Language: C++

#include<bits/stdc++.h>
 
using namespace std;

#define int long double
const double EPS = 1e-20, PI = acos(-1);
 
inline bool eq(double a, double b) { return abs(b - a) < EPS; }
 
#define curr(P, i) P[i]
#define next(P, i) P[(i+1)%P.size()]
#define prev(P, i) P[(i+P.size()-1) % P.size()]
enum
{
  OUT, ON, IN
};
namespace Geometory
{
  struct Point
  {
    double x, y;
 
    Point() {};
 
    Point(double x, double y) : x(x), y(y) {};
 
    Point operator+(const Point &b) const { return Point(x + b.x, y + b.y); }
 
    Point operator-(const Point &b) const { return Point(x - b.x, y - b.y); }
 
    Point operator*(const double b) const { return Point(x * b, y * b); }
 
    Point operator*(const Point &b) const { return Point(x * b.x - y * b.y, x * b.y + y * b.x); }
 
    Point operator/(const double b) const { return Point(x / b, y / b); }
 
    bool operator<(const Point &b) const { return x != b.x ? x < b.x : y < b.y; }
 
    bool operator==(const Point &b) const { return eq(x, b.x) && eq(y, b.y); }
 
    double norm() { return x * x + y * y; }
 
    double arg() { return atan2(x, y); }
 
    double abs() { return sqrt(norm()); }
 
    Point rotate(double theta) { return Point(cos(theta) * x - sin(theta) * y, sin(theta) * x + cos(theta) * y); }
 
    Point rotate90() { return Point(-y, x); }
 
    friend ostream &operator<<(ostream &os, Point &p) { return os << "(" << p.x << "," << p.y << ")"; }
 
    friend istream &operator>>(istream &is, Point &a) { return is >> a.x >> a.y; }
  };
 
  struct Line
  {
    Point a, b;
 
    Line() {};
 
    Line(Point a, Point b) : a(a), b(b) {};
 
    friend ostream &operator<<(ostream &os, Line &p) { return os << "(" << p.a.x << "," << p.a.y << ") to (" << p.b.x << "," << p.b.y << ")"; }
 
    friend istream &operator>>(istream &is, Line &a) { return is >> a.a.x >> a.a.y >> a.b.x >> a.b.y; }
  };
 
  struct Segment
  {
    Point a, b;
 
    Segment() {};
 
    Segment(Point a, Point b) : a(a), b(b) {};
 
    friend ostream &operator<<(ostream &os, Segment &p) { return os << "(" << p.a.x << "," << p.a.y << ") to (" << p.b.x << "," << p.b.y << ")"; }
 
    friend istream &operator>>(istream &is, Segment &a) { return is >> a.a.x >> a.a.y >> a.b.x >> a.b.y; }
  };
 
  struct Circle
  {
    Point p;
    double r;
 
    Circle() {};
 
    Circle(Point p, double r) : p(p), r(r) {};
  };
 
  typedef vector< Point > Polygon;
  typedef vector< Segment > Segments;
  typedef vector< Line > Lines;
  typedef vector< Circle > Circles;
  typedef pair< Point, Point > PointPoint;
 
  double cross(const Point &a, const Point &b)
  {
    return a.x * b.y - a.y * b.x;
  }
 
  double dot(const Point &a, const Point &b)
  {
    return a.x * b.x + a.y * b.y;
  }
 
  int ccw(const Point &a, Point b, Point c)
  {
    b = b - a, c = c - a;
    if(cross(b, c) > EPS) return +1;  // a ??? b ???§ ????????¨??????????????????? c
    if(cross(b, c) < -EPS) return -1; // a ??? b ???§ ?????¨??????????????????? c
    if(dot(b, c) < 0) return +2;  // c -- a -- b???§??????´??????
    if(b.norm() < c.norm()) return -2; // a -- b -- c???§??????´??????
    return 0;  // a -- c -- b???§??????´??????
  }
 
