QOJ.ac

QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#714774#5679. Linked Triangleszeyu#AC ✓0ms3916kbC++235.4kb2024-11-06 06:57:402024-11-06 06:57:41

Judging History

你现在查看的是最新测评结果

  • [2024-11-06 06:57:41]
  • 评测
  • 测评结果:AC
  • 用时:0ms
  • 内存:3916kb
  • [2024-11-06 06:57:40]
  • 提交

answer

#include <bits/stdc++.h>
#define fi first
#define se second
#define ll long long
#define pl pair<ll, ll>
#define pi pair<int, int>
#define minpq priority_queue<ll, vector<ll>, greater<ll>>
using namespace std;

#if 1
void __print(int x) {cerr << x;}
void __print(long x) {cerr << x;}
void __print(long long x) {cerr << x;}
void __print(unsigned x) {cerr << x;}
void __print(unsigned long x) {cerr << x;}
void __print(unsigned long long x) {cerr << x;}
void __print(float x) {cerr << x;}
void __print(double x) {cerr << x;}
void __print(long double x) {cerr << x;}
void __print(char x) {cerr << '\'' << x << '\'';}
void __print(const char *x) {cerr << '\"' << x << '\"';}
void __print(const string &x) {cerr << '\"' << x << '\"';}
void __print(bool x) {cerr << (x ? "true" : "false");}
template<typename T, typename V>
void __print(const pair<T, V> &x) {cerr << '{'; __print(x.first); cerr << ','; __print(x.second); cerr << '}';}
template<typename T>
void __print(const T &x) {int f = 0; cerr << '['; for (auto &i: x) cerr << (f++ ? "," : ""), __print(i); cerr << "]";}
void _print() {cerr << endl << flush;}
template <typename T, typename... V>
void _print(T t, V... v) {__print(t); if (sizeof...(v)) cerr << ", "; _print(v...);}
#define debug(x...) cerr << "*["<<__LINE__<<"]\t"<< #x << " = "; _print(x)
#endif

const ll mod = 1e9 + 7;

template<typename T> bool chkmin(T &a, T b){return (b < a) ? a = b, 1 : 0;}
template<typename T> bool chkmax(T &a, T b){return (b > a) ? a = b, 1 : 0;}
ll gcd(ll a, ll b) {if(b == 0){return a;} return gcd(b, a % b);}

// Define a small epsilon for floating-point comparisons
const double EPSILON = 1e-8;

template<typename T>
struct Point {
    T x, y, z;

    // Overload subtraction operator
    Point operator-(const Point& p) const {
        return Point{x - p.x, y - p.y, z - p.z};
    }

    // Overload addition operator
    Point operator+(const Point& p) const {
        return Point{x + p.x, y + p.y, z + p.z};
    }

    // Overload scalar multiplication
    Point operator*(T scalar) const {
        return Point{x * scalar, y * scalar, z * scalar};
    }

    // Overload scalar division
    Point operator/(T scalar) const {
        return Point{x / scalar, y / scalar, z / scalar};
    }

    // Compute dot product
    T dot(const Point& p) const {
        return x * p.x + y * p.y + z * p.z;
    }

    // Compute cross product
    Point cross(const Point& p) const {
        return Point{
            y * p.z - z * p.y,
            z * p.x - x * p.z,
            x * p.y - y * p.x
        };
    }

    // Compute norm (magnitude)
    double norm() const {
        return sqrt(double(x * x + y * y + z * z));
    }
};

using point = Point<double>;

void dbg(point p){
	cout << p.x << ' ' << p.y << ' ' << p.z << '\n';
}

bool isPointInTriangle(const point& A, const point& B, const point& C, const point& P) {
    // Compute normal of the triangle's plane
    point N = (B - A).cross(C - A);

    // Check if point P lies in the plane of triangle ABC
    double plane_check = (P - A).dot(N);
    if (std::fabs(plane_check) > EPSILON)
        return false; // Point is not in the plane

    // Compute vectors
    point v0 = B - A;
    point v1 = C - A;
    point v2 = P - A;

