LA 4973 Ardenia (3D Geometry + Simulation)

ACM-ICPC Live Archive

　　三维几何，题意是要求求出两条空间线段的距离。题目难度在于要求用有理数的形式输出，这就要求写一个有理数类了。

　　开始的时候写出来的有理数类就各种疯狂乱套，TLE的结果是显然的。后来发现，在计算距离前都是不用用到有理数类的，所以就将开始的部分有理数改成直接用long long。其实好像可以用int来做的，不过我的方法比较残暴，中间运算过程居然爆int了。所以就只好用long long了。

代码如下，附带debug以及各种强的数据：

#include <cstdio>
#include <iostream>
#include <cstring>
#include <algorithm>
#include <cmath>

using namespace std;

template<class T> T gcd(T a, T b) { return b ? gcd(b, a % b) : a;}
template <class T> T sqr(T x) { return x * x;}
typedef long long LL;
struct Rat {
LL a, b;
Rat() {}
Rat(LL x) { a = x, b = 1;}
Rat(LL _a, LL _b) {
LL GCD = gcd(_b, _a);
a = _a / GCD, b = _b / GCD;
}
double val() { return (double) a / b;}
bool operator < (Rat x) const { return a * x.b < b * x.a;}
bool operator > (Rat x) const { return a * x.b > b * x.a;}
bool operator == (Rat x) const { return a * x.b == b * x.a;}
bool operator < (LL x) const { return Rat(a, b) < Rat(x);}
bool operator > (LL x) const { return Rat(a, b) > Rat(x);}
bool operator == (LL x) const { return Rat(a, b) == Rat(x);}
Rat operator + (Rat x) {
LL tb = b * x.b, ta = a * x.b + b * x.a;
LL GCD = gcd(abs(tb), abs(ta));
return Rat(ta / GCD, tb / GCD);
}
Rat operator - (Rat x) {
LL tb = b * x.b, ta = a * x.b - b * x.a;
LL GCD = gcd(abs(tb), abs(ta));
return Rat(ta / GCD, tb / GCD);
}
Rat operator * (Rat x) {
if (a * x.a == 0) return Rat(0, 1);
//        if (b * x.b == 0) { puts("..."); while (1) ;}
LL tb = b * x.b, ta = a * x.a;
LL GCD = gcd(abs(tb), abs(ta));
return Rat(ta / GCD, tb / GCD);
}
Rat operator / (Rat x) {
if (a * x.b == 0) return Rat(0, 1);
//        if (b * x.a == 0) { puts("!!!"); while (1) ;}
LL GCD, tb = b * x.a, ta = a * x.b;
GCD = gcd(abs(tb), abs(ta));
return Rat(ta / GCD, tb / GCD);
}
void fix() {
a = abs(a), b = abs(b);
LL GCD = gcd(b, a);
a /= GCD, b /= GCD;
}
} ;

struct Point {
LL x[3];
Point operator + (Point a) {
Point ret;
for (int i = 0; i < 3; i++) ret.x[i] = x[i] + a.x[i];
return ret;
}
Point operator - (Point a) {
Point ret;
for (int i = 0; i < 3; i++) ret.x[i] = x[i] - a.x[i];
return ret;
}
Point operator * (LL p) {
Point ret;
for (int i = 0; i < 3; i++) ret.x[i] = x[i] * p;
return ret;
}
bool operator == (Point a) const {
for (int i = 0; i < 3; i++) if (!(x[i] == a.x[i])) return false;
return true;
}
void print() {
for (int i = 0; i < 3; i++) cout << x[i] << ' ';
cout << endl;
}
} ;
typedef Point Vec;

struct Line {
Point s, t;
Line() {}
Line (Point s, Point t) : s(s), t(t) {}
Vec vec() { return t - s;}
} ;
typedef Line Seg;

LL dotDet(Vec a, Vec b) {
LL ret = 0;
for (int i = 0; i < 3; i++) ret = ret + a.x[i] * b.x[i];
return ret;
}

Vec crossDet(Vec a, Vec b) {
Vec ret;
for (int i = 0; i < 3; i++) {
ret.x[i] = a.x[(i + 1) % 3] * b.x[(i + 2) % 3] - a.x[(i + 2) % 3] * b.x[(i + 1) % 3];
}
return ret;
}

inline LL vecLen(Vec x) { return dotDet(x, x);}
inline bool parallel(Line a, Line b) { return vecLen(crossDet(a.vec(), b.vec())) == 0;}
inline bool onSeg(Point x, Point a, Point b) { return parallel(Line(a, x), Line(b, x)) && dotDet(a - x, b - x) < 0;}
inline bool onSeg(Point x, Seg s) { return onSeg(x, s.s, s.t);}