  Point Projection(const Line &l, const Point &p)
  {
    double t = dot(p - l.a, l.a - l.b) / (l.a - l.b).norm();
    return l.a + (l.a - l.b) * t;
  }
 
  Point Projection(const Segment &l, const Point &p)
  {
    double t = dot(p - l.a, l.a - l.b) / (l.a - l.b).norm();
    return l.a + (l.a - l.b) * t;
  }
 
  Point Reflection(const Line &l, const Point &p)
  {
    return p + (Projection(l, p) - p) * 2.0;
  }
 
  double Distance(const Line &l, const Point &p)
  { //OK
    return (p - Projection(l, p)).abs();
  }
 
  bool Intersect(const Line &l, const Line &m)
  {
    return abs(cross(l.b - l.a, m.b - m.a)) > EPS || abs(cross(l.b - l.a, m.b - l.a)) < EPS;
  }
 
  bool Intersect(const Line &l, const Segment &s)
  {
    return cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) < EPS;
  }
 
  bool Intersect(const Line &l, const Point &p)
  {
    return abs(ccw(l.a, l.b, p)) != -1;
  }
 
  bool Intersect(const Segment &s, const Segment &t)
  {
    return ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) <= 0 && ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) <= 0;
  }
 
  bool Intersect(const Segment &s, const Point &p)
  {
    return ccw(s.a, s.b, p) == 0;
  }
 
  bool Intersect(const Circle &c, const Line &l)
  {
    return Distance(l, c.p) <= c.r + EPS;
  }
 
  bool Intersect(const Circle &c, const Point &p)
  {
    return abs((p - c.p).abs() - c.r) < EPS;
  }
 
  int Intersect(const Circle &c, const Segment &l)
  {
    if((Projection(l, c.p) - c.p).norm() - c.r * c.r > EPS) return 0;
    const double d1 = (c.p - l.a).abs(), d2 = (c.p - l.b).abs();
    if(d1 < c.r + EPS && d2 < c.r + EPS) return 0;
    if(d1 < c.r - EPS && d2 > c.r + EPS || d1 > c.r + EPS && d2 < c.r - EPS) return 1;
    const Point h = Projection(l, c.p);
    if(dot(l.a - h, l.b - h) < 0) return 2;
    return 0;
  }
 
  bool Intersect(const Circle &a, const Circle &b)
  {
    return ((a.p - b.p).norm() - (a.r + b.r) * (a.r + b.r) < EPS) &&
           ((a.p - b.p).norm() - (a.r - b.r) * (a.r - b.r) > -EPS);
  }
 
  double Distance(const Segment &s, const Point &p)
  {
    Point r = Projection(s, p);
    if(Intersect(s, r)) return (r - p).abs();
    return min((s.a - p).abs(), (s.b - p).abs());
  }
 
  double Distance(const Segment &a, const Segment &b)
  {
    if(Intersect(a, b)) return 0;
    return min(min(Distance(a, b.a), Distance(a, b.b)), min(Distance(b, a.a), Distance(b, a.b)));
  }
 
  double Distance(const Line &l, const Line &m)
  {
    return Intersect(l, m) ? 0 : Distance(l, m.a);
  }
 
  double Distance(const Line &l, const Segment &s)
  { //OK
    if(Intersect(l, s)) return 0;
    return min(Distance(l, s.a), Distance(l, s.b));
  }
 
  double Distance(const Point &a, const Point &b)
  { //OK
    return (a - b).abs();
  }
 
  Point Crosspoint(const Segment &l, const Segment &m)
  { //OK
    double A = cross(l.b - l.a, m.b - m.a);
    double B = cross(l.b - l.a, l.b - m.a);
    if(abs(A) < EPS && abs(B) < EPS) return m.a; // same line
    return m.a + (m.b - m.a) * B / A;
  }
 
  PointPoint Crosspoint(const Circle &c, const Line l)
  {
    Point hp = Projection(l, c.p), h = hp - c.p;
    const double d2 = h.norm();
    Point v = (l.b - l.a) * sqrt(c.r * c.r - d2) / (l.b - l.a).abs();
    return PointPoint(hp - v, hp + v);
  }
 
