Language: C++

#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <climits>
#include <cfloat>
#include <ctime>
#include <cassert>
#include <map>
#include <utility>
#include <set>
#include <iostream>
#include <memory>
#include <string>
#include <vector>
#include <algorithm>
#include <functional>
#include <sstream>
#include <complex>
#include <stack>
#include <queue>
#include <numeric>
#include <list>
#include <iomanip>
#include <fstream>
#include <bitset>
   
using namespace std;
   
 
#define rep(i, n) for (int i = 0; i < (int)(n); ++i)
#define foreach(it, c) for (__typeof__((c).begin()) it=(c).begin(); it != (c).end(); ++it)
#define rforeach(it, c) for (__typeof__((c).rbegin()) it=(c).rbegin(); it != (c).rend(); ++it)
#define all(c) (c).begin(), (c).end()
#define rall(c) (c).rbegin(), (c).rend()
#define CL(arr, val) memset(arr, val, sizeof(arr))
#define COPY(dest, src) memcpy(dest, src, sizeof(dest))
#define ten(n) ((long long)(1e##n))
#define bin(n) (1LL << (n))
#define erep(i, n) for (int i = 0; i <= (int)(n); ++i)
#define revrep(i, n) for (int i = (n); i >= 0; --i)
#define pb push_back

template <class T> void chmax(T& a, const T& b) { a = max(a, b); }
template <class T> void chmin(T& a, const T& b) { a = min(a, b); }

template <class T> void uniq(T& c) { sort(c.begin(), c.end()); c.erase(unique(c.begin(), c.end()), c.end()); }
 
template <class T> string to_s(const T& a) { ostringstream os; os << a; return os.str(); }
template <class T> T to_T(const string& s) { istringstream is(s); T res; is >> res; return res; }

template <typename T> void print_container(ostream& os, const T& c) { const char* _s = " "; if (!c.empty()) { __typeof__(c.begin()) last = --c.end(); foreach (it, c) { os << *it; if (it != last) cout << _s; } } }
template <typename T> ostream& operator<<(ostream& os, const vector<T>& c) { print_container(os, c); return os; }
template <typename T> ostream& operator<<(ostream& os, const set<T>& c) { print_container(os, c); return os; }
template <typename T> ostream& operator<<(ostream& os, const multiset<T>& c) { print_container(os, c); return os; }
template <typename T> ostream& operator<<(ostream& os, const deque<T>& c) { print_container(os, c); return os; }
template <typename T, typename U> ostream& operator<<(ostream& os, const map<T, U>& c) { print_container(os, c); return os; }
template <typename T, typename U> ostream& operator<<(ostream& os, const pair<T, U>& p) { os << "( " << p.first << ", " << p.second << " )"; return os; }

template <class T> void print(T a, int n, const string& deli = " ", int br = 1) { for (int i = 0; i < n; ++i) { cout << a[i]; if (i + 1 != n) cout << deli; } while (br--) cout << endl; }
template <class T> void print2d(T a, int w, int h, int width = -1, int br = 1) { for (int i = 0; i < h; ++i) { for (int j = 0; j < w; ++j) {    if (width != -1) cout.width(width); cout << a[i][j] << ' '; } cout << endl; } while (br--) cout << endl; }

template <class T> void input(T& a, int n) { for (int i = 0; i < n; ++i) cin >> a[i]; }
template <class T> void input(T* a, int n) { for (int i = 0; i < n; ++i) cin >> a[i]; }

void fix_pre(int n) { cout.setf(ios::fixed, ios::floatfield); cout.precision(10); }
void fast_io() { cin.tie(0); ios::sync_with_stdio(false); }
#define trace(x) (cout << #x << ": " << (x) << endl)
 
bool in_rect(int x, int y, int w, int h) { return 0 <= x && x < w && 0 <= y && y < h; }
bool in_seg(int n, int l, int r) { return l <= n && n < r; } // n in [l, r)?

typedef long long ll;
typedef pair<int, int> pint;

