QOJ.ac

QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#112208#5679. Linked TrianglesPetroTarnavskyi#AC ✓2ms3684kbC++173.1kb2023-06-10 16:48:552023-06-10 16:48:59

Judging History

你现在查看的是最新测评结果

  • [2023-08-10 23:21:45]
  • System Update: QOJ starts to keep a history of the judgings of all the submissions.
  • [2023-06-10 16:48:59]
  • 评测
  • 测评结果:AC
  • 用时:2ms
  • 内存:3684kb
  • [2023-06-10 16:48:55]
  • 提交

answer

#include <bits/stdc++.h>

using namespace std;
using LL = long long;
using ULL = unsigned long long;
using VI = vector<int>;
using VL = vector<LL>;
using PII = pair<int, int>;
using PLL = pair<LL, LL>;

#define SZ(a) (int)a.size()
#define ALL(a) a.begin(), a.end()
#define MP make_pair
#define PB push_back
#define EB emplace_back
#define F first
#define S second
#define FOR(i, a, b) for (int i = (a); i<(b); ++i)
#define RFOR(i, b, a) for (int i = (b)-1; i>=(a); --i)
#define FILL(a, b) memset(a, b, sizeof(a))

typedef double db;

const db EPS = 1e-9;

struct Point {
	db x, y, z;
	Point() {}
	Point(db _x, db _y, db _z): x(_x), y(_y), z(_z) {}
	Point operator+(const Point& p) const {
		return {x + p.x, y + p.y, z + p.z};
	}
	Point operator-(const Point& p) const {
		return {x - p.x, y - p.y, z - p.z};
	}
	Point operator*(db k) const {
		return {k * x, k * y, k * z};
	}
	Point operator*(const Point& p) const {
		return {y * p.z - z * p.y, z * p.x - x * p.z, x * p.y - y * p.x};
	}
	db d2() const {
		return x * x + y * y + z * z;
	}
	db len() const {
		return sqrt(d2());
	}
};

db findArea(const Point& p1, const Point& p2, const Point& p3) {
	return ((p3 - p1) * (p2 - p1)).len();
}

db mixedProduct(const Point& p1, const Point& p2, const Point& p3) {
	return p1.x * p2.y * p3.z + p1.y * p2.z * p3.x + p1.z * p2.x * p3.y
		- p1.z * p2.y * p3.x - p1.x * p2.z * p3.y - p1.y * p2.x * p3.z;
}

int sgn(db x) {
	return x > EPS ? 1 : (x < -EPS ? -1 : 0);
}

bool strictlyInside(const vector<Point>& tr, const Point& p, db area) {
	db sumArea = 0;
	FOR(j, 0, 3) {
		db curArea = findArea(p, tr[j], tr[(j + 1) % 3]);
		if (curArea / area < EPS) {
			return false;
		}
		sumArea += curArea;
	}
	return sgn(sumArea / area - 1) == 0;
}

int main()
{
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	vector<Point> p(6);
	for (Point& pi : p) {
		cin >> pi.x >> pi.y >> pi.z;
	}
	vector<pair<int, int>> ans;
	FOR(m, 1, 6) FOR(n, m + 1, 6) {
		vector<Point> tr1 = {p[0], p[m], p[n]}, tr2;
		FOR(i, 1, 6) {
			if (i != m && i != n) {
				tr2.push_back(p[i]);
			}
		}
		db area = findArea(tr2[0], tr2[1], tr2[2]);
		if (findArea(tr1[0], tr1[1], tr1[2]) < EPS || area < EPS) {
			continue;
		}
		int cntEdges = 0, cntVertices = 0;
		FOR(i, 0, 3) {
			const Point& q1 = tr1[i], q2 = tr1[(i + 1) % 3], q3 = tr1[(i + 2) % 3];
			db prod1 = mixedProduct(tr2[0] - q1, tr2[1] - q1, tr2[2] - q1),
				prod2 = mixedProduct(tr2[0] - q2, tr2[1] - q2, tr2[2] - q2);
			int s1 = sgn(prod1 / area), s2 = sgn(prod2 / area);
			if (s1 * s2 != -1) {
				continue;
			}
			double alpha = prod2 / (prod2 - prod1);
			assert(alpha > EPS && alpha < 1 - EPS);
			Point q = q1 * alpha + q2 * (1 - alpha);
			assert(sgn(mixedProduct(tr2[0] - q, tr2[1] - q, tr2[2] - q) / area) == 0);
			if (strictlyInside(tr2, q, area)) {
				cntEdges++;
			}
			if (strictlyInside(tr2, q3, area)) {
				cntVertices++;
			}
		}
		if (cntEdges + cntVertices == 1) {
			ans.emplace_back(m, n);
		}
	}
	cout << SZ(ans) << "\n";
	for (auto [m, n] : ans) {
		cout << m + 1 << " " << n + 1 << "\n";
	}
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 0ms
memory: 3552kb

