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QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#593981#8779. Square of TrianglesbettererWA 658ms6036kbC++238.9kb2024-09-27 17:44:402024-09-27 17:44:40

Judging History

你现在查看的是最新测评结果

  • [2024-09-27 17:44:40]
  • 评测
  • 测评结果:WA
  • 用时:658ms
  • 内存:6036kb
  • [2024-09-27 17:44:40]
  • 提交

answer

#ifndef ONLINE_JUDGE
// #define ONLINE_JUDGE
#endif
#include <bits/stdc++.h>
using namespace std;
#define int long long
using ull = unsigned long long;

#ifdef ONLINE_JUDGE
#define des(...)
#define de(...)
#else
#define des(x) cerr<<(x)<<endl
#endif

struct point {
    double x, y;

    bool operator<(const point& p) const {
        return x < p.x || (x == p.x && y < p.y);
    }

    point operator-(const point& p) const {
        return {x - p.x, y - p.y};
    }

    point operator+(const point& p) const {
        return {x + p.x, y + p.y};
    }

    double operator*(const point& p) const {
        return x * p.y - y * p.x;
    }

    [[nodiscard]] point complex_mul(const point& p) const {
        return {x * p.x - y * p.y, x * p.y + y * p.x};
    }

    [[nodiscard]] point complex_div(const point& p) const {
        return {x * p.x + y * p.y, y * p.x - x * p.y};
    }

    point operator*(const double v) const {
        return {x * v, y * v};
    }

    point operator/(const double v) const {
        return {x / v, y / v};
    }

    [[nodiscard]] double hypot() const {
        return ::hypot(x, y);
    }

    [[nodiscard]] point unit() const {
        return *this / hypot();
    }

    [[nodiscard]] double dot(const point& p) const {
        return x * p.x + y * p.y;
    }
#ifndef ONLINE_JUDGE
    void print() const {
        ::print(make_pair(x, y));
    }
#endif
};

struct line {
    point p1, p2;

    [[nodiscard]] bool separate(const point& q1, const point& q2) const {
        double t1 = (q1 - p1) * (p2 - p1), t2 = (q2 - p1) * (p2 - p1);
        return abs(t1) > 1e-6 && abs(t2) > 1e-6 && t1 * t2 < 0;
    }

    [[nodiscard]] bool intersect(const line& l) const {
        return separate(l.p1, l.p2) && l.separate(p1, p2);
    }
};

struct triangle {
    vector<point> ps;


    static triangle from_edge(double x, double y, double z) {
        triangle ret;
        ret.ps.emplace_back(0, 0);
        ret.ps.emplace_back(sqrt(x), 0);
        double cos_angle = (x + y - z) / (2 * sqrt(x * y));
        ret.ps.emplace_back(sqrt(y) * cos_angle, sqrt(y) * sqrt(1 - cos_angle * cos_angle));
        return ret;
    }

    [[nodiscard]] double size() const {
        return abs((ps[1] - ps[0]) * (ps[2] - ps[0])) / 2;
    }

    [[nodiscard]] bool intersect(const triangle& t) const {
        for (int i = 0; i < ps.size(); ++i) {
            for (int j = 0; j < t.ps.size(); ++j) {
                if (line{ps[i], ps[(i + 1) % ps.size()]}.intersect({t.ps[j], t.ps[(j + 1) % t.ps.size()]}))return true;
            }
        }
        return false;
    }
#ifndef ONLINE_JUDGE
    void print() const {
        ::print(ps);
    }
#endif
};

double area;

struct many_triangle {
    vector<triangle> ts;

