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QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#694978#9520. Concave Hullanswerend42AC ✓72ms10696kbC++175.8kb2024-10-31 19:03:552024-10-31 19:03:56

Judging History

This is the latest submission verdict.

  • [2024-10-31 19:03:56]
  • Judged
  • Verdict: AC
  • Time: 72ms
  • Memory: 10696kb
  • [2024-10-31 19:03:55]
  • Submitted

answer

#include <bits/stdc++.h>
using namespace std;
using i64 = long long;
using f64 = double;
const double eps = 1e-9;

template <class T>
bool eq(T a, T b) { return abs(a - b) < eps; }  // ==
template <class T>
bool gt(T a, T b) { return a - b > eps; }  // >
template <class T>
bool lt(T a, T b) { return a - b < -eps; }  // <
template <class T>
bool ge(T a, T b) { return a - b > -eps; }  // >=
template <class T>
bool le(T a, T b) { return a - b < eps; }  // <=



template <class T>
struct Point {
    T x, y;
    Point(T x_ = 0, T y_ = 0) : x(x_), y(y_) {}
    template <class U>
    operator Point<U>() { return Point<U>(U(x), U(y)); }
    Point& operator+=(Point p) & { x += p.x, y += p.y;return *this; }
    Point& operator-=(Point p) & { x -= p.x, y -= p.y;return *this; }
    Point& operator*=(T v) & { x *= v, y *= v;return *this; }
    Point operator-() const { return Point(-x, -y); }
    friend Point operator+(Point a, Point b) { return a += b; }
    friend Point operator-(Point a, Point b) { return a -= b; }
    friend Point operator*(Point a, T b) { return a *= b; }
    friend Point operator*(T a, Point b) { return b *= a; }
    friend bool operator==(Point a, Point b) { return a.x == b.x && a.y == b.y; }
    friend bool operator!=(Point a, Point b) { return !(a == b); }
    friend bool operator<(Point a, Point b) {
        if(eq(a.x, b.x)) return lt(a.y, b.y);
        return lt(a.x, b.x);
    }
    friend istream &operator>>(istream &is, Point& p) { return is >> p.x >> p.y; }
    friend ostream &operator<<(ostream &os, Point p) { return os << "(" << p.x << ", " << p.y << ")"; }
};
template <class T>
using Vec = Point<T>;

template <class T>
struct Line {
    Point<T> a, b;
    Line(Point<T> a_ = Point<T>(), Point<T> b_ = Point<T>()) : a(a_), b(b_) {}
};
template <class T>
using Seg = Line<T>;

// 点乘
template <class T>
T dot(Vec<T> a, Vec<T> b) { return a.x * b.x + a.y * b.y; }

// 模长平方
template <class T>
T square(Vec<T> p) { return dot(p, p); }

// 叉乘
template <class T>
T cross(Vec<T> a, Vec<T> b) { return a.x * b.y - a.y * b.x; }

// 向量长度
// square
template <class T>
double len(Vec<T> p) { return sqrt(double(square(p))); }

// 求凸包
template <class T>
vector<Point<T>> hull(vector<Point<T>> p) {
    vector<Point<T>> h, l;
    sort(p.begin(), p.end(), [&](auto a, auto b) {
        if (a.x != b.x) {
            return a.x < b.x;
        } else {
            return a.y < b.y;
        }
    });
    p.erase(unique(p.begin(), p.end()), p.end());
    if (p.size() <= 1) {
        return p;
    }

    for (auto a : p) {
        while (h.size() > 1 && le(cross(a - h.back(), a - h[h.size() - 2]), (T)0)) {
            h.pop_back();
        }
        while (l.size() > 1 && ge(cross(a - l.back(), a - l[l.size() - 2]), (T)0)) {
            l.pop_back();
        }
        l.push_back(a);
        h.push_back(a);
    }

    l.pop_back();
    reverse(h.begin(), h.end());
    h.pop_back();
    l.insert(l.end(), h.begin(), h.end());
    return l;
}