// y(v): v>^<  y(^): ^>v<
const int dx[] = { 0, 1, 0, -1 };
const int dy[] = { 1, 0, -1, 0 };

const double PI = acos(-1.0);
#define mp make_pair



/////////////////////////////////////////////
typedef double gtype;
const gtype EPS_FOR_LIB = 1e-9;
typedef complex<gtype> Point;
gtype to_rad(gtype deg)
{
    return deg * PI / 180;
}
gtype to_deg(gtype rad)
{
    return rad * 180 / PI;
}

namespace std
{
	bool operator<(const Point& a, const Point& b)
	{
		return a.real() != b.real() ? a.real() < b.real() : a.imag() < b.imag();
	}
	std::istream& operator>>(std::istream& is, Point& p)
	{
		gtype a, b;
        is >> a >> b;
		p = Point(a, b);
		return is;
	}
	std::ostream& operator<<(std::ostream& os, const Point& p)
	{
		return os << "(" << p.real() << ", " << p.imag() << ")";
	}
};
struct Line
{
	Point first, second;
	Line() {}
    Line(const Point& first, const Point& second)
        : first(first), second(second)
    {
        // 距離で割るときにNaNになるのを防ぐ
        if (first == second)
            this->first.real() += 1e-12;
    }
};
typedef Line Seg;
ostream& operator<<(ostream& os, const Line& line)
{
    return os << "(" << line.first << ", " << line.second << ")";
}

struct Circle
{
    Point p;
    gtype r;
    Circle() {}
    Circle(const Point& p, gtype r)
        : p(p), r(r)
    {
    }
};
ostream& operator<<(ostream& os, const Circle& c)
{
    return os << "(" << c.p << ", " << c.r << ")";
}
typedef vector<Point> G;
typedef G Convex;

gtype dot(const Point& a, const Point& b)
{
	return a.real() * b.real() + a.imag() * b.imag();
}
gtype cross(const Point& a, const Point& b)
{
	return a.real() * b.imag() - a.imag() * b.real();
}

enum res_ccw
{
	counter_clockwise = +1,
	clockwise = -1,
	on = 0,
};
res_ccw ccw(const Point& a, const Point& b, const Point& c)
{
    const gtype feps = 1e-10;
	Point p = b - a, q = c - a;
	if (cross(p, q) > feps) return counter_clockwise;
	else if (cross(p, q) < -feps) return clockwise;
	return on;
}


// gは凸多角形
// lineより左側の凸多角形を返す
// AOJ1213(正方形に2回カットなので緩い)
Convex convex_cut(const Convex& g, const Line& line)
{
    Convex left;
    rep(i, g.size())
    {
        const Point& a = g[i], b = g[(i + 1) % g.size()];
        if (ccw(line.first, line.second, a) != clockwise)
            left.push_back(a);
        if (ccw(line.first, line.second, a) * ccw(line.first, line.second, b) < 0)
            left.push_back(ip_LL(Line(a, b), line));
    }
    return left;
}
Convex convex_cut(const Convex& g, const Point& a, const Point& b)
{
    return convex_cut(g, Line(a, b));
}



/////////////////// 


bool ok(const Convex& g, double d)
{
    Convex rem = g;
    rep(i, g.size())
    {
        Point v = (g[i + 1] - g[i]) * Point(0, 1);
        v *= d / abs(v);
        rem = convex_cut(rem, g[i] + v, g[i + 1] + v);
    }
    return !rem.empty();
}
int main()
{
    int n;
    while (cin >> n, n)
    {
        Convex g(n);
        rep(i, n)
            cin >> g[i];

        double low = 0, high = 1e9;
        rep(i, 100)
        {
            double mid = (low + high) / 2;
            (ok(g, mid) ? low : high) = mid;
        }
        printf("%.8f\n", low);
    }
}

Compiler output:
a.cc: In constructor 'Line::Line(const Point&, const Point&)':
a.cc:125:29: error: lvalue required as left operand of assignment
  125 |             this->first.real() += 1e-12;
      |             ~~~~~~~~~~~~~~~~^~
a.cc: In function 'Convex convex_cut(const Convex&, const Line&)':
a.cc:188:28: error: 'ip_LL' was not declared in this scope
  188 |             left.push_back(ip_LL(Line(a, b), line));
      |                            ^~~~~