QOJ.ac

QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#697668#9520. Concave HullNephrennAC ✓118ms15624kbC++209.3kb2024-11-01 15:16:592024-11-01 15:17:00

Judging History

你现在查看的是最新测评结果

  • [2024-11-01 15:17:00]
  • 评测
  • 测评结果:AC
  • 用时:118ms
  • 内存:15624kb
  • [2024-11-01 15:16:59]
  • 提交

answer

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> PII;
typedef pair<ll, ll> PLL;

const int MAXN = 2e5 + 10;
const int INF = 0x3f3f3f3f;
const ll INFLL = 0x3f3f3f3f3f3f3f3f;

namespace Geometry {
using T = ll;
constexpr T eps = 1e-8;
 
bool eq(const T &x, const T &y) { return abs(x - y) <= eps; }
inline constexpr int type(T x, T y) {
    if(x == 0 and y == 0) return 0;
    if(y < 0 or (y == 0 and x > 0)) return -1;
    return 1;
}
struct Point {
    T x, y;
    constexpr Point(T _x = 0, T _y = 0) : x(_x), y(_y) {}
    constexpr Point operator+() const noexcept { return *this; }
    constexpr Point operator-() const noexcept { return Point(-x, -y); }
    constexpr Point operator+(const Point &p) const { return Point(x + p.x, y + p.y); }
    constexpr Point operator-(const Point &p) const { return Point(x - p.x, y - p.y); }
    constexpr Point &operator+=(const Point &p) { return x += p.x, y += p.y, *this; }
    constexpr Point &operator-=(const Point &p) { return x -= p.x, y -= p.y, *this; }
    constexpr T operator*(const Point &p) const { return x * p.x + y * p.y; }
    constexpr Point &operator*=(const T &k) { return x *= k, y *= k, *this; }
    constexpr Point operator*(const T &k) { return Point(x * k, y * k); }
    constexpr bool operator==(const Point &r) const noexcept { return r.x == x and r.y == y; }
    constexpr T cross(const Point &r) const { return x * r.y - y * r.x; }
 
    constexpr bool operator<(const Point &r) const { return pair(x, y) < pair(r.x, r.y); }
 
    // 1 : left, 0 : same, -1 : right
    constexpr int toleft(const Point &r) const {
        auto t = cross(r);
        return t > eps ? 1 : t < -eps ? -1 : 0;
    }
 
    constexpr bool arg_cmp(const Point &r) const {
        int L = type(x, y), R = type(r.x, r.y);
        if(L != R) return L < R;
 
        T X = x * r.y, Y = r.x * y;
        if(X != Y) return X > Y;
        return x < r.x;
    }
};
bool arg_cmp(const Point &l, const Point &r) { return l.arg_cmp(r); }
ostream &operator<<(ostream &os, const Point &p) { return os << p.x << " " << p.y; }
istream &operator>>(istream &is, Point &p) {
    is >> p.x >> p.y;
    return is;
}
 
struct Line {
    Point a, b;
    Line() = default;
    Line(Point a, Point b) : a(a), b(b) {}
    // ax + by = c
    Line(T A, T B, T C) {
        if(A == 0) {
            a = Point(0, C / B), b = Point(1, C / B);
        } else if(B == 0) {
            a = Point(C / A, 0), b = Point(C / A, 1);
        } else {
            a = Point(0, C / B), b = Point(C / A, 0);
        }
    }
    // 1 : left, 0 : same, -1 : right
    constexpr int toleft(const Point &r) const {
        auto t = (b - a).cross(r - a);
        return t > eps ? 1 : t < -eps ? -1 : 0;
    }
 
    friend std::ostream &operator<<(std::ostream &os, Line &ls) {
        return os << "{"
                  << "(" << ls.a.x << ", " << ls.a.y << "), (" << ls.b.x << ", " << ls.b.y << ")}";
    }
};
istream &operator>>(istream &is, Line &p) { return is >> p.a >> p.b; }
 