  PointPoint Crosspoint(const Circle &c, const Segment &l)
  {
    Line aa = Line(l.a, l.b);
    if(Intersect(c, l) == 2) return Crosspoint(c, aa);
    PointPoint ret = Crosspoint(c, aa);
    if(dot(l.a - ret.first, l.b - ret.first) < 0) ret.second = ret.first;
    else ret.first = ret.second;
    return ret;
  }
 
  PointPoint Crosspoint(const Circle &c1, const Circle &c2)
  { //OK
    double d = (c1.p - c2.p).abs();
    double s = (c1.r + c2.r + d) / 2;
    double S = sqrt(s * (s - c1.r) * (s - c2.r) * (s - d));
    double h = 2 * S / d;
    Point v = (c2.p - c1.p) / (c2.p - c1.p).abs();
    double m = sqrt(c1.r * c1.r - h * h);
    return PointPoint(c1.p + v * m + Point(0, 1) * h * v, c1.p + v * m - Point(0, 1) * h * v);
  }
 
  bool parallel(const Line &a, const Line &b)
  {
    return abs(cross(a.b - a.a, b.b - b.a)) < EPS;
  }
 
  bool orthogonal(const Line &a, const Line &b)
  {
    return abs(dot(a.a - a.b, b.a - b.b)) < EPS;
  }
 
  int Contains(const Polygon &Q, const Point &p)
  {
    bool in = false;
    for(int i = 0; i < Q.size(); i++) {
      Point a = curr(Q, i) - p, b = next(Q, i) - p;
      if(a.y > b.y) swap(a, b);
      if(a.y <= 0 && 0 < b.y && cross(a, b) < 0) in = !in;
      if(cross(a, b) == 0 && dot(a, b) <= 0) return ON;
    }
    return in ? IN : OUT;
  }
 
  bool Contains(const Circle &c, const Point &p)
  {
    return (c.p - p).abs() < c.r + EPS;
  }
 
  double Area2(const Polygon &p)
  { //OK
    double A = 0;
    for(int i = 0; i < p.size(); ++i) {
      A += cross(curr(p, i), next(p, i));
    }
    return A;
  }
 
  bool IsConvex(const Polygon &p)
  {
    for(int i = 0; i < p.size(); i++) {
      if(ccw(prev(p, i), curr(p, i), next(p, i)) == -1) return false;
    }
    return true;
  }
 
  Polygon Convex_Hull(Polygon &p)
  {
    int n = p.size(), k = 0;
    if(n >= 3) {
      sort(p.begin(), p.end());
      vector< Point > ch(2 * n);
      for(int i = 0; i < n; ch[k++] = p[i++]) {
        while(k >= 2 && cross(ch[k - 1] - ch[k - 2], p[i] - ch[k - 1]) < 0) --k;
      }
      for(int i = n - 2, t = k + 1; i >= 0; ch[k++] = p[i--]) {
        while(k >= t && cross(ch[k - 1] - ch[k - 2], p[i] - ch[k - 1]) < 0) --k;
      }
      ch.resize(k - 1);
      return ch;
    } else {
      return p;
    }
  }
 
  double Convex_Diameter(Polygon &p)
  {
    int n = p.size();
    int is = 0, js = 0;
    for(int i = 1; i < n; i++) {
      if(p[i].y > p[is].y) is = i;
      if(p[i].y < p[js].y) js = i;
    }
    double maxdis = (p[is] - p[js]).norm();
 
    int maxi, maxj, i, j;
    i = maxi = is;
    j = maxj = js;
    do {
      if(cross(next(p, i) - curr(p, i), next(p, j) - curr(p, j)) >= 0) {
        j = (j + 1) % n;
      } else {
        i = (i + 1) % n;
      }
      if((p[i] - p[j]).norm() > maxdis) {
        maxdis = (p[i] - p[j]).norm();
        maxi = i;
        maxj = j;
      }
    } while(i != is || j != js);
    return maxdis;
  }
};
 