    [[nodiscard]] vector<many_triangle> combine_with(const triangle& tri) const {
        vector<many_triangle> ret;
        for (auto& t : ts) {
            vector<int> perm(3);
            iota(perm.begin(), perm.end(), 0);
            do {
                auto vec1 = t.ps[perm[1]] - t.ps[perm[0]];
                auto vec2 = t.ps[perm[2]] - t.ps[perm[0]];
                auto angle = vec1 * vec2 > 0 ? vec1.unit().complex_div(tri.ps[2].unit()).unit() : vec1.unit();
                auto pos = t.ps[perm[0]];
                auto tri2 = tri;
                for (auto& p : tri2.ps)p = p.complex_mul(angle) + pos;
                // 剪枝,去掉过远点
                for (auto& p : tri2.ps) {
                    for (auto& t2 : ts) {
                        for (auto& p2 : t2.ps) {
                            if ((p - p2).hypot() > sqrt(area * 2) * (1 + .01)) {
                                goto end;
                            }
                        }
                    }
                }
                for (auto& t2 : ts) {
                    if (t2.intersect(tri2)) {
                        goto end;
                    }
                }
                {
                    many_triangle rt = *this;
                    rt.ts.push_back(tri2);
                    ret.push_back(rt);
                }
            end:;
            } while (ranges::next_permutation(perm).found);
        }
        return ret;
    }

    [[nodiscard]] bool check() const {
        vector<point> vp;
        for (auto& t : ts)for (auto& p : t.ps)vp.push_back(p);
        // 求凸包
        sort(vp.begin(), vp.end());
        sort(vp.begin() + 1, vp.end(), [&](const point& u, const point& v) {
            auto t = (u - vp[0]) * (v - vp[0]);
            if (t)return t > 0;
            return u < v;
        });
        vector<point> sta;
        sta.push_back(vp[0]);
        for (int i = 1; i < vp.size(); ++i) {
            while (sta.size() >= 2 && (sta.back() - sta[sta.size() - 2]) * (vp[i] - sta.back()) <= 1e-6) {
                sta.pop_back();
            }
            sta.push_back(vp[i]);
        }
        // sta.push_back(vp[0]); //sta+1
        // if (sta.size() != 4) {
        //     // de(*this);
        //     // des("not 4 edges");
        //     return false;
        // }
        double s = 0, c = 0;
        for (int i = 1; i < sta.size(); ++i) {
            s += (sta[i - 1] - sta[0]) * (sta[i] - sta[0]) / 2;
        }
        vector<double> edges;
        for (int i = 0; i < sta.size(); ++i) {
            edges.push_back((sta[i] - sta[(i + 1) % sta.size()]).hypot());
            c += edges.back();
        }
        if (abs(s / area - 1) > 1e-6) {
            // des("not same area");
            // de(ans, area);
            return false;
        }
        if (abs(c / (4 * sqrt(area)) - 1) > 1e-6) {
            return false;
        }
        de(*this);
        de(s, area, c, 4 * sqrt(area), sta);
        // ranges::sort(edges);
        // while (edges.front() < 1e-6) edges.erase(edges.begin());
        // de(edges.size(), edges);
        // if (edges.size() != 4) {
        //     des("not 4 edges");
        //     return false;
        // }
        // if (abs(edges.front() - edges.back()) > 1e-6) {
        //     des("not equal edges");
        //     // de(edges);
        //     return false;
        // }
        return true;
        if (abs((sta[0] - sta[1]).hypot() - (sta[1] - sta[2]).hypot()) > 1e-6) {
            des("not perpendicular");
            return false;
        }
        if (abs((sta[0] - sta[2]).dot((sta[1] - sta[3]))) > 1e-6) {
            // des("not square");
            return false;
        }
        // de(edges);
        return true;
    }
#ifndef ONLINE_JUDGE
    void print() const {
        ::print(ts);
    }
#endif
};

struct triangle_order {
    vector<int> v;
    int id;

    bool operator<(const triangle_order& t) const {
        return v < t.v;
    }
};

int T;
vector<int> a(3);