    // Compute dot products
    double dot00 = v0.dot(v0);
    double dot01 = v0.dot(v1);
    double dot02 = v0.dot(v2);
    double dot11 = v1.dot(v1);
    double dot12 = v1.dot(v2);

    // Compute denominator
    double denom = dot00 * dot11 - dot01 * dot01;
    if (std::fabs(denom) < EPSILON)
        return false; // Triangle is degenerate

    // Compute barycentric coordinates
    double u = (dot11 * dot02 - dot01 * dot12) / denom;
    double v = (dot00 * dot12 - dot01 * dot02) / denom;

    // Check if point is inside the triangle
    return (u >= -EPSILON) && (v >= -EPSILON) && (u + v <= 1 + EPSILON);
}


bool linked(vector<point> t1, vector<point> t2){
	int cnt = 0;
	for (int i = 0; i < 3; i ++){
		point v = (t1[0] - t1[1]).cross(t1[0] - t1[2]);
		point p1 = t2[(i + 1) % 3], p2 = t2[(i + 2) % 3];
		if ((p1 - t1[0]).dot(v) > 0 && (p2 - t1[0]).dot(v) < 0 || (p1 - t1[0]).dot(v) < 0 && (p2 - t1[0]).dot(v) > 0){
			point le = p1, ri = p2;
			for (int _ = 0; _ < 100; _ ++){
				point mid = (le + ri) / 2;
				if ((p1 - t1[0]).dot(v) * (mid - t1[0]).dot(v) > 0){
					le = mid;
				} else{
					ri = mid;
				}
			}
			if (isPointInTriangle(t1[0], t1[1], t1[2], le)) cnt ++;
		}
	}
	return cnt == 1;
}
 
int main(){
	ios::sync_with_stdio(false);
	cin.tie(0);
	vector<point> a(6);
	for (int i = 0; i < 6; i ++){
		cin >> a[i].x >> a[i].y >> a[i].z;
	}
	set<pi> ans;
	for (int i = 0; i < (1 << 6); i ++){
		vector<point> t1, t2;
		for (int j = 0; j < 6; j ++){
			if ((i >> j) & 1) t1.push_back(a[j]);
			else t2.push_back(a[j]);
		}
		if (t1.size() != 3 || t2.size() != 3) continue;
		if (linked(t1, t2)){
			pi cur = {-1, -1};
			if (i & 1){
				for (int j = 1; j < 6; j ++){
					if ((i >> j) & 1){
						if (cur.fi == -1) cur.fi = j + 1;
						else cur.se = j + 1;
					}
				}
				ans.insert(cur);
			} else{
				for (int j = 1; j < 6; j ++){
					if (!((i >> j) & 1)){
						if (cur.fi == -1) cur.fi = j + 1;
						else cur.se = j + 1;
					}
				}
				ans.insert(cur);
			}
		}
	}
	cout << ans.size() << '\n';
	for (pi p : ans) cout << p.fi << ' ' << p.se << '\n';
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 0ms
memory: 3720kb

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: 0ms
memory: 3712kb

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: 0ms
memory: 3752kb

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: 0ms
memory: 3776kb

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: 0ms
memory: 3716kb

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: 3712kb

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: 0ms
memory: 3716kb

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: 0ms
memory: 3776kb

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: 0ms
memory: 3888kb

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: 0ms
memory: 3748kb

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: 0ms
memory: 3720kb

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: 3716kb

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: 3916kb

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: 0ms
memory: 3792kb

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: 0ms
memory: 3716kb

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: 0ms
memory: 3748kb

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: 0ms
memory: 3724kb

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: 0ms
memory: 3884kb

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: 0ms
memory: 3716kb

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: 0ms
memory: 3664kb

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: 0ms
memory: 3916kb

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: 0ms
memory: 3772kb

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: 0ms
memory: 3716kb

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: 0ms
memory: 3708kb

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: 0ms
memory: 3720kb

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: 0ms
memory: 3752kb

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: 0ms
memory: 3716kb

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: 0ms
memory: 3664kb

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: 3776kb

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: 0ms
memory: 3788kb

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