QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#714774 | #5679. Linked Triangles | zeyu# | AC ✓ | 0ms | 3916kb | C++23 | 5.4kb | 2024-11-06 06:57:40 | 2024-11-06 06:57:41 |
Judging History
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