signed main() {
    bool output = false;
    cin.tie(nullptr)->sync_with_stdio(false);
    cin >> T;
    int div = 0;
    while (T--) {
        area = 0;
        vector<vector<triangle>> vvt;
        vector<triangle_order> vto;
        for (int i = 0; i < 4; ++i) {
            for (auto& j : a) {
                int x;
                cin >> x;
                if (div == 0) {
                    div = 1;
                    while (x > div * 1000) div *= 10;
                }
                j = x;
                // if (T == 19 && i == 0 && x == 2352936)output = true;
            }
            if (output && T <= 20 - 5) {
                for (auto& j : a)cout << j << ' ';
                continue;
            }
            vvt.emplace_back();
            ranges::sort(a);
            if (i)vto.push_back({a, i});
            do {
                vvt.back().push_back(triangle::from_edge(a[0] * 1. / div, a[1] * 1. / div, a[2] * 1. / div));
            } while (ranges::next_permutation(a).found);
            area += vvt.back().back().size();
        }
        if (output) {
            cout << endl;
            continue;
        }
        for (int i = 0; i < 4; ++i) {
            de(i, vvt[i].size(), vvt[i]);
        }
        // exit(0);
        sort(vto.begin(), vto.end());
        do {
            vector<many_triangle> vmt, vmt2;
            vmt.push_back({{vvt[0][0]}});
            for (int i = 1; i < 4; ++i) {
                for (auto& mt : vmt) {
                    for (auto& t : vvt[vto[i - 1].id]) {
                        auto res = mt.combine_with(t);
                        vmt2.insert(vmt2.end(), res.begin(), res.end());
                    }
                }
                vmt = move(vmt2);
            }
            for (auto& mt : vmt) {
                if (mt.check()) {
                    cout << 1 << endl;
                    goto end;
                }
            }
        } while (next_permutation(vto.begin(), vto.end()));
        // de(vmt);
        cout << 0 << endl;
    end:;
        // exit(0);
    }
    return 0;
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 27ms
memory: 4168kb

input:

3
1 1 2
2 1 1
2 1 1
1 2 1
1 1 1
1 1 1
1 1 1
1 1 1
5 125 130
125 20 145
45 130 145
145 145 80

output:

1
0
1

result:

ok 3 lines

Test #2:

score: 0
Accepted
time: 274ms
memory: 3960kb

input:

20
1998001 7984010 9982009
1998001 7984010 1994005
7984010 9978013 9982009
9978013 1994005 7984010
9958045 7968034 9962037
7968034 1994005 9962037
9958045 1990013 7968034
1994005 1990013 7968034
7952074 9938097 1986025
7952074 9942085 1990013
7952074 9942085 9938097
1986025 7952074 1990013
7936130 9...

output:

1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

result:

ok 20 lines

Test #3:

score: 0
Accepted
time: 377ms
memory: 4352kb

input:

20
1148639 3581051 1216206
9999916 7026968 270268
6013463 6013463 6756700
6013463 6013463 6756700
2608850 8630930 9445800
9862940 6448880 6939290
8631650 3682160 5184310
7504700 6652150 1917140
2359505 3170711 2299108
4027811 6760781 2960240
4679918 6106006 3178400
8153446 7975057 5222088
8849500 88...

output:

0
0
0
1
1
1
1
0
1
1
1
1
1
0
0
0
0
1
1
1

result:

ok 20 lines

Test #4:

score: 0
Accepted
time: 658ms
memory: 4664kb

input:

20
7300000 8100000 10000000
8100000 7300000 1000000
1000000 7300000 2900000
2900000 10000000 7300000
61728 8950560 9999936
7901184 4012320 4999968
8950560 3950592 4999968
4012320 123456 4999968
4494200 9932182 9932182
8381683 112355 9932182
5505395 9460291 9932182
9999595 4494200 9190639
5994936 671...

output:

1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0

result:

ok 20 lines

Test #5:

score: 0
Accepted
time: 505ms
memory: 4404kb

input:

20
10000000 5078125 3828125
78125 5000000 5078125
1250000 10000000 6250000
5000000 6250000 1250000
7079600 5663680 1415920
7079600 796455 9999935
5663680 9999935 5752175
5663680 88495 5752175
4410468 1135368 9999972
5676840 4541472 5676840
4541472 5676840 5676840
8078580 742356 6288192
8345560 44707...

