QOJ.ac

QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#714506#9520. Concave Hull0x3fffffffAC ✓48ms9284kbC++235.5kb2024-11-05 23:43:202024-11-05 23:43:21

Judging History

This is the latest submission verdict.

  • [2024-11-05 23:43:21]
  • Judged
  • Verdict: AC
  • Time: 48ms
  • Memory: 9284kb
  • [2024-11-05 23:43:20]
  • Submitted

answer

#include <bits/stdc++.h>
using namespace std;
using LL = long long;
using point_t = long long;
//using point_t = long double;  //全局数据类型

constexpr point_t eps = 1e-8;
constexpr point_t INF = numeric_limits<point_t>::max();
constexpr long double PI = 3.1415926535897932384l;

// 点与向量
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 (abs(x - a.x) <= eps) return y < a.y - eps; return x < a.x - eps; }
    bool operator>(const point& a) const { return !(*this < a || *this == a); }
    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 { return { -x,-y }; }
    point operator*(const T k) const { return { k * x,k * y }; }
    point operator/(const T k) const { return { x / k,y / k }; }
    T operator*(const point& a) const { return x * a.x + y * a.y; }  // 点积
    T operator^(const point& a) const { return x * a.y - y * a.x; }  // 叉积,注意优先级
    int toleft(const point& a) const { const auto t = (*this) ^ a; return (t > eps) - (t < -eps); }  // to-left 测试
    T len2() const { return (*this) * (*this); }  // 向量长度的平方
    T dis2(const point& a) const { return (a - (*this)).len2(); }  // 两点距离的平方

    // 涉及浮点数
    long double len() const { return sqrtl(len2()); }  // 向量长度
    long double dis(const point& a) const { return sqrtl(dis2(a)); }  // 两点距离
    long double ang(const point& a) const { return acosl(max(-1.0l, min(1.0l, ((*this) * a) / (len() * a.len())))); }  // 向量夹角
    point rot(const long double rad) const { return { x * cos(rad) - y * sin(rad),x * sin(rad) + y * cos(rad) }; }  // 逆时针旋转(给定角度)
    point rot(const long double cosr, const long double sinr) const { return { x * cosr - y * sinr,x * sinr + y * cosr }; }  // 逆时针旋转(给定角度的正弦与余弦)
};

using Point = point<point_t>;

LL cross(Point a, Point b, Point c) { //叉积  
    return (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x);
}

int t = 0;
vector<int>convex(vector<Point>& p) {
    sort(p.begin() + 1, p.end());
    int n = p.size() - 1;
    if (n == 1) {
        t = 1;
        return { 0,1 };
    }
    if (n == 2) {
        t = 2;
        return { 0,1,2 };
    }
    vector<int>s(n + 10);
    t = 0;
    for (int i = 1;i <= n;i++) {
        while (t > 1 and cross(p[s[t - 1]], p[s[t]], p[i]) <= 0) {
            t--;
        }
        s[++t] = i;
    }
    int k = t;
    for (int i = n - 1;i >= 1;i--) {
        while (t > k and cross(p[s[t - 1]], p[s[t]], p[i]) <= 0) {
            t--;
        }
        s[++t] = i;
    }
    t--;
    return s;
}

void solve() {

    int n;
    cin >> n;
    vector<Point>a(n + 1);
    for (int i = 1;i <= n;i++) {
        cin >> a[i].x >> a[i].y;
    }
    vector<Point>b, wd, nd;
    b.push_back({ 0,0 });
    auto s = convex(a);

    if (t == n || n <= 3) {
        cout << "-1\n";return;
    }

    vector<int>vis(n + 1);
    for (int i = 1;i <= t;i++) {
        vis[s[i]] = 1;
        wd.push_back(a[s[i]]);
    }

    for (int i = 1;i <= n;i++) {
        if (!vis[i])b.push_back(a[i]);
    }

    s = convex(b);

    for (int i = 1;i <= t;i++) {
        nd.push_back(b[s[i]]);
    }

    LL sum = 0, ans = INF;


    int wn = wd.size(), nn = nd.size();

    for (int i = 1;i < wn - 1;i++) {
        sum += (wd[i] - wd[0]) ^ (wd[i + 1] - wd[0]);
    }

    auto nxtj = [&](int x, int t = 1) {
        return (x + t) % nn;
    };
    auto nxti = [&](int x, int t = 1) {
        return (x + t) % wn;
    };