struct Segment : Line {
    Segment() = default;
    Segment(Point a, Point b) : Line(a, b) {}
};
 
ostream &operator<<(ostream &os, Segment &p) { return os << p.a << " to " << p.b; }
istream &operator>>(istream &is, Segment &p) {
    is >> p.a >> p.b;
    return is;
}
 
struct Circle {
    Point p;
    T r;
    Circle() = default;
    Circle(Point p, T r) : p(p), r(r) {}
};
 
using pt = Point;
using Points = vector<pt>;
using Polygon = Points;
T cross(const pt &x, const pt &y) { return x.x * y.y - x.y * y.x; }
T dot(const pt &x, const pt &y) { return x.x * y.x + x.y * y.y; }
 
T abs2(const pt &x) { return dot(x, x); }
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_C
// 点の回転方向
int ccw(const Point &a, Point b, Point c) {
    b = b - a, c = c - a;
    if(cross(b, c) > 0) return +1;   // "COUNTER_CLOCKWISE"
    if(cross(b, c) < 0) return -1;   // "CLOCKWISE"
    if(dot(b, c) < 0) return +2;     // "ONLINE_BACK"
    if(abs2(b) < abs2(c)) return -2; // "ONLINE_FRONT"
    return 0;                        // "ON_SEGMENT"
}
 
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_A
// 平行判定
bool parallel(const Line &a, const Line &b) { return (cross(a.b - a.a, b.b - b.a) == 0); }
 
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_A
// 垂直判定
bool orthogonal(const Line &a, const Line &b) { return (dot(a.a - a.b, b.a - b.b) == 0); }
 
bool intersect(const Line &l, const Point &p) { return abs(ccw(l.a, l.b, p)) != 1; }
 
bool intersect(const Line &l, const Line &m) { return !parallel(l, m); }
 
bool intersect(const Segment &s, const Point &p) { return ccw(s.a, s.b, p) == 0; }
 
bool intersect(const Line &l, const Segment &s) { return cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) <= 0; }
 
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_B
bool intersect(const Segment &s, const Segment &t) { return ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) <= 0 && ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) <= 0; }
 
bool intersect(const Polygon &ps, const Polygon &qs) {
    int pl = ps.size(), ql = qs.size(), i = 0, j = 0;
    while((i < pl or j < ql) and (i < 2 * pl) and (j < 2 * ql)) {
        auto ps0 = ps[(i + pl - 1) % pl], ps1 = ps[i % pl];
        auto qs0 = qs[(j + ql - 1) % ql], qs1 = qs[j % ql];
        if(intersect(Segment(ps0, ps1), Segment(qs0, qs1))) return true;
        Point a = ps1 - ps0;
        Point b = qs1 - qs0;
        T v = cross(a, b);
        T va = cross(qs1 - qs0, ps1 - qs0);
        T vb = cross(ps1 - ps0, qs1 - ps0);
 
        if(!v and va < 0 and vb < 0) return false;
        if(!v and !va and !vb) {
            i += 1;
        } else if(v >= 0) {
            if(vb > 0)
                i += 1;
            else
                j += 1;
        } else {
            if(va > 0)
                j += 1;
            else
                i += 1;
        }
    }
    return false;
}
 
T norm(const Point &p) { return p.x * p.x + p.y * p.y; }
Point projection(const Segment &l, const Point &p) {
    T t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
    return l.a + (l.a - l.b) * t;
}
 
Point crosspoint(const Line &l, const Line &m) {
    T A = cross(l.b - l.a, m.b - m.a);
    T B = cross(l.b - l.a, l.b - m.a);
    if(A == 0 and B == 0) return m.a;
    return m.a + (m.b - m.a) * (B / A);
}
 
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_C
Point crosspoint(const Segment &l, const Segment &m) { return crosspoint(Line(l), Line(m)); }
 