output:

1
1
0
0
0
1
1
1
1
1
1
0
0
1
0
1
0
1
0
0

result:

ok 20 lines

Test #6:

score: 0
Accepted
time: 607ms
memory: 4452kb

input:

20
10000000 5078125 3828125
2031250 78125 1953125
703125 5078125 2031250
5000000 10000000 5000000
5000000 10000000 5000000
5000000 2890625 390625
6250000 1250000 10000000
1250000 2890625 3515625
6711400 9999986 3288586
4899322 4295296 604026
6979856 9999986 4899322
6711400 6979856 268456
9767552 645...

output:

1
1
1
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
0

result:

ok 20 lines

Test #7:

score: 0
Accepted
time: 576ms
memory: 4432kb

input:

20
3063559 8439238 9999919
3063559 9999919 3005756
8381435 9999919 8439238
8381435 3005756 9999919
6923007 4319483 4852022
2130156 4319483 769223
9999899 3076892 6923007
6923007 2899379 4852022
3271584 4999968 493824
6049344 61728 5246880
4999968 4999968 9999936
5246880 3271584 3950592
7398784 99999...

output:

1
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0

result:

ok 20 lines

Test #8:

score: 0
Accepted
time: 588ms
memory: 6036kb

input:

20
5524800 4475088 9999888
55248 4475088 4530336
9999888 5580048 5524800
55248 4530336 5580048
7123920 8940020 2698748
6206580 7677584 8296048
6252164 6473284 9023920
7524124 4702788 5944204
7901120 7901120 6320896
6320896 7901120 7901120
9135670 9999855 913567
1506151 1111095 98764
2222220 3555552 ...

output:

1
0
0
1
0
1
1
0
0
1
1
1
1
1
0
1
0
0
1
0

result:

ok 20 lines

Test #9:

score: 0
Accepted
time: 459ms
memory: 4628kb

input:

20
3404348 6811514 5073762
1575108 4047618 3481696
6589302 6594868 4559458
5124278 2664770 3517574
5393960 2157584 5393960
5393960 2157584 5393960
2199076 9999572 2821456
2157584 8972645 8723693
2091488 4248335 9999927
9999927 9542414 7385567
4248335 9542414 9999927
9999927 2091488 7385567
5867350 7...

output:

0
0
1
0
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1

result:

ok 20 lines

Test #10:

score: 0
Accepted
time: 471ms
memory: 4748kb

input:

20
4753532 8244880 6269438
3937444 762818 4555348
7280126 5303718 8327606
9077712 1705788 9903866
4999968 9999936 4999968
555552 7222176 9999936
6543168 1543200 4999968
7222176 6543168 61728
1360000 6560000 3664000
6560000 6560000 4608000
10000000 2960000 6560000
1152000 2320000 3664000
1709400 5470...

output:

0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
1
0
1
0
0

result:

ok 20 lines

Test #11:

score: 0
Accepted
time: 439ms
memory: 4480kb

input:

20
2615382 9846144 9999990
9846144 9999990 9999990
9999990 2769228 2615382
9999990 2769228 9999990
9191125 9999944 4779385
1323522 9191125 6544081
6544081 9999944 9191125
1323522 9191125 4779385
7028892 1743768 1991340
7028892 7028892 1743768
8234460 4865328 7028892
2378844 7599384 9999756
9731530 4...

output:

1
1
0
1
1
1
0
0
1
0
0
0
1
1
1
1
0
1
1
1

result:

ok 20 lines

Test #12:

score: 0
Accepted
time: 609ms
memory: 4248kb

input:

20
4999960 6173420 3316300
4999960 4999960 9999920
459180 459180 918360
1632640 459180 3316300
6328125 5078125 156250
5078125 6328125 10000000
6328125 5078125 10000000
6328125 156250 5078125
9979836 8089680 8280504
7601784 7634364 7141536
5377824 7028244 4492560
5815068 7928868 4377312
720000 800000...

output:

