
// for(int i = 0; i < m; i ++){
// for(int j = 0; j + 1 < out.size(); j ++){
// assert(cross(out[j] - in[i], out[j + 1] - in[i]) >= 0);
// mn = min(mn, cross(out[j] - in[i], out[j + 1] - in[i]));
// }
// }
// cout << ans - mn << endl;
// }
Polygon in = Andrew(A);
int pos = -1; ll mn = 5e18;
int m = sz(in);
for(int i = 0; i < sz(in); i ++){
ll area = cross(out[0] - in[i], out[1] - in[i]);
assert(area >= 0);
if(area < mn){
pos = i;
mn = min(mn, area);
}
}
// {
// for(auto &p : out){
// cout << p << endl;
// }
// }
int siz = out.size();
for(int i = 1; i < sz(out); i ++){
Point x = out[i], y = out[(i + 1) % siz];
mn = min(mn, cross(x - in[pos], y - in[pos]));
while(cross(x - in[pos], y - in[pos]) > cross(x - in[(pos + 1) % m], y - in[(pos + 1) % m])){
assert(cross(x - in[pos], y - in[pos]) >= 0);
assert(cross(x - in[(pos + 1) % m], y - in[(pos + 1) % m]) >= 0);
mn = min(mn, cross(x - in[(pos + 1) % m], y - in[(pos + 1) % m]));
pos = (pos + 1) % m;
}
}
cout << ans - mn << endl;
}
signed main(){
ios::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
int Case; cin >> Case; while(Case --) solve();
return 0;
}
这程序好像有点Bug,我给组数据试试?
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 0ms
memory: 3760kb
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: 3856kb
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: 0
Accepted
time: 33ms
memory: 3644kb
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 4...
result:
ok 1000 lines
Test #4:
score: 0
Accepted
time: 49ms
memory: 3688kb
input:
10000 9 484630042 51929469 -40468396 -517784096 98214104 -103353239 629244333 -475172587 106398764 153884485 49211709 -44865749 1 10 166321833 -247717657 406208245 668933360 13 548702216 -631976459 37150086 -292461024 707804811 -486185860 239775286 -903166050 10096571 -541890068 686103484 558731937 ...
output:
950319193795831919 1661025342421008544 1285164852091455548 1159924751776806668 1206071151805176722 794021230296144371 699991678992587791 1133990718508584290 1486311831172661605 984875884297072200 1327767982175057345 758247019006396699 1355381234262206155 1139262078529131471 1613462877860621700 12392...
result:
ok 10000 lines
Test #5:
score: 0
Accepted
time: 80ms
memory: 4452kb
input:
100 439 471536154 -312612104 155692036 -937312180 -461624056 -357636609 236656684 -911414873 -288656914 -74788431 -465779694 -381475149 -334197401 -903065737 491513067 -447615916 337664889 -852236281 -281689379 -53519178 -159101704 -920779200 -326159514 -95396204 21868593 -994282736 488425383 -41046...
output:
1973162724053130487 2054612790507830954 1726805687754843724 1699420177872986528 2129388571309147631 2198295137903288810 1697185883164440272 1219697450095721478 2027023581922285255 1674691247127206655 1673105966817209954 2179188692918747442 2146544318743443141 2230356305133660648 1676850321902993764 ...
result:
ok 100 lines
Test #6:
score: 0
Accepted
time: 66ms
memory: 4372kb
input:
100 1362 -467257672 -466669 -467054869 -478108 -466973270 -481776 -466556983 -499770 -466329414 -508693 -466248017 -511805 -466158865 -513786 -466101273 -515035 -465927700 -518748 -465717624 -522106 -465303448 -528127 -465124548 -530726 -464649746 -536693 -464554872 -537799 -464478196 -538680 -46416...
output:
1666097696993497 1791366071767866 1806187278469532 1683419854733713 1685891971828916 1730190225081651 1787048201197565 1850308098208660 1710694884375502 1826363113637639 1816375352374659 2047431269497691 1549806516003854 1829438662895747 1678707854135065 1687423392883819 2121960009997761 16687219538...
result:
ok 100 lines
Test #7:
score: 0
Accepted
time: 37ms
memory: 10784kb
input:
2 62666 -486101704 -505730259 -486101698 -506082699 -486101689 -506111362 -486101682 -506126031 -486101528 -506293759 -486101259 -506556385 -486101196 -506613483 -486101154 -506648604 -486100935 -506831392 -486100631 -507083675 -486100470 -507199151 -486100233 -507368923 -486100193 -507397039 -48609...
output:
2178736946152219010 1825181940245096152
result:
ok 2 lines
Test #8:
score: 0
Accepted
time: 123ms
memory: 15072kb
input:
2 100000 301945097 76373292 467957663 -286424714 8245445 -597212507 -474204621 -708828667 184159460 105942538 443435905 -429212625 490658771 -382198656 82512047 -612522436 -228221388 -965890088 394789011 -145801151 -106120174 -528202395 428939626 -194437311 497429477 -527407728 365739746 -114818962 ...
output:
2502889432701099511 2267250485735988121
result:
ok 2 lines
Test #9:
score: 0
Accepted
time: 130ms
memory: 15048kb
input:
2 100000 221128057 -975244780 -618765360 -785575858 422567455 -906331476 -988680318 -150037424 -929870145 367887908 -757813541 -652471177 291995621 -956419655 -785381507 619012026 468864522 -883270094 -588416522 808557973 859345881 511394814 988105866 153775152 216931298 -976186873 467050734 8842305...
output:
6283183114882825575 6283183188903854361
result:
ok 2 lines
Test #10:
score: 0
Accepted
time: 0ms
memory: 3536kb
input:
7 5 -1000000000 -1000000000 1000000000 -1000000000 1000000000 1000000000 1 0 -1 0 5 1000000000 1000000000 -1000000000 -1000000000 -2 0 -1 0 1 -1 6 1000000000 1000000000 -1000000000 -1000000000 -3 0 -1 0 0 -1 1 -1 4 -1000000000 -1000000000 1000000000 -1000000000 1000000000 1000000000 -1000000000 1000...
output:
4000000000000000000 7000000000 9000000001 -1 6000000002000000000 7999999998000000000 -1
result:
ok 7 lines
Extra Test:
score: 0
Extra Test Passed