Rat pt2Seg(Point p, Point a, Point b) {
if (a == b) return Rat(vecLen(p - a));
Vec v1 = b - a, v2 = p - a, v3 = p - b;
if (dotDet(v1, v2) < 0) return Rat(vecLen(v2));
else if (dotDet(v1, v3) > 0) return Rat(vecLen(v3));
else return Rat(vecLen(crossDet(v1, v2)), vecLen(v1));
}
inline Rat pt2Seg(Point p, Seg s) { return pt2Seg(p, s.s, s.t);}
inline Rat pt2Plane(Point p, Point p0, Vec n) { return Rat(sqr(dotDet(p - p0, n)), vecLen(n));}
inline bool segIntersect(Line a, Line b) {
Vec v1 = crossDet(a.s - b.s, a.t - b.s);
Vec v2 = crossDet(a.s - b.t, a.t - b.t);
Vec v3 = crossDet(b.s - a.s, b.t - a.s);
Vec v4 = crossDet(b.s - a.t, b.t - a.t);
//    v1.print();
//    v2.print();
//    cout << dotDet(v1, v2).val() << "= =" << endl;
return dotDet(v1, v2) < 0 && dotDet(v3, v4) < 0;
}//        cout << "same plane" << endl;

pair<Rat, Rat> getIntersect(Line a, Line b) {
Point p = a.s, q = b.s;
Vec v = a.vec(), u = b.vec();
LL uv = dotDet(u, v), vv = dotDet(v, v), uu = dotDet(u, u);
LL pv = dotDet(p, v), qv = dotDet(q, v), pu = dotDet(p, u), qu = dotDet(q, u);
if (uv == 0) return make_pair(Rat(qv - pv, vv), Rat(pu - qu, uu));
//    if (vv == 0 || uv == 0 || uv / vv - uu / uv == 0) { puts("shit!"); while (1) ;}
Rat y = (Rat(pv - qv, vv) - Rat(pu - qu, uv)) / (Rat(uv, vv) - Rat(uu, uv));
Rat x = (y * uv - pv + qv) / vv;
//    cout << x.a << ' ' << x.b << ' ' << y.a << ' ' << y.b << endl;
return make_pair(x, y);
}

void work(Point *pt) {
Line a = Line(pt[0], pt[1]);
Line b = Line(pt[2], pt[3]);
if (parallel(a, b)) {
if (onSeg(pt[0], b) || onSeg(pt[1], b)) { puts("0 1"); return ;}
if (onSeg(pt[2], a) || onSeg(pt[3], a)) { puts("0 1"); return ;}
//        cout << "parallel" << endl;
Rat tmp = min(min(pt2Seg(pt[0], b), pt2Seg(pt[1], b)), min(pt2Seg(pt[2], a), pt2Seg(pt[3], a)));
tmp.fix();
printf("%lld %lld\n", tmp.a, tmp.b);
return ;
}
Vec nor = crossDet(a.vec(), b.vec());
Rat ans = pt2Plane(pt[0], pt[2], nor);
//    cout << "~~~" << endl;
if (ans == 0) {
//        cout << "same plane" << endl;
if (segIntersect(a, b)) { puts("0 1"); return ;}
Rat tmp = min(min(pt2Seg(pt[0], b), pt2Seg(pt[1], b)), min(pt2Seg(pt[2], a), pt2Seg(pt[3], a)));
tmp.fix();
printf("%lld %lld\n", tmp.a, tmp.b);
return ;
} else {
//        cout << "diff plane" << endl;
pair<Rat, Rat> tmp = getIntersect(a, b);
//        cout << tmp.first.val() << "= =" << tmp.second.val() << endl;
//        cout << (tmp.first > 0) << endl;
if (tmp.first > 0 && tmp.first < 1 && tmp.second > 0 && tmp.second < 1) {
//            cout << "cross" << endl;
ans.fix();
printf("%lld %lld\n", ans.a, ans.b);
} else {
//            cout << "not cross" << endl;
Rat t = min(min(pt2Seg(pt[0], b), pt2Seg(pt[1], b)), min(pt2Seg(pt[2], a), pt2Seg(pt[3], a)));
t.fix();
printf("%lld %lld\n", t.a, t.b);
}
}
}

int main() {
//    freopen("in", "r", stdin);
//    freopen("out", "w", stdout);
Point pt[4];
int T;
cin >> T;
while (T--) {
for (int i = 0; i < 4; i++) {
for (int j = 0; j < 3; j++) {
scanf("%lld", &pt[i].x[j]);
}
}
work(pt);
}
return 0;
}

/*
13

-20 -20 -20 20 20 19
0 0 0 1 1 1

-20 -20 -20 20 19 20
-20 -20 20 20 20 -20

0 0 0 20 20 20
0 0 10 0 20 10

0 0 0 1 1 1
2 3 4 1 2 2

0 0 0 0 0 0
0 1 1 1 2 3

0 0 0 10 10 10
11 12 13 10 11 11

0 0 0 1 1 1
1 1 1 2 2 2

1 0 0 0 1 0
1 1 0 2 2 0

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

0 0 0 0 0 20
20 0 10 0 20 10

0 0 0 20 20 20
1 1 2 1 1 2

0 0 0 20 20 20
0 20 20 0 20 20

0 0 0 0 0 20
20 20 0 20 20 20
*/

View Code

——written by Lyon