    // for (auto [x, y] : wd) {
    //     cout << x << " " << y << "\n";
    // }
    // cout << "\n";
    // for (auto [x, y] : nd) {
    //     cout << x << " " << y << "\n";
    // }
    for (int i = 0, j = 0;i < wn;i++) {
        for (;;) {
            LL cur = cross(wd[i], wd[nxti(i)], nd[j]);
            LL ne = cross(wd[i], wd[(nxti(i))], nd[nxtj(j)]);
            ans = min({ ans,cur,ne });
            if (ne >= cur)break;
            j = nxtj(j);
        }
    }
    // auto [x, y] = wd[3];
    // cout << x << " " << y << "\n";
    // cout << sum << "\n";
    // for (int i = 0, j = 0;i < wn;i++) {
    //     while (cross(nd[j], wd[i], wd[nxti(i)]) >= cross(nd[nxtj(j)], wd[i], wd[nxti(i)]))j = nxtj(j);
    //     // cerr << i << " " << nxti(i) << "\n";
    //     // cerr << i << " " << j << "\n\n";
    //     // cerr << cross(nd[j], wd[i], wd[nxti(i)]) << "\n";
    //     // cerr << cross(nd[nxtj(j)], wd[i], wd[nxti(i)]) << "\n\n";
    //     // cerr << wd[i] << " " << wd[nxti(i)] << "\n";
    //     // auto [x, y] = wd[i];
    //     // auto [xz, zy] = wd[nxti(i)];
    //     // auto [xx, yy] = nd[j];
    //     ans = max(ans, sum - cross(nd[j], wd[i], wd[nxti(i)]));
    // }

    cout << sum - ans << "\n";
    // for (int i = 1;i <= t;i++) {
    //     nd.push_back(b[s[i]]);
    // }

    // for (auto [x, y] : wd) {
    //     cout << x << " " << y << "\n";
    // }
    // cout << "\n";
    // for (auto [x, y] : nd) {
    //     cout << x << " " << y << "\n";
    // }
}

signed main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
    int T = 1;
#ifdef LOCAL
    freopen("data.in", "r", stdin);
    freopen("data.out", "w", stdout);
#endif
    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: 1ms
memory: 3600kb

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: 0ms
memory: 3556kb

input:

10
243
-494423502 -591557038
-493438474 -648991734
-493289308 -656152126
-491185085 -661710614
-489063449 -666925265
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-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: 18ms
memory: 3868kb

input:

1000
125
64661186 -13143076
302828013 -185438065
-418713797 -191594241
430218126 -397441626
354327250 -836704374
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468137 -584752683
258775829 96211747
-358669612 -134890109
-129221188 -998432368
-277309896 -140056561
356901185 420557649
-51...

output:

1986320445246155278
1900093336073022078
1612088392301142476
2012259136539173407
1819942017252118749
1772230185841892196
1164835025329039520
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1868728080720036006
667458140583450322
2127932992585026491
4...

result:

ok 1000 lines

Test #4:

score: 0
Accepted
time: 34ms
memory: 3616kb

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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1355381234262206155
1139262078529131471
1613462877860621700
12392...

result:

ok 10000 lines

Test #5:

score: 0
Accepted
time: 48ms
memory: 4080kb

input:

100
439
471536154 -312612104
155692036 -937312180
-461624056 -357636609
236656684 -911414873
-288656914 -74788431
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337664889 -852236281
-281689379 -53519178
-159101704 -920779200
-326159514 -95396204
21868593 -994282736
488425383 -41046...

output:

1973162724053130487
2054612790507830954
1726805687754843724
1699420177872986528
2129388571309147631
2198295137903288810
1697185883164440272
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2027023581922285255
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2179188692918747442
2146544318743443141
2230356305133660648
1676850321902993764
...

result:

ok 100 lines

Test #6:

score: 0
Accepted
time: 37ms
memory: 3800kb

input:

100
1362
-467257672 -466669
-467054869 -478108
-466973270 -481776
-466556983 -499770
-466329414 -508693
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-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: 6524kb

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: 47ms
memory: 9284kb

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: 44ms
memory: 8168kb

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: 3752kb

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