QOJ.ac

QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#690487#9520. Concave HullkinuruAC ✓130ms15072kbC++236.5kb2024-10-30 22:28:142024-10-30 22:28:23

Judging History

你现在查看的是最新测评结果

  • [2024-10-30 22:28:23]
  • 评测
  • 测评结果:AC
  • 用时:130ms
  • 内存:15072kb
  • [2024-10-30 22:28:14]
  • 提交

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