DistanceBetweenSegments.cpp

#include <iostream>
#include <string>
#include <vector>
#include<cmath>

const double eps = 1e-10;
const size_t output_precision = 10;

struct Point {
  double x_;
  double y_;
  double z_;
  Point(double x, double y, double z) : x_(x), y_(y), z_(z) {};
  friend Point operator+(const Point& a, const Point& b);
  friend Point operator*(const Point& a, double x);
  friend Point operator/(const Point& a, double x);
};

Point operator+(const Point& a, const Point& b) {
  return Point(a.x_ + b.x_, a.y_ + b.y_, a.z_ + b.z_);
}

Point operator*(const Point& a, const double x) {
  return Point(a.x_ * x, a.y_ * x, a.z_ * x);
}

Point operator/(const Point& a, const double x) {
  return Point(a.x_ / x, a.y_ / x, a.z_ / x);
}

double DistancePointPoint(Point& a, Point& b) {
  return std::sqrt((a.x_ - b.x_) * (a.x_ - b.x_) + 
                   (a.y_ - b.y_) * (a.y_ - b.y_) + 
                   (a.z_ - b.z_) * (a.z_ - b.z_));
}

template <typename Function, typename Set>
double TernarySearch(Point& a, Point& b, Function& f, Set& p) {   
  // тернарный поиск для нахождения минимума унимодальной функции F
  
  double fa = f(a, p);                                 
  double fb = f(b, p);
  double fm;
  double fn;
  Point m(0, 0, 0);
  Point n(0, 0, 0);
  if (DistancePointPoint(a, b) >= eps) {
    m = (b + a * 2) / 3;
    n = (a + b * 2) / 3;
    fm = f(m, p);
    fn = f(n, p);
    if (fm > fn) {
      return TernarySearch(m, b, f, p);
    }
    return TernarySearch(a, n, f, p);
  }
  return fa;
}

double DistancePointSegment(Point& p, std::pair<Point, Point>& segment) {
  return TernarySearch(segment.first, segment.second, DistancePointPoint, p);
}
double DistanceSegmentSegment(Point& a, Point& b, Point& c, Point& d) {
  std::pair<Point, Point> p = {c, d};
  return TernarySearch(a, b, DistancePointSegment, p);
}
int main() {
  double x;
  double y;
  double z;
  std::cin >> x >> y >> z;
  Point a(x, y, z);
  std::cin >> x >> y >> z;
  Point b(x, y, z);
  std::cin >> x >> y >> z;
  Point c(x, y, z);
  std::cin >> x >> y >> z;
  Point d(x, y, z);
  std::cout.precision(output_precision);
  std::cout << DistanceSegmentSegment(a, b, c, d) << '\n';
  return 0;
}