1
1
0
1
0
0
1
1
0
0
1
1
0
0
1
1
1
1
0
1

result:

ok 20 lines

Test #13:

score: 0
Accepted
time: 551ms
memory: 4692kb

input:

20
9999916 1689175 5743195
5743195 878371 4999958
9999916 4999958 4999958
1689175 878371 4999958
6301605 4049556 6301605
2024778 4049556 2024778
7293333 330576 6301605
9999924 6115656 3388404
617280 7901184 6543168
617280 123456 987648
4999968 4999968 9999936
1543200 6543168 4999968
3828125 1953125 ...

output:

1
0
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1

result:

ok 20 lines

Test #14:

score: 0
Accepted
time: 400ms
memory: 4396kb

input:

20
9999720 2888808 3555456
7610898 3555456 7610898
4944306 8805309 1805505
7610898 7610898 3555456
4999968 4999968 9999936
6543168 1543200 2530848
987648 9999936 6543168
1543200 987648 2530848
4999967 2358475 5471662
754712 5471662 9999934
754712 4999967 2358475
4999967 9999934 4999967
5371860 20661...

output:

0
1
1
0
0
1
1
1
0
1
0
0
1
0
1
1
1
1
1
0

result:

ok 20 lines

Test #15:

score: 0
Accepted
time: 609ms
memory: 4172kb

input:

20
4999968 4999968 9999936
4999968 5555520 555552
5555520 3402756 1180548
1180548 2222208 1736100
2207678 4505792 4722268
6840476 4330164 8510736
5829672 8496568 9904306
4191336 5368108 9200414
2644740 821072 2890020
3199420 6624380 4992680
6593608 7493780 2880304
9678732 5684644 8431388
9999920 433...

output:

1
0
0
1
0
0
0
1
1
0
1
1
1
1
0
1
0
1
1
0

result:

ok 20 lines

Test #16:

score: 0
Accepted
time: 502ms
memory: 4616kb

input:

20
8136144 6408528 8054156
7239584 6536596 1012996
1884652 5391096 6567204
1480764 5442988 5704872
9999936 4999968 4999968
902772 5069412 6944400
4999968 902772 5069412
3611088 4999968 277776
6358573 6634433 717236
2110329 2013778 1558609
9737858 9999925 6634433
717236 6634433 6634433
8820735 572387...

output:

0
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
1
1
0

result:

ok 20 lines

Test #17:

score: 0
Accepted
time: 472ms
memory: 4388kb

input:

20
1479580 2551000 2499980
1479580 5408120 2499980
4999960 9999920 4999960
408160 5408120 4999960
1418208 6119592 6943616
4717024 1703128 4933672
8516320 2379048 9953024
6649448 9056784 2567000
6639370 1661665 8301033
6639370 8297389 8301033
1658021 6639370 1661665
8297389 6639370 1658021
8390964 71...

output:

1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1

result:

ok 20 lines

Test #18:

score: 0
Accepted
time: 477ms
memory: 4656kb

input:

20
7346880 3775480 2551000
408160 3775480 3775480
4999960 3775480 204080
4999960 9999920 4999960
1493307 3497157 3289248
8523972 9198432 4312377
9709335 6351264 6294204
6821208 8165214 7286535
3024672 1543200 1111104
4999968 5246880 246912
4444416 5246880 1543200
4999968 4999968 9999936
3773520 1886...

output:

1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1

result:

ok 20 lines

Test #19:

score: -100
Wrong Answer
time: 596ms
memory: 4300kb

input:

20
2352936 2941170 9999978
6522477 1470585 8062266
9999978 4999989 4999989
1245672 4999989 1470585
816320 1326520 1734680
4999960 9999920 4999960
5306080 2653040 2653040
5306080 1020400 9999920
1592350 9745182 5222908
5222908 9999958 9745182
6369400 9745182 1592350
6369400 9745182 9999958
5103567 38...

output:

0
0
1
0
0
0
1
0
1
1
1
1
1
0
1
0
1
1
1
1

result:

wrong answer 5th lines differ - expected: '1', found: '0'