using namespace Geometory;
 
int N, W;
int X[10], Y[10], H[10];
 
bool check(double r)
{
  auto getPadding = [&](double height)
  {
    if(r > height) return (r - sqrt(r * r - (r - height) * (r - height)));
    return ((long double)0.0);
  };
 
  vector< Circle > circles(N);
  for(int i = 0; i < N; i++) {
    circles[i].p = Point(X[i], Y[i]);
    circles[i].r = r - getPadding(H[i]);
  }
  double padding = r - getPadding(W);
  if(2 * padding >= 100) return (false);
  Polygon rectangle(4);
  rectangle[0] = Point(padding, padding);
  rectangle[1] = Point(100 - padding, padding);
  rectangle[2] = Point(100 - padding, 100 - padding);
  rectangle[3] = Point(padding, 100 - padding);
 
  vector< Point > crossed;
  for(int i = 0; i < N; i++) {
    for(int j = 0; j < i; j++) {
      if(Intersect(circles[i], circles[j])) {
        auto get = Crosspoint(circles[i], circles[j]);
        crossed.push_back(get.first);
        crossed.push_back(get.second);
      }
    }
  }
  for(int i = 0; i < 4; i++) {
    auto seg = Segment(curr(rectangle, i), next(rectangle, i));
    if(Intersect(circles[i], seg)) {
      auto get = Crosspoint(circles[i], seg);
      crossed.push_back(get.first);
      crossed.push_back(get.second);
    }
    crossed.push_back(rectangle[i]);
  }
 
  for(auto &p : crossed) {
    bool isin = true;
    for(auto &c : circles) {
      isin &= (p - c.p).abs() + (1e-12) >= c.r;
    }
    isin &= Contains(rectangle, p) != OUT;
    if(isin) return (true);
  }
  return (false);
}
 
int main()
{
  while(scanf("%d %d", &N, &W), N) {
    for(int i = 0; i < N; i++) {
      scanf("%d %d %d", &X[i], &Y[i], &H[i]);
    }
    double low = 0, high = 200;
    for(int i = 0; i < 150; i++) {
      double mid = (low + high) * 0.5;
      if(check(mid)) low = mid;
      else high = mid;
    }
    printf("%.10lf\n", low);
  }
 