input:

1 0 0
-1 0 0
0 1 0.2
0 -1 0.2
0.2 0.2 1
0.2 0.2 -1

output:

3
2 3
2 5
3 4

result:

ok 4 lines

Test #2:

score: 0
Accepted
time: 2ms
memory: 3604kb

input:

-7.8212 6.0669 8.5429
6.8601 5.7125 6.4651
-1.4178 7.0540 -0.0678
3.3535 -0.2770 1.2726
-2.4538 -5.0173 1.3681
0.5774 -4.3039 -5.4755

output:

1
4 6

result:

ok 2 lines

Test #3:

score: 0
Accepted
time: 2ms
memory: 3584kb

input:

-0.7297 0.1660 8.8249
0.2927 -7.0325 6.5672
8.8653 8.8948 3.6222
-7.0054 5.8303 9.7899
-5.2537 2.5352 -9.9275
0.0807 -4.4782 -5.9199

output:

1
2 5

result:

ok 2 lines

Test #4:

score: 0
Accepted
time: 2ms
memory: 3536kb

input:

-0.6478 8.5319 4.8899
-0.3780 -5.7694 -5.9423
-1.7597 4.0013 -4.0520
6.7414 -3.4843 7.1844
6.8234 -8.6367 -2.1165
9.0166 -6.8566 -6.5933

output:

1
2 5

result:

ok 2 lines

Test #5:

score: 0
Accepted
time: 2ms
memory: 3592kb

input:

-8.1542 -3.5082 -9.4465
7.5776 -4.0828 -6.4696
-8.0569 8.8116 -5.2878
-6.7636 -2.1570 5.8144
1.6530 -7.3579 9.3215
-2.9592 3.0434 -9.9900

output:

1
5 6

result:

ok 2 lines

Test #6:

score: 0
Accepted
time: 0ms
memory: 3644kb

input:

-1.4895 -9.2239 4.9174
-1.2844 -5.8982 -7.2312
-8.3142 5.2566 2.7348
9.8243 3.4760 -7.7570
3.0870 -8.5288 -1.3170
-0.7327 -3.4846 -3.6615

output:

1
4 6

result:

ok 2 lines

Test #7:

score: 0
Accepted
time: 2ms
memory: 3644kb

input:

2.6602 -6.6905 -3.7999
-5.5756 8.0805 -7.6713
-1.2337 -8.1267 -2.1753
-8.7845 -1.5313 -1.7837
-9.6123 -9.6594 3.7709
-3.8460 7.7783 6.5572

output:

3
2 5
4 5
4 6

result:

ok 4 lines

Test #8:

score: 0
Accepted
time: 2ms
memory: 3644kb

input:

-3.4596 -6.1669 5.8628
6.7265 -6.3462 -0.4187
7.3097 3.7265 -8.8461
-0.8005 -3.0356 -5.0364
-9.1143 -4.2919 -0.2931
3.4024 9.6496 -8.3551

output:

1
4 6

result:

ok 2 lines

Test #9:

score: 0
Accepted
time: 1ms
memory: 3612kb

input:

-2.7245 -1.7476 -5.5523
0.3886 0.5709 2.4341
1.8639 7.1395 5.1457
-5.6447 -4.8931 1.3328
2.2310 -0.9524 -5.4822
2.5867 -3.9042 3.7924

output:

1
3 6

result:

ok 2 lines

Test #10:

score: 0
Accepted
time: 2ms
memory: 3600kb

input:

5.8832 4.2308 -0.5738
-3.3329 7.0130 -6.9039
-8.7819 7.5500 -3.0628
-8.2697 -2.8331 -8.3711
7.4996 3.2136 -7.4336
-4.5882 -2.4783 -1.6155

output:

3
2 4
2 6
3 4

result:

ok 4 lines

Test #11:

score: 0
Accepted
time: 2ms
memory: 3536kb

input:

7.6850 5.2805 9.4561
5.6332 -4.3292 -1.5505
8.4928 3.1573 2.9439
-3.4751 4.2336 -6.2825
2.0533 1.5089 -5.1904
1.9290 7.1246 -5.6887

output:

1
5 6

result:

ok 2 lines

Test #12:

score: 0
Accepted
time: 0ms
memory: 3544kb

input:

-6.4631 -6.0018 -8.3013
-4.2504 -1.9595 0.0015
9.1460 -9.8983 1.9107
-1.3431 -4.4299 -8.9080
8.8338 4.5798 -4.8447
-9.5794 9.2495 -1.9444

output:

1
3 5

result:

ok 2 lines

Test #13:

score: 0
Accepted
time: 0ms
memory: 3528kb

input:

8.1098 8.7662 -0.5323
-2.7080 1.0147 9.3257
3.3181 -6.7925 -0.2656
-6.2061 -3.7029 6.6701
4.8109 0.9043 -7.7916
8.2971 9.3408 7.4590

output:

1
4 6

result:

ok 2 lines

Test #14:

score: 0
Accepted
time: 2ms
memory: 3588kb

input:

0.7030 -4.2527 -3.3542
4.9892 4.6405 0.1936
6.4665 3.6603 -0.7573
-2.7292 -9.5903 2.4434
2.1488 4.7420 -1.6722
1.4563 -2.9071 0.0344

output:

1
2 4

result:

ok 2 lines

Test #15:

score: 0
Accepted
time: 2ms
memory: 3540kb

input:

2.2889 5.7114 -3.2417
6.2896 -9.2879 -7.6487
8.2127 0.8676 5.0007
0.4564 0.7301 6.3646
-1.3067 3.2770 -3.7341
4.1332 -0.8919 3.0173

output:

1
4 6

result:

ok 2 lines

Test #16:

score: 0
Accepted
time: 2ms
memory: 3656kb

input:

2.2900 -9.7090 -8.5439
8.0837 7.1754 -5.7574
5.5256 -7.1201 -1.8606
-0.3155 4.7771 0.0365
1.5703 8.1374 -1.9806
5.2074 5.9649 4.9484

output:

3
2 4
2 6
5 6

result:

ok 4 lines

Test #17:

score: 0
Accepted
time: 2ms
memory: 3652kb

input:

-6.4601 4.3204 7.3006
7.8092 -4.2867 3.3257
-3.0653 -2.2210 4.2164
-9.4836 -8.0321 -7.2147
-4.4158 -8.7707 8.1745
3.6565 7.4014 5.1368

output:

1
2 4

result:

ok 2 lines

Test #18:

score: 0
Accepted
time: 2ms
memory: 3684kb

input:

-4.6283 -7.3800 4.9382
6.0522 -4.6880 -5.6545
-9.7257 4.1153 2.0589
-0.5804 -6.0445 -9.3820
4.9191 0.4055 9.1288
5.2645 -6.2096 0.3280

output:

3
2 3
2 5
4 5

result:

ok 4 lines

Test #19:

score: 0
Accepted
time: 1ms
memory: 3548kb

input:

1.6735 0.7915 3.4557
-8.6249 -2.1781 7.2110
9.9849 0.8844 4.1306
7.2401 8.6278 -4.6113
9.4239 -5.7525 4.7497
9.6454 4.1612 1.1931

output:

1
5 6

result:

ok 2 lines

Test #20:

score: 0
Accepted
time: 2ms
memory: 3596kb

input:

5.2341 -3.0318 -9.1944
-5.8134 0.1070 3.9918
-3.2804 8.4528 6.6702
7.9394 9.5833 6.9070
-3.8144 -3.6164 -4.7621
1.1059 2.9455 9.5251

output:

1
2 3

result:

ok 2 lines

Test #21:

score: 0
Accepted
time: 2ms
memory: 3580kb

input:

-1.8943 -5.1851 -4.0217
4.9502 4.1022 -9.9857
-6.8457 4.8856 5.9649
-4.6211 -2.1717 5.9769
-8.7984 -2.6598 -2.0037
-8.4303 -7.5469 -6.4235

output:

1
4 5

result:

ok 2 lines

Test #22:

score: 0
Accepted
time: 1ms
memory: 3612kb

input:

7.9195 6.4394 0.3951
9.0419 -7.7326 -5.9354
-0.8932 -5.5514 -7.2127
-3.5689 4.0074 7.3452
-2.6154 -3.7425 2.1830
-4.4288 -8.1715 1.7615

output:

1
3 6

result:

ok 2 lines

Test #23:

score: 0
Accepted
time: 2ms
memory: 3540kb

input:

3.2933 -0.1218 -6.5570
5.3489 2.9165 -7.4639
0.8178 -5.3210 7.7209
9.8004 1.3036 -3.7399
1.3227 3.0378 7.2653
-7.1111 -8.4844 6.4210

output:

1
4 5

result:

ok 2 lines

Test #24:

score: 0
Accepted
time: 2ms
memory: 3552kb

input:

1.4225 5.3619 -6.7873
2.9499 -9.0353 -0.2296
-6.2206 -7.0195 4.1848
-2.7755 0.9867 5.2128
9.6494 6.1635 -6.6496
-9.7593 -2.1909 -2.9135

output:

1
2 3

result:

ok 2 lines

Test #25:

score: 0
Accepted
time: 2ms
memory: 3536kb

input:

-6.9537 -3.4442 5.1607
-0.1657 1.2895 9.0296
0.8678 3.3507 -3.7537
9.9973 -4.0755 -2.0537
-6.6049 2.6974 -5.2174
0.0799 8.4297 -2.6491

output:

1
3 6

result:

ok 2 lines

Test #26:

score: 0
Accepted
time: 2ms
memory: 3544kb

input:

-8.3444 -5.5013 -8.1463
6.3489 -4.8776 -2.2804
3.0889 -5.2444 -4.6936
-8.4036 2.2604 -7.6446
8.4213 3.5109 8.4365
4.7077 9.6175 -3.7947

output:

1
2 4

result:

ok 2 lines

Test #27:

score: 0
Accepted
time: 2ms
memory: 3664kb

input:

3.8723 -8.9602 2.1167
-9.9734 -5.5953 7.7640
8.8383 7.7135 -7.6538
-5.4866 6.5595 1.6564
1.8371 2.6273 2.5534
3.6605 6.8036 6.1923

output:

1
4 6

result:

ok 2 lines

Test #28:

score: 0
Accepted
time: 2ms
memory: 3592kb

input:

-6.2893 -2.7872 1.2822
-4.4563 8.1937 -7.7488
2.3549 -6.7210 9.6031
2.4225 5.5183 -7.2111
3.5653 4.8626 2.5859
-0.7371 6.9050 2.4314

output:

1
4 5

result:

ok 2 lines

Test #29:

score: 0
Accepted
time: 0ms
memory: 3684kb

input:

-8.2571 0.3790 0.5212
-6.4419 7.5129 -1.1452
-0.1440 1.4809 -6.9502
-1.5524 -2.0594 6.4582
-3.4961 8.8344 9.4882
9.7382 9.2265 -6.2893

output:

3
3 5
4 6
5 6

result:

ok 4 lines

Test #30:

score: 0
Accepted
time: 2ms
memory: 3584kb

input:

2.2798 7.0880 4.4285
9.6110 1.6666 7.4605
-5.3077 -9.0711 -6.9948
-3.7607 -1.7572 0.2891
2.5287 -9.1059 4.9583
0.3704 -0.5527 0.8149

output:

1
5 6

result:

ok 2 lines