原題鏈接：http://codeforces.com/gym/100523/attachments/download/2798/20142015-ct-s02e07-codeforces-trainings-season-2-episode-7-en.pdf

題意

給你一堆三維點，問你他們是否共面

題解

模板題，套版就好，需要注意的是共線

代碼

#include<iostream> #include<cmath> #include<cstdio> #define MAX_N 100005 using namespace std;const double eps=1e-10;inline double Sqrt(double a) {return a <= 0 ? 0 : sqrt(a); }inline double Sqr(double a) {return a * a; }class Point_3 { public:double x, y, z;Point_3() { }Point_3(double xx, double yy, double zz) : x(xx), y(yy), z(zz) { }Point_3 operator-(Point_3 a) {return Point_3(x - a.x, y - a.y, z - a.z);}double Length() const {return Sqrt(Sqr(x) + Sqr(y) + Sqr(z));} };Point_3 Det(const Point_3 &a,const Point_3 &b) {return Point_3(a.y * b.z - a.z * b.y, a.z * b.x - a.x * b.z, a.x * b.y - a.y * b.x); }double Dot(const Point_3 &a,const Point_3 &b) {return a.x * b.x + a.y * b.y + a.z * b.z; }double vlen(Point_3 P){return P.Length();}int dot_inline(Point_3 p1,Point_3 p2,Point_3 p3) {return vlen(Det(p1 - p2, p2 - p3)) < eps; }bool zero(double x) {return fabs(x) < eps; }Point_3 pvec(Point_3 s1,Point_3 s2,Point_3 s3) {return Det((s1 - s2), (s2 - s3)); }int dots_onplane(Point_3 a,Point_3 b,Point_3 c,Point_3 d) {return zero(Dot(pvec(a, b, c), d - a)); }int n; Point_3 point3[MAX_N];int main() {scanf("%d", &n);for (int i = 0; i < n; i++) {int a, b, c;scanf("%d%d%d", &a, &b, &c);point3[i] = Point_3(a, b, c);}if (n <= 3) {cout << "TAK" << endl;return 0;}int p = -1;for (int i = 2; i < n; i++) {if (dot_inline(point3[0], point3[1], point3[i]) == 0) {p = i;break;}}if (p == -1) {cout << "TAK" << endl;return 0;}for (int i = 2; i < n; i++) {if (i == p)continue;if (dots_onplane(point3[0], point3[1], point3[p], point3[i]) == 0) {cout << "NIE" << endl;return 0;}}cout << "TAK" << endl;return 0; }

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轉載于:https://www.cnblogs.com/HarryGuo2012/p/4730935.html

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