}

Compiler output:
a.cc: In function 'long double Geometory::Contains(const Polygon&, const Point&)':
a.cc:11:27: error: invalid operands of types 'long double' and 'std::vector<Geometory::Point>::size_type' {aka 'long unsigned int'} to binary 'operator%'
   11 | #define next(P, i) P[(i+1)%P.size()]
      |                      ~~~~~^
      |                        |
      |                        long double
a.cc:272:37: note: in expansion of macro 'next'
  272 |       Point a = curr(Q, i) - p, b = next(Q, i) - p;
      |                                     ^~~~
a.cc: In function 'double Geometory::Area2(const Polygon&)':
a.cc:11:27: error: invalid operands of types 'long double' and 'std::vector<Geometory::Point>::size_type' {aka 'long unsigned int'} to binary 'operator%'
   11 | #define next(P, i) P[(i+1)%P.size()]
      |                      ~~~~~^
      |                        |
      |                        long double
a.cc:289:30: note: in expansion of macro 'next'
  289 |       A += cross(curr(p, i), next(p, i));
      |                              ^~~~
a.cc: In function 'bool Geometory::IsConvex(const Polygon&)':
a.cc:12:37: error: invalid operands of types 'long double' and 'std::vector<Geometory::Point>::size_type' {aka 'long unsigned int'} to binary 'operator%'
   12 | #define prev(P, i) P[(i+P.size()-1) % P.size()]
      |                      ~~~~~~~~~~~~~~ ^
      |                                 |
      |                                 long double
a.cc:297:14: note: in expansion of macro 'prev'
  297 |       if(ccw(prev(p, i), curr(p, i), next(p, i)) == -1) return false;
      |              ^~~~
a.cc:11:27: error: invalid operands of types 'long double' and 'std::vector<Geometory::Point>::size_type' {aka 'long unsigned int'} to binary 'operator%'
   11 | #define next(P, i) P[(i+1)%P.size()]
      |                      ~~~~~^
      |                        |
      |                        long double
a.cc:297:38: note: in expansion of macro 'next'
  297 |       if(ccw(prev(p, i), curr(p, i), next(p, i)) == -1) return false;
      |                                      ^~~~
a.cc: In function 'double Geometory::Convex_Diameter(Polygon&)':
a.cc:11:27: error: invalid operands of types 'long double' and 'std::vector<Geometory::Point>::size_type' {aka 'long unsigned int'} to binary 'operator%'
   11 | #define next(P, i) P[(i+1)%P.size()]
      |                      ~~~~~^
      |                        |
      |                        long double
a.cc:335:16: note: in expansion of macro 'next'
  335 |       if(cross(next(p, i) - curr(p, i), next(p, j) - curr(p, j)) >= 0) {
      |                ^~~~
a.cc:11:27: error: invalid operands of types 'long double' and 'std::vector<Geometory::Point>::size_type' {aka 'long unsigned int'} to binary 'operator%'
   11 | #define next(P, i) P[(i+1)%P.size()]
      |                      ~~~~~^
      |                        |
      |                        long double
a.cc:335:41: note: in expansion of macro 'next'
  335 |       if(cross(next(p, i) - curr(p, i), next(p, j) - curr(p, j)) >= 0) {
      |                                         ^~~~
a.cc:336:21: error: invalid operands of types 'long double' and 'long double' to binary 'operator%'
  336 |         j = (j + 1) % n;
      |             ~~~~~~~ ^ ~
      |                |      |
      |                |      long double
      |                long double
a.cc:338:21: error: invalid operands of types 'long double' and 'long double' to binary 'operator%'
  338 |         i = (i + 1) % n;
      |             ~~~~~~~ ^ ~
      |                |      |
      |                |      long double
      |                long double
a.cc: In lambda function:
a.cc:360:13: error: inconsistent types 'double' and 'long double' deduced for lambda return type
  360 |     return ((long double)0.0);
      |            ~^~~~~~~~~~~~~~~~~
a.cc: In function 'bool check(double)':
a.cc:365:27: error: invalid types 'long double [10][long double]' for array subscript
  365 |     circles[i].p = Point(X[i], Y[i]);
      |                           ^
a.cc:365:33: error: invalid types 'long double [10][long double]' for array subscript
  365 |     circles[i].p = Point(X[i], Y[i]);
      |                                 ^
a.cc:366:36: error: invalid types 'long double [10][long double]' for array subscript
  366 |     circles[i].r = r - getPadding(H[i]);
      |                                    ^
a.cc:11:27: error: invalid operands of types 'long double' and 'std::vector<Geometory::Point>::size_type' {aka 'long unsigned int'} to binary 'operator%'
   11 | #define next(P, i) P[(i+1)%P.size()]
      |                      ~~~~~^
      |                        |
      |                        long double
a.cc:387:44: note: in expansion of macro 'next'
  387 |     auto seg = Segment(curr(rectangle, i), next(rectangle, i));
      |                                            ^~~~
a.cc: At global scope:
a.cc:5:18: error: '::main' must return 'int'
    5 | #define int long double
      |                  ^~~~~~
a.cc:407:1: note: in expansion of macro 'int'
  407 | int main()
      | ^~~
a.cc: In function 'int main()':
a.cc:411:27: error: invalid types 'long double [10][long double]' for array subscript
  411 |       scanf("%d %d %d", &X[i], &Y[i], &H[i]);
      |                           ^
a.cc:411:34: error: invalid types 'long double [10][long double]' for array subscript
  411 |       scanf("%d %d %d", &X[i], &Y[i], &H[i]);
      |                                  ^
a.cc:411:41: error: invalid types 'long double [10][long double]' for array subscript
  411 |       scanf("%d %d %d", &X[i], &Y[i], &H[i]);
      |                                         ^