// 直线相交
template <class T>
Point<T> inter(Line<T> l1, Line<T> l2) {
    return l1.a + (l1.b - l1.a) * (cross(l2.b - l2.a, l1.a - l2.a) / cross(l2.b - l2.a, l1.a - l1.b));
}

// 点到线段最近点
template <class T>
Point<T> closet_seg(Point<T> p, Line<T> l) {
    auto t = p;
    t.x += l.a.y - l.b.y;
    t.y += l.b.x - l.a.x;
    if (gt(cross(l.a - p, t - p) * cross(l.b - p, t - p), (T)0)) {
        return lt(dis(p, l.a), dis(p, l.b)) ? l.a : l.b;
    }
    return inter(Line<T>(p, t), l);
}

// 线段间最近距离
template <class T>
T dis_seg(Seg<T> s1, Seg<T> s2) {
    return min(min(closet_seg(s1.a, s2), closet_seg(s1.b, s2), 
                min(closet_seg(s2.a, s1), closet_seg(s2.b, s1))));
}

template <class T>
i64 area_t(Point<T> p, Seg<T> s) {
    return abs(cross(s.a - p, s.b - p));
};

template <class T>
i64 RotateCalipers(vector<Point<T>> P1, vector<Point<T>> P2) {
    int n = P1.size(), m = P2.size();
    int j = 0;
    i64 res = LONG_LONG_MAX;
    for(int i = 0; i < n; i++) {
        auto u = P1[i], v = P1[(i + 1) % n];
        while(abs(cross(u - P2[(j + 1) % m], v - P2[(j + 1) % m])) < 
              abs(cross(u - P2[j], v - P2[j]))) j = (j + 1) % m;
        res = min(res, area_t(P2[j], {u, v}));
    }
    return res;
}

template <class T> 
i64 calculateArea(const vector<Point<T>>& P) {
    int n = P.size();
    i64 area = 0;
    for (int i = 0; i < n; i++) {
        int j = (i + 1) % n;
        area += cross(P[i], P[j]);
    }
    return area;
}

template<typename T>
struct std::hash<Point<T>> {
    size_t operator()(const Point<T>& p) const noexcept {  // 添加 noexcept
        return std::hash<T>()(p.x) ^ (std::hash<T>()(p.y) << 1);
    }
};


void solve() {
    int n;
    cin >> n;
    vector<Point<i64>> P(n);
    for(auto &i : P) cin >> i;
    auto tu1 = hull(P);
    vector<Point<i64>> left;
    unordered_set<Point<i64>> tu1_set(tu1.begin(), tu1.end());
    for(int i = 0; i < n; i++) {
        if(tu1_set.find(P[i]) == tu1_set.end()) {
            left.push_back(P[i]);
        }
    }
    auto tu2 = hull(left);
    i64 Area = abs(calculateArea(tu1));
    if(tu2.size() == 0) {
        cout << "-1\n";
        return;
    }
    if(tu2.size() <= 2) {
        i64 d = LONG_LONG_MAX;
        for(int i = 0; i < tu2.size(); i++) {
            for(int j = 0; j < tu1.size(); j++) {
                d = min(area_t(tu2[i], {tu1[j], tu1[(j + 1) % tu1.size()]}), d);
            }
        }
        cout << (i64)(Area - d) << '\n';
        return;
    }
    i64 ans = RotateCalipers(tu1, tu2);
    cout << (i64)(Area - ans) << '\n';
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0), cout.tie(0);
    int t = 1;
    cin >> t;
    while(t--) {
        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: 3628kb

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: 3604kb

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: 29ms
memory: 3696kb

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: 43ms
memory: 3584kb

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: 62ms
memory: 4244kb

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: 48ms
memory: 3988kb

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: 25ms
memory: 7872kb

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: 72ms
memory: 10188kb

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: 66ms
memory: 10696kb

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: 3632kb

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