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_B
// 凸性判定
bool is_convex(const Points &p) {
    int n = (int)p.size();
    for(int i = 0; i < n; i++) {
        if(ccw(p[(i + n - 1) % n], p[i], p[(i + 1) % n]) == -1) return false;
    }
    return true;
}
 
Points convex_hull(Points p) {
    int n = p.size(), k = 0;
    if(n <= 2) return p;
    sort(begin(p), end(p), [](pt x, pt y) { return (x.x != y.x ? x.x < y.x : x.y < y.y); });
    Points ch(2 * n);
    for(int i = 0; i < n; ch[k++] = p[i++]) {
        while(k >= 2 && cross(ch[k - 1] - ch[k - 2], p[i] - ch[k - 1]) <= 0) --k;
    }
    for(int i = n - 2, t = k + 1; i >= 0; ch[k++] = p[i--]) {
        while(k >= t && cross(ch[k - 1] - ch[k - 2], p[i] - ch[k - 1]) <= 0) --k;
    }
    ch.resize(k - 1);
    return ch;
}
 
// 面積の 2 倍
T area2(const Points &p) {
    T res = 0;
    for (int i = 0; i < p.size(); ++i) { res += cross(p[i], p[i == p.size() - 1 ? 0 : i + 1]); }
    return res;
}

}

using namespace Geometry;

void solve () {
    int n;
    cin >> n;
    Points a(n);
    for (int i = 0; i < n; ++i) {
        cin >> a[i];
    }

    auto c1 = convex_hull(a);
    set<pt> tmp;
    for (auto i : c1) tmp.insert(i);
    Points b;
    for (int i = 0; i < n; ++i) {
        if (!tmp.count(a[i])) b.push_back(a[i]);
    }
    auto c2 = convex_hull(b);

    if (c1.size() <= 2 || c2.empty()) {
        cout << "-1\n";
        return;
    }

    ll S1 = area2(c1);

    if (c2.size() <= 2) {
        ll res = 5e18;
        for (int i = 0; i < c2.size(); ++i) {
            for (int j = 0; j < c1.size(); ++j) {
                int k = (j + 1) % c1.size();
                res = min(res, abs(cross(c1[j] - c2[i], c1[k] - c2[i])));
            }
        }
        cout << S1 - res << "\n";
    } else {
        int p = 0;
        Line ini(c1[0], c1[1]);
        for (int i = 0; i < c2.size(); ++i) {
            if (abs(cross(c1[0] - c2[i], c1[1] - c2[i])) < abs(cross(c1[0] - c2[i], c1[1] - c2[i]))) p = i;
        }

        ll res = 5e18;

        for (int i = 0; i < c1.size(); ++i) {
            int j = (i + 1) % c1.size();
            Line now(c1[i], c1[j]);
            res = min(res, abs(cross(c1[i] - c2[p], c1[j] - c2[p])));
            while (abs(cross(c1[i] - c2[(p + 1) % c2.size()], c1[j] - c2[(p + 1) % c2.size()])) < abs(cross(c1[i] - c2[p], c1[j] - c2[p]))) p = (p + 1) % c2.size();
            res = min(res, abs(cross(c1[i] - c2[p], c1[j] - c2[p])));
        }

        cout << S1 - res << "\n";
    }
}

int main () {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    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: 3816kb

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: 3660kb

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: 30ms
memory: 3736kb

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: 41ms
memory: 3700kb

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
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1327767982175057345
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1355381234262206155
1139262078529131471
1613462877860621700
12392...

result:

ok 10000 lines

Test #5:

score: 0
Accepted
time: 68ms
memory: 4336kb

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: 54ms
memory: 4444kb

input:

100
1362
-467257672 -466669
-467054869 -478108
-466973270 -481776
-466556983 -499770
-466329414 -508693
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-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: 19ms
memory: 10572kb

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: 83ms
memory: 15624kb

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: 118ms
memory: 14956kb

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